Datasets:

MU-NLPC

/

Calc-math_qa

like 4

Follow

NLP Centre, Faculty of Informatics, Masaryk University 15

math_qa__3GSDWwH7mvDxmn8m

The maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : Choose the most appropriate option: A) 1 B) 10 C) 11 D) 19 E) none of these

<gadget id="calculator">gcd(1_802, 1_203)</gadget> <output>1</output> <result>A</result>

A

The maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

gcd(1802, 1203)

gcd(n0,n1)

solution required number of student = h . c . f of 1802 and 1203 = 1 . answer a

general

math_qa__174V9GaOhq2aHdni

If the cost price of 35 chocolates is equal to the selling price of 21 chocolates, the gain percent is : Choose the most appropriate option: A) 66.55 % B) 66.66 % C) 66 % D) 55 % E) 66.33 %

<gadget id="calculator">35 - 21</gadget> <output>14</output> <gadget id="calculator">21 / 14</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">100 / (3/2)</gadget> <output>200/3 = around 66.666667</output> <result>B</result>

B

If the cost price of 35 chocolates is equal to the selling price of 21 chocolates, the gain percent is :

divide(const_100, divide(21, subtract(35, 21)))

subtract(n0,n1)|divide(n1,#0)|divide(const_100,#1)|

"explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 21 chocolates = rs . 21 ; s . p . of 21 chocolates = rs . 35 . . ' . gain % = 14 * 100 / 21 = 66.66 % answer : b"

gain

math_qa__6UedOaeLjvNffw4U

nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm? Choose the correct choice from the following choices A) 766 cm 2 B) 535 cm 2 C) 285 cm 2 D) 324 cm 2 E) 235 cm 2

<gadget id="calculator">20 + 18</gadget> <output>38</output> <gadget id="calculator">15 * 38</gadget> <output>570</output> <gadget id="calculator">570 / 2</gadget> <output>285</output> <result>C</result>

C

nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?

divide(multiply(15, add(20, 18)), const_2)

add(n0,n1)|multiply(n2,#0)|divide(#1,const_2)

area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c

physics

math_qa__uhEPWp1qgBIZus12

If (10^4 * 3.456789)^11 is written as a single term, how many digits would be to the right of the decimal place? Choose the correct choice from the following answers: A) 12 B) 18 C) 22 D) 28 E) 36

<gadget id="calculator">11 * 2</gadget> <output>22</output> <result>C</result>

C

If (10^4 * 3.456789)^11 is written as a single term, how many digits would be to the right of the decimal place?

multiply(11, const_2)

multiply(n3,const_2)|

"3.456789 ^ 11 has 6 * 11 = 66 decimal places . 10 ^ 44 moves the decimal place to the right 44 places . ( 10 ^ 4 * 3.456789 ) ^ 11 has 66 - 44 = 22 digits after the decimal point . the answer is c ."

general

math_qa__TtzwdM5phAzEBjeO

A 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec. What is the length of the platform? Choose the correct choice from the following. A) 288 B) 300 C) 889 D) 276 E) 234

<gadget id="calculator">300 / 18</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">(50/3) * 36</gadget> <output>600</output> <gadget id="calculator">600 - 300</gadget> <output>300</output> <result>B</result>

B

A 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec. What is the length of the platform?

subtract(multiply(speed(300, 18), 36), 300)

speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)|

"speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 36 = 50 / 3 3 x + 900 = 1800 = > x = 300 m . answer : b"

physics

math_qa__OLYo9DwpD3J4AdMu

The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 63.0. What is the quiz score of the student who dropped the class? Pick: A) 10 B) 25 C) 40 D) 55 E) 70

<gadget id="calculator">16 * 62.5</gadget> <output>1_000</output> <gadget id="calculator">16 - 1</gadget> <output>15</output> <gadget id="calculator">15 * 63</gadget> <output>945</output> <gadget id="calculator">1_000 - 945</gadget> <output>55</output> <result>D</result>

D

The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 63.0. What is the quiz score of the student who dropped the class?

subtract(multiply(16, 62.5), multiply(subtract(16, const_1), 63))

multiply(n0,n1)|subtract(n0,const_1)|multiply(n2,#1)|subtract(#0,#2)

total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 63 = 945 so , the score of the person who left is 55 ( 1000 - 945 ) answer will be ( d )

general

math_qa__8ixIF0wZjsTnp9eM

How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? Select the correct option: A) 3 B) 16 C) 75 D) 24 E) 26

<gadget id="calculator">300 - 200</gadget> <output>100</output> <gadget id="calculator">100 + 1</gadget> <output>101</output> <gadget id="calculator">300 / 2</gadget> <output>150</output> <gadget id="calculator">200 / 2</gadget> <output>100</output> <gadget id="calculator">150 - 100</gadget> <output>50</output> <gadget id="calculator">50 + 1</gadget> <output>51</output> <gadget id="calculator">101 - 51</gadget> <output>50</output> <gadget id="calculator">300 / 3</gadget> <output>100</output> <gadget id="calculator">200 / 3</gadget> <output>200/3 = around 66.666667</output> <gadget id="calculator">100 - (200/3)</gadget> <output>100/3 = around 33.333333</output> <gadget id="calculator">(100/3) + 1</gadget> <output>103/3 = around 34.333333</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">10 + 7</gadget> <output>17</output> <gadget id="calculator">(103/3) - 17</gadget> <output>52/3 = around 17.333333</output> <gadget id="calculator">50 - (52/3)</gadget> <output>98/3 = around 32.666667</output> <gadget id="calculator">300 / 5</gadget> <output>60</output> <gadget id="calculator">200 / 5</gadget> <output>40</output> <gadget id="calculator">60 - 40</gadget> <output>20</output> <gadget id="calculator">20 + 1</gadget> <output>21</output> <gadget id="calculator">10 + 5</gadget> <output>15</output> <gadget id="calculator">21 - 15</gadget> <output>6</output> <gadget id="calculator">(98/3) - 6</gadget> <output>80/3 = around 26.666667</output> <result>E</result>

E

How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

subtract(subtract(subtract(add(subtract(300, 200), const_1), add(subtract(divide(300, 2), divide(200, 2)), const_1)), subtract(add(subtract(divide(300, 3), divide(200, 3)), const_1), add(const_10, add(const_3, const_4)))), subtract(add(subtract(divide(300, 5), divide(200, 5)), const_1), add(const_10, 5)))

add(const_3,const_4)|add(n4,const_10)|divide(n1,n2)|divide(n0,n2)|divide(n1,n3)|divide(n0,n3)|divide(n1,n4)|divide(n0,n4)|subtract(n1,n0)|add(#8,const_1)|add(#0,const_10)|subtract(#2,#3)|subtract(#4,#5)|subtract(#6,#7)|add(#11,const_1)|add(#12,const_1)|add(#13,const_1)|subtract(#9,#14)|subtract(#15,#10)|subtract(#16,#1)|subtract(#17,#18)|subtract(#20,#19)

1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .

other

math_qa__Qaj9QR72q5QaoJ2o

The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 25%? Options A) 37.5 % B) 37.6 % C) 38.5 % D) 17.1 % E) 37.2 %

<gadget id="calculator">100 - 25</gadget> <output>75</output> <gadget id="calculator">75 / 64</gadget> <output>75/64 = around 1.171875</output> <gadget id="calculator">(75/64) - 1</gadget> <output>11/64 = around 0.171875</output> <gadget id="calculator">(11/64) * 100</gadget> <output>275/16 = around 17.1875</output> <result>D</result>

D

The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 25%?

multiply(subtract(divide(subtract(const_100, 25), 64), const_1), const_100)

subtract(const_100,n1)|divide(#0,n0)|subtract(#1,const_1)|multiply(#2,const_100)|

"let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 75 gain % = 11 / 64 * 100 = 17.1 % . answer : d"

gain

math_qa__E2M915A4ZTzNiaMN

one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 40 workers in the Palabras bookstore, how many of them have read both books? Choose the correct choice from the following answers A) 3 B) 2 C) 9 D) 8 E) 7

<gadget id="calculator">40 / 4</gadget> <output>10</output> <gadget id="calculator">10 + 10</gadget> <output>20</output> <gadget id="calculator">40 / 8</gadget> <output>5</output> <gadget id="calculator">5 * 5</gadget> <output>25</output> <gadget id="calculator">20 + 25</gadget> <output>45</output> <gadget id="calculator">45 - 40</gadget> <output>5</output> <gadget id="calculator">5 - 1</gadget> <output>4</output> <gadget id="calculator">4 / 2</gadget> <output>2</output> <result>B</result>

B

one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 40 workers in the Palabras bookstore, how many of them have read both books?

divide(subtract(subtract(add(add(divide(40, const_4), divide(40, const_4)), multiply(divide(40, 8), 5)), 40), const_1), const_2)

divide(n2,const_4)|divide(n2,n1)|add(#0,#0)|multiply(n0,#1)|add(#2,#3)|subtract(#4,n2)|subtract(#5,const_1)|divide(#6,const_2)

there are total 40 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 10 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 40 = 25 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 10 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 40 = 10 + 25 - b + ( 10 - b - 1 ) b = 2 answer ( b )

general

math_qa__g7AEsQQtpvA0BxA7

A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time, how many books of the special collection were loaned out during that month? Choose the correct choice from the following answers. A) 20 B) 30 C) 35 D) 40 E) 60

<gadget id="calculator">75 - 57</gadget> <output>18</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">1 - (7/10)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">18 / (3/10)</gadget> <output>60</output> <result>E</result>

E

A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time, how many books of the special collection were loaned out during that month?

divide(subtract(75, 57), subtract(const_1, divide(70, const_100)))

divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2)|

"i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 57 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 18 - - > { loaned out } = 60 . answer : e ."

gain

math_qa__ko2IdUb1AeVGcDug

A train 330 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the correct choice from the following answers: A) 18 sec B) 15 sec C) 4 sec D) 16 sec E) 12 sec

<gadget id="calculator">330 / 1_000</gadget> <output>33/100 = around 0.33</output> <gadget id="calculator">60 + 6</gadget> <output>66</output> <gadget id="calculator">(33/100) / 66</gadget> <output>1/200 = around 0.005</output> <gadget id="calculator">3_600 * (1/200)</gadget> <output>18</output> <result>A</result>

A

A train 330 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

multiply(const_3600, divide(divide(330, const_1000), add(60, 6)))

add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)|

"speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 330 * 3 / 55 ] sec = 18 sec answer : a"

physics

math_qa__ZMyStTnvtjLSULQZ

A shopkeeper loses 15%,if an article is sold for Rs. 136. What should be the selling price of the article to gain 20%? Options. A) s . 147 B) s . 148 C) s . 144 D) s . 189 E) s . 192

<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">1 - (3/20)</gadget> <output>17/20 = around 0.85</output> <gadget id="calculator">136 / (17/20)</gadget> <output>160</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">160 * (1/5)</gadget> <output>32</output> <gadget id="calculator">160 + 32</gadget> <output>192</output> <result>E</result>

E

A shopkeeper loses 15%,if an article is sold for Rs. 136. What should be the selling price of the article to gain 20%?

add(divide(136, subtract(const_1, divide(15, const_100))), multiply(divide(136, subtract(const_1, divide(15, const_100))), divide(20, const_100)))

divide(n0,const_100)|divide(n2,const_100)|subtract(const_1,#0)|divide(n1,#2)|multiply(#3,#1)|add(#3,#4)|

"given that sp = rs . 136 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 136 ) / 85 = rs . 160 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 160 * 120 ) / 100 = rs . 192 answer : e"

gain

math_qa__IEdEwuSLSaTqqYHQ

On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 47 centimeters assuming that 1-inch is 2.54 centimeters? Select: A) 174.2 B) 212 C) 288.1 D) 296 E) 282.4

<gadget id="calculator">47 / 2.54</gadget> <output>18.503937</output> <gadget id="calculator">24 / 1.5</gadget> <output>16</output> <gadget id="calculator">18.503937 * 16</gadget> <output>296.062992</output> <result>D</result>

D

On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 47 centimeters assuming that 1-inch is 2.54 centimeters?

multiply(divide(47, 2.54), divide(24, 1.5))

divide(n2,n4)|divide(n1,n0)|multiply(#0,#1)

1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 47 cm . : 47 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 47 / ( 4.81 ) = 296 answer will be d .

physics

math_qa__cPajSj0MZ1ycNCAa

A train 800 m long can cross an electric pole in 20 sec and then find the speed of the train? Choose the correct choice from the following options: A) 87 kmph B) 97 kmph C) 72 kmph D) 144 kmph E) 120 kmph

<gadget id="calculator">800 / 1_000</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">20 / 3_600</gadget> <output>1/180 = around 0.005556</output> <gadget id="calculator">(4/5) / (1/180)</gadget> <output>144</output> <result>D</result>

D

A train 800 m long can cross an electric pole in 20 sec and then find the speed of the train?

divide(divide(800, const_1000), divide(20, const_3600))

divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)|

"length = speed * time speed = l / t s = 800 / 20 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"

physics

math_qa__FPRV2cRzQebUztpy

If it is 5:14 in the evening on a certain day, what time in the morning was it exactly 2,880,702 minutes earlier? (Assume standard time in one location.) Answers: A) 5 : 32 B) 5 : 36 C) 5 : 48 D) 5 : 54 E) 5 : 58

<gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">5 + 12</gadget> <output>17</output> <gadget id="calculator">17 * 60</gadget> <output>1_020</output> <gadget id="calculator">1_020 + 14</gadget> <output>1_034</output> <gadget id="calculator">2 * 1_000</gadget> <output>2_000</output> <gadget id="calculator">2_000 * 1_000</gadget> <output>2_000_000</output> <gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">8 * 11</gadget> <output>88</output> <gadget id="calculator">88 * 10</gadget> <output>880</output> <gadget id="calculator">880 * 1_000</gadget> <output>880_000</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">7 * 100</gadget> <output>700</output> <gadget id="calculator">700 + 2</gadget> <output>702</output> <gadget id="calculator">880_000 + 702</gadget> <output>880_702</output> <gadget id="calculator">2_000_000 + 880_702</gadget> <output>2_880_702</output> <gadget id="calculator">12 * 2</gadget> <output>24</output> <gadget id="calculator">24 * 60</gadget> <output>1_440</output> <gadget id="calculator">2_880_702 % 1_440</gadget> <output>702</output> <gadget id="calculator">1_034 - 702</gadget> <output>332</output> <gadget id="calculator">332 / 60</gadget> <output>83/15 = around 5.533333</output> <gadget id="calculator">floor(83/15)</gadget> <output>5</output> <gadget id="calculator">332 % 60</gadget> <output>32</output> <gadget id="calculator">5 / 32</gadget> <output>5/32 = around 0.15625</output> <result>A</result>

A

If it is 5:14 in the evening on a certain day, what time in the morning was it exactly 2,880,702 minutes earlier? (Assume standard time in one location.)

divide(floor(divide(subtract(add(multiply(add(5, multiply(const_3, const_4)), const_60), 14), reminder(add(multiply(multiply(2, const_1000), const_1000), add(multiply(multiply(multiply(multiply(const_2, const_4), add(const_10, const_1)), const_10), const_1000), add(multiply(add(const_3, const_4), const_100), const_2))), multiply(multiply(multiply(const_3, const_4), const_2), const_60))), const_60)), reminder(subtract(add(multiply(add(5, multiply(const_3, const_4)), const_60), 14), reminder(add(multiply(multiply(2, const_1000), const_1000), add(multiply(multiply(multiply(multiply(const_2, const_4), add(const_10, const_1)), const_10), const_1000), add(multiply(add(const_3, const_4), const_100), const_2))), multiply(multiply(multiply(const_3, const_4), const_2), const_60))), const_60))

add(const_3,const_4)|add(const_1,const_10)|multiply(const_3,const_4)|multiply(const_2,const_4)|multiply(n2,const_1000)|add(n0,#2)|multiply(#0,const_100)|multiply(#1,#3)|multiply(#4,const_1000)|multiply(#2,const_2)|add(#6,const_2)|multiply(#5,const_60)|multiply(#7,const_10)|multiply(#9,const_60)|add(n1,#11)|multiply(#12,const_1000)|add(#10,#15)|add(#16,#8)|reminder(#17,#13)|subtract(#14,#18)|divide(#19,const_60)|reminder(#19,const_60)|floor(#20)|divide(#22,#21)

5 : 14 minus 2 , 880,702 must end with 2 , the only answer choice which ends with 2 is a . answer : a .

physics

math_qa__FoQxwkxixe420TIY

4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 14 weavers in 14 days? Choose the correct choice from the following choices. A) 40 B) 45 C) 49 D) 53 E) 58

<gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">4 / 16</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">14 * (1/4)</gadget> <output>7/2 = around 3.5</output> <gadget id="calculator">14 * (7/2)</gadget> <output>49</output> <result>C</result>

C

4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 14 weavers in 14 days?

multiply(14, multiply(14, divide(4, multiply(4, 4))))

multiply(n0,n0)|divide(n0,#0)|multiply(n3,#1)|multiply(n3,#2)|

"1 weaver can weave 1 mat in 4 days . 14 weavers can weave 14 mats in 4 days . 14 weavers can weave 49 mats in 14 days . the answer is c ."

gain

math_qa__fCgUWYvieClA4F3C

Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint? Select the correct option: A) 10 B) 20 C) 28 D) 14 E) 19

<gadget id="calculator">7 / 8</gadget> <output>7/8 = around 0.875</output> <gadget id="calculator">1 / 16</gadget> <output>1/16 = around 0.0625</output> <gadget id="calculator">(7/8) / (1/16)</gadget> <output>14</output> <result>D</result>

D

Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?

divide(divide(7, 8), divide(1, 16))

divide(n0,n1)|divide(n2,n3)|divide(#0,#1)

number of statues = all the paint ÷ amount used per statue = 7 / 8 ÷ 1 / 16 = 7 / 8 * 16 / 1 = 112 / 8 = 14 . answer is d .

general

math_qa__TdnUSJsHJWWnap5u

When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.40 for every box, and if the university needs 2.4 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes? Choose the most appropriate option: A) $ 200 B) $ 275 C) $ 510 D) $ 1,250 E) $ 2,550

<gadget id="calculator">1_000 * 1_000</gadget> <output>1_000_000</output> <gadget id="calculator">2.4 * 1_000_000</gadget> <output>2_400_000</output> <gadget id="calculator">20 * 20</gadget> <output>400</output> <gadget id="calculator">400 * 12</gadget> <output>4_800</output> <gadget id="calculator">2_400_000 / 4_800</gadget> <output>500</output> <gadget id="calculator">500 * 0.4</gadget> <output>200</output> <result>A</result>

A

When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.40 for every box, and if the university needs 2.4 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?

multiply(divide(multiply(2.4, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 12)), 0.40)

multiply(const_1000,const_1000)|multiply(n0,n0)|multiply(n4,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4)|

"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 × $ 0.4 = $ 200 the answer is a ."

general

math_qa__YSK3DSQVry6XCRJ8

If PINTU is coded as 79523 in a certain code language, how would you code JUMBO in the same language? Choose the correct choice from the following options A) 13426 B) 14236 C) 13436 D) 14263 E) 15263

<gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">79_523 / 6</gadget> <output>79_523/6 = around 13_253.833333</output> <result>A</result>

A

If PINTU is coded as 79523 in a certain code language, how would you code JUMBO in the same language?

divide(79523, add(const_3, const_3))

add(const_3,const_3)|divide(n0,#0)

1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . jumbo is 13426 . . . answer : a

general

math_qa__Ki7uklw54mxhDYUo

Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 10 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone? Choose the most appropriate option: A) 4 B) 5 C) 6 D) 12 E) none of these

<gadget id="calculator">9 / 15</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 - (3/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 10</gadget> <output>4</output> <result>A</result>

A

Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 10 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?

multiply(subtract(const_1, divide(9, 15)), 10)

divide(n2,n0)|subtract(const_1,#0)|multiply(n1,#1)|

"the part of job that suresh completes in 9 hours = 9 ⁄ 15 = 3 ⁄ 5 remaining job = 1 - 3 ⁄ 5 = 2 ⁄ 5 remaining job can be done by ashutosh in 2 ⁄ 5 × 10 = 4 hours answer a"

physics

math_qa__h5uQkv74ugZEkBVk

In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 3 Ohms and y is 5 Ohms? Options: A) 15 / 8 B) 3 / 8 C) 5 / 8 D) 7 / 15 E) 8 / 15

<gadget id="calculator">5 * 3</gadget> <output>15</output> <gadget id="calculator">3 + 5</gadget> <output>8</output> <gadget id="calculator">15 / 8</gadget> <output>15/8 = around 1.875</output> <result>A</result>

A

In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 3 Ohms and y is 5 Ohms?

divide(multiply(5, 3), add(3, 5))

add(n0,n1)|multiply(n0,n1)|divide(#1,#0)|

"1 / r = 1 / x + 1 / y 1 / r = 1 / 3 + 1 / 5 = 8 / 15 r = 15 / 8 the answer is a ."

general

math_qa__MN1zcXM1CJAt81CP

On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will be the remainder? Pick: A) 0 B) 1 C) 2 D) 3 E) 4

<gadget id="calculator">68 * 269</gadget> <output>18_292</output> <gadget id="calculator">18_292 % 67</gadget> <output>1</output> <result>B</result>

B

On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will be the remainder?

reminder(multiply(68, 269), 67)

multiply(n0,n1)|reminder(#0,n3)|

"number = 269 * 68 + 0 = 18292 67 ) 18292 ( 273 18291 - - - - - - - - 1 required number = 1 . answer : b"

general

math_qa__HU1v0I1sqnlJONrA

A person want to give his money of $4500 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share? Choose the most appropriate option: A) $ 2000 B) $ 1500 C) $ 2500 D) $ 1800 E) $ 1600

<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">5 + 4</gadget> <output>9</output> <gadget id="calculator">3 / 9</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 4_500</gadget> <output>1_500</output> <result>B</result>

B

A person want to give his money of $4500 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?

multiply(divide(3, add(add(2, 3), 4)), 4500)

add(n1,n2)|add(n4,#0)|divide(n1,#1)|multiply(n0,#2)

b ' s share = 4500 * 3 / 9 = $ 1500 answer is b

other

math_qa__cxlW2WmnkFNWrEB9

Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $105. What is the share of Rahul? Choose the most appropriate option: A) $ 50 B) $ 42 C) $ 60 D) $ 100 E) $ 90

<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 105</gadget> <output>42</output> <result>B</result>

B

Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $105. What is the share of Rahul?

multiply(divide(2, add(3, 2)), 105)

add(n0,n1)|divide(n1,#0)|multiply(n2,#1)|

"rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 105 * 2 / 5 = $ 42 answer is b"

physics

math_qa__e7dPgbcaFEgPHY3V

What least number must be subtracted from 427398 so that remaining number is divisible by 15 Choose the correct choice from the following A) 3 B) 5 C) 7 D) 9 E) none of these

<gadget id="calculator">427_398 / 15</gadget> <output>142_466/5 = around 28_493.2</output> <gadget id="calculator">floor(142_466/5)</gadget> <output>28_493</output> <gadget id="calculator">28_493 * 15</gadget> <output>427_395</output> <gadget id="calculator">427_398 - 427_395</gadget> <output>3</output> <result>A</result>

A

What least number must be subtracted from 427398 so that remaining number is divisible by 15

subtract(427398, multiply(floor(divide(427398, 15)), 15))

divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)|

"explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a"

general

math_qa__JwmzvTsVJgYRYIC1

if 3 eighth of a number is 141 . what will be the approximately value of 32.08 % of this number ? Choose one. A) 119 B) 187 C) 181 D) 120 E) 891

<gadget id="calculator">4 + 4</gadget> <output>8</output> <gadget id="calculator">141 * 8</gadget> <output>1_128</output> <gadget id="calculator">1_128 / 3</gadget> <output>376</output> <gadget id="calculator">376 * 32.08</gadget> <output>12_062.08</output> <gadget id="calculator">12_062.08 / 100</gadget> <output>120.6208</output> <result>D</result>

D

if 3 eighth of a number is 141 . what will be the approximately value of 32.08 % of this number ?

divide(multiply(divide(multiply(141, add(const_4, const_4)), 3), 32.08), const_100)

add(const_4,const_4)|multiply(n1,#0)|divide(#1,n0)|multiply(n2,#2)|divide(#3,const_100)

explanation : x * 3 / 8 = 141 = > x = 376 376 * 32.08 / 100 = 120 answer : d

gain

math_qa__XMqE5Gf0Jbe2GmMd

A can do a piece of work in 4 hours; B and C together can do it in 2 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? Choose the correct choice from the following: A) 12 B) 9 C) 8 D) 6 E) 4

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/2) - (1/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 / (1/4)</gadget> <output>4</output> <result>E</result>

E

A can do a piece of work in 4 hours; B and C together can do it in 2 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

divide(const_1, subtract(divide(const_1, 2), subtract(divide(const_1, 2), divide(const_1, 4))))

divide(const_1,n1)|divide(const_1,n2)|divide(const_1,n0)|subtract(#1,#2)|subtract(#0,#3)|divide(const_1,#4)|

"a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 2 ) = 3 / 4 . b ' s 1 hour ' s work = ( 3 / 4 - 1 / 2 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"

physics

math_qa__Bhinn2Q7s1Otthjb

A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 40%? Choose one A) 700 B) 882 C) 772 D) 652 E) 271

<gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">500 * (2/5)</gadget> <output>200</output> <gadget id="calculator">500 + 200</gadget> <output>700</output> <result>A</result>

A

A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 40%?

add(500, multiply(500, divide(40, const_100)))

divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|

"cost price = rs . 500 profit = 40 % of 500 = rs . 200 selling price = cost price + profit = 500 + 200 = 700 answer : a"

gain

math_qa__dToLc6gQBNlOuEcg

Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $250. What is the share of Rahul? Select the correct option. A) $ 50 B) $ 40 C) $ 60 D) $ 100 E) $ 90

<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 250</gadget> <output>100</output> <result>D</result>

D

Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $250. What is the share of Rahul?

multiply(divide(2, add(3, 2)), 250)

add(n0,n1)|divide(n1,#0)|multiply(n2,#1)

rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 250 * 2 / 5 = $ 100 answer is d

physics

math_qa__Qe1BCZPbnDDjPFho

How many numbers from 10 to 46 are exactly divisible by 3? Choose the correct choice A) 13 B) 12 C) 16 D) 17 E) 18

<gadget id="calculator">46 / 3</gadget> <output>46/3 = around 15.333333</output> <gadget id="calculator">floor(46/3)</gadget> <output>15</output> <gadget id="calculator">15 * 3</gadget> <output>45</output> <gadget id="calculator">10 / 3</gadget> <output>10/3 = around 3.333333</output> <gadget id="calculator">floor(10/3)</gadget> <output>3</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">45 - 12</gadget> <output>33</output> <gadget id="calculator">33 / 3</gadget> <output>11</output> <gadget id="calculator">11 + 1</gadget> <output>12</output> <result>B</result>

B

How many numbers from 10 to 46 are exactly divisible by 3?

add(divide(subtract(multiply(floor(divide(46, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1)

divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)|

"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 . 12 numbers . 10 / 3 = 3 and 46 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits b )"

general

math_qa__icHwvfFBOn3RI2ZW

The total number of digits used in numbering the pages of a book having 366 pages is Choose the correct choice from the following choices. A) 732 B) 990 C) 1098 D) 1305 E) 1605

<gadget id="calculator">366 * 3</gadget> <output>1_098</output> <gadget id="calculator">100 - 1</gadget> <output>99</output> <gadget id="calculator">1_098 - 99</gadget> <output>999</output> <gadget id="calculator">10 - 1</gadget> <output>9</output> <gadget id="calculator">999 - 9</gadget> <output>990</output> <result>B</result>

B

The total number of digits used in numbering the pages of a book having 366 pages is

subtract(subtract(multiply(366, const_3), subtract(const_100, const_1)), subtract(const_10, const_1))

multiply(n0,const_3)|subtract(const_100,const_1)|subtract(const_10,const_1)|subtract(#0,#1)|subtract(#3,#2)|

"explanation : total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 267 ) = ( 9 + 180 + 801 ) = 990 . answer : b"

general

math_qa__CJwU9JEK1e5FgxXf

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 15 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel? Choose the correct choice from the following options. A) 54 B) 66 C) 80 D) 45 E) 96

<gadget id="calculator">36 / 2</gadget> <output>18</output> <gadget id="calculator">18 / 6</gadget> <output>3</output> <gadget id="calculator">15 * 3</gadget> <output>45</output> <result>D</result>

D

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 15 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?

multiply(15, divide(divide(36, 2), 6))

divide(n1,n3)|divide(#0,n0)|multiply(n2,#1)|

"d 45 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 45 miles"

physics

math_qa__8GmPCKkuOceyyYwf

In a public show 45 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant? Select A) 330 B) 110 C) 120 D) 140 E) 150

<gadget id="calculator">100 - 45</gadget> <output>55</output> <gadget id="calculator">600 * 55</gadget> <output>33_000</output> <gadget id="calculator">33_000 / 100</gadget> <output>330</output> <result>A</result>

A

In a public show 45 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?

divide(multiply(600, subtract(const_100, 45)), const_100)

subtract(const_100,n0)|multiply(n1,#0)|divide(#1,const_100)

75 % of 600 = 45 / 100 × 600 = 270 therefore , the number of vacant seats = 600 - 270 = 330 . answer : a

gain

math_qa__K0PZ51MxKIhzcrs1

If (1/5)^m * (1/4)^2 = 1/((10)^4), then m = Choose the correct choice from the following options A) 4 B) 5 C) 6 D) 3 E) 2

<gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * 10</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 10</gadget> <output>2</output> <gadget id="calculator">(5/2) + 2</gadget> <output>9/2 = around 4.5</output> <gadget id="calculator">5 / 10</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(9/2) - (1/2)</gadget> <output>4</output> <result>A</result>

A

If (1/5)^m * (1/4)^2 = 1/((10)^4), then m =

subtract(add(multiply(divide(1, 4), 10), multiply(divide(1, 5), 10)), divide(5, 10))

divide(n0,n3)|divide(n0,n1)|divide(n1,n6)|multiply(n6,#0)|multiply(n6,#1)|add(#3,#4)|subtract(#5,#2)

1 / 5 ^ m * 1 / 4 ^ 2 = 1 / 2 ^ 4 * 5 ^ 4 2 ^ 4 * 5 ^ 4 / 2 ^ 4 = 5 ^ m or 5 ^ 4 = 5 ^ m therefore m = 4 a

general

math_qa__8Yxtkt31LBEKBA8J

frank is 15 years younger then john . in 3 years john will be twice as old as frank . how old will frank be in 4 years ? Pick: A) 8 B) 10 C) 12 D) 14 E) 16

<gadget id="calculator">2 * 15</gadget> <output>30</output> <gadget id="calculator">15 + 3</gadget> <output>18</output> <gadget id="calculator">30 - 18</gadget> <output>12</output> <gadget id="calculator">12 + 4</gadget> <output>16</output> <result>E</result>

E

frank is 15 years younger then john . in 3 years john will be twice as old as frank . how old will frank be in 4 years ?

add(subtract(multiply(const_2, 15), add(15, 3)), 4)

add(n0,n1)|multiply(n0,const_2)|subtract(#1,#0)|add(n2,#2)

frank is 15 years younger then john - - > f + 15 = j ; in 5 years john will be twice as old as frank ( in 3 year john will be j + 3 years old and frank will be f + 3 years old ) - - > j + 3 = 2 * ( f + 3 ) - - > ( f + 15 ) + 3 = 2 * ( f + 3 ) - - > f = 12 ; in 4 years frank will be 12 + 4 = 16 years old . answer : e .

general

math_qa__lpHsIRmWepMaGqUJ

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 72. What is the total number of students in the school? Choose one: A) 72 B) 80 C) 120 D) 40 E) 150

<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">72 * (2/3)</gadget> <output>48</output> <gadget id="calculator">72 + 48</gadget> <output>120</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">120 / (4/5)</gadget> <output>150</output> <result>E</result>

E

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 72. What is the total number of students in the school?

divide(add(72, multiply(72, divide(2, 3))), subtract(const_1, divide(20, const_100)))

divide(n3,n4)|divide(n0,const_100)|multiply(n6,#0)|subtract(const_1,#1)|add(n6,#2)|divide(#4,#3)|

"explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 72 + 2 / 3 of 72 80 / 100 x = 120 x = 150 . answer : option e"

general

math_qa__jfnRVuAcBFN1xj2V

Mike needs 30% to pass. If he scored 212 marks and falls short by 28 marks, what was the maximum marks he could have got? Choose the correct choice from the following answers A) 343 B) 677 C) 800 D) 867 E) 932

<gadget id="calculator">212 + 28</gadget> <output>240</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">240 / (3/10)</gadget> <output>800</output> <result>C</result>

C

Mike needs 30% to pass. If he scored 212 marks and falls short by 28 marks, what was the maximum marks he could have got?

divide(add(212, 28), divide(30, const_100))

add(n1,n2)|divide(n0,const_100)|divide(#0,#1)|

"if mike had scored 28 marks more , he could have scored 30 % therefore , mike required 212 + 28 = 240 marks let the maximum marks be m . then 30 % of m = 240 ( 30 / 100 ) × m = 240 m = ( 240 × 100 ) / 30 m = 24000 / 30 m = 800 answer : c"

gain

math_qa__hC2sTXJbPnbKZW9Z

A man can ride on motorcycle at 50 kmph upward road and 100 kmph downward road. He takes 12 hours to ride motorcycle uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 12 hours? He must return back to base point A in remaining time. Pick. A) 1000 B) 900 C) 800 D) 400 E) 1200

<gadget id="calculator">50 * 100</gadget> <output>5_000</output> <gadget id="calculator">5_000 * 2</gadget> <output>10_000</output> <gadget id="calculator">50 + 100</gadget> <output>150</output> <gadget id="calculator">10_000 / 150</gadget> <output>200/3 = around 66.666667</output> <gadget id="calculator">(200/3) * 12</gadget> <output>800</output> <result>C</result>

C

A man can ride on motorcycle at 50 kmph upward road and 100 kmph downward road. He takes 12 hours to ride motorcycle uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 12 hours? He must return back to base point A in remaining time.

multiply(divide(multiply(multiply(50, 100), const_2), add(50, 100)), 12)

add(n0,n1)|multiply(n0,n1)|multiply(#1,const_2)|divide(#2,#0)|multiply(n2,#3)

upward distance traveled per hour - 50 km , distance traveled after 8 hours = 400 km . he remained with 4 hours travel downward , i . e . distance traveled in remaining 4 hours downward = 400 km so total distance traveled from a to b and back to point a = 400 km upward + 400 km downhill = 800 km ( answer : c )

physics

math_qa__8S9Im12wmrp1PI01

7 machines at a certain factory operate at the same constant rate . if 6 of these machines , operating simultaneously , take 42 hours to fill a certain production order , how many fewer hours does it take all 7 machines , operating simultaneously , to fill the same production order ? Choose the correct choice from the following choices: A) 3 B) 4 C) 5 D) 6 E) 7

<gadget id="calculator">6 * 42</gadget> <output>252</output> <gadget id="calculator">252 / 7</gadget> <output>36</output> <gadget id="calculator">42 - 36</gadget> <output>6</output> <result>D</result>

D

7 machines at a certain factory operate at the same constant rate . if 6 of these machines , operating simultaneously , take 42 hours to fill a certain production order , how many fewer hours does it take all 7 machines , operating simultaneously , to fill the same production order ?

subtract(42, divide(multiply(6, 42), 7))

multiply(n1,n2)|divide(#0,n0)|subtract(n2,#1)

the total work is 6 * 42 = 252 machine hours the time required for seven machines is 252 / 7 = 36 hours , thus 6 fewer hours . the answer is d .

other

math_qa__0NRMfhCIDRdLpO3z

What number is obtained by adding the units digits of 734^99 and 347^83? Choose the correct choice: A) 7 B) 8 C) 9 D) 10 E) 11

<gadget id="calculator">99 - 83</gadget> <output>16</output> <gadget id="calculator">1 + 10</gadget> <output>11</output> <gadget id="calculator">99 / 11</gadget> <output>9</output> <gadget id="calculator">16 - 9</gadget> <output>7</output> <result>A</result>

A

What number is obtained by adding the units digits of 734^99 and 347^83?

subtract(subtract(99, 83), divide(99, add(const_1, const_10)))

add(const_1,const_10)|subtract(n1,n3)|divide(n1,#0)|subtract(#1,#2)

the units digit of 734 ^ 99 is 4 because 4 raised to the power of an odd integer ends in 4 . the units digit of 347 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 4 + 3 = 7 . the answer is a .

general

math_qa__lnDHSedmNPEK8D2F

The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 1 year is Pick one: A) s . 9621 B) s . 6921 C) s . 8400 D) s . 6261 E) s . 6361

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">1 + (1/20)</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">(21/20) ** 1</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">8_000 * (21/20)</gadget> <output>8_400</output> <result>C</result>

C

The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 1 year is

multiply(8000, power(add(const_1, divide(5, const_100)), 1))

divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)|

"c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) = rs 8400 answer : c"

gain

math_qa__XVu8I3lZmnddTkBR

The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 150 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire? Choose one: A) 90 B) 120 C) 160 D) 360 E) 600

<gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 - (3/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">150 / (1/4)</gadget> <output>600</output> <result>E</result>

E

The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 150 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?

divide(150, subtract(const_1, divide(3, 4)))

divide(n1,n2)|subtract(const_1,#0)|divide(n0,#1)|

"if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 150 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 150 n = 600 answer = ( e )"

general

math_qa__Gaxs6DFwCJ2ZkEFi

What is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45? Choose the most appropriate option: A) 26 B) 36 C) 16 D) 06 E) 40

<gadget id="calculator">10 - 1</gadget> <output>9</output> <gadget id="calculator">9 * 9</gadget> <output>81</output> <gadget id="calculator">81 % 45</gadget> <output>36</output> <result>B</result>

B

What is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45?

reminder(multiply(subtract(const_10, const_1), subtract(const_10, const_1)), 45)

subtract(const_10,const_1)|multiply(#0,#0)|reminder(#1,n1)

explanation : let ' s call : a = 123456789101112131415161718192021222324252627282930313233343536373839404142434481 = > a = b * 100 + 81 [ with b = 1234567 . . . . . 424344 ] we have : b x 100 is divisible by 45 because : - sum of all digits in b = 1 + 2 + 3 + . . . . + 44 = ( 1 + 44 ) + ( 2 + 43 ) + . . . . + ( 22 + 23 ) ( 22 pairs ) = 22 * 45 = > b divisible for 9 since b is divisible by 9 , b * 100 will be divisible by 9 * 5 = 45 81 divided 45 gives a remainder of 36 therefore , a divided by 45 reminder 36 answer : b

general

math_qa__OKs9G9FV7YfF6iuf

In a race where 10 cars are running, the chance that car X will win is 1/7, that Y will win is 1/3 and that Z will win is 1/5. Assuming that a dead heat is impossible, find the chance that one of them will win. Pick: A) 1 / 140 B) 1 / 180 C) 71 / 105 D) 21 / 113 E) 57 / 120

<gadget id="calculator">1 / 7</gadget> <output>1/7 = around 0.142857</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/7) + (1/3)</gadget> <output>10/21 = around 0.47619</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(10/21) + (1/5)</gadget> <output>71/105 = around 0.67619</output> <result>C</result>

C

In a race where 10 cars are running, the chance that car X will win is 1/7, that Y will win is 1/3 and that Z will win is 1/5. Assuming that a dead heat is impossible, find the chance that one of them will win.

add(add(divide(1, 7), divide(1, 3)), divide(1, 5))

divide(n1,n2)|divide(n1,n4)|divide(n1,n6)|add(#0,#1)|add(#3,#2)|

"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 7 + 1 / 3 + 1 / 5 = 71 / 105 answer : c"

general

math_qa__inhZaaRJEHEevDrT

A person decided to build a house in 100 days. He employed 100 men in the beginning and 100 more after 20 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished? Choose the correct choice from the following options: A) 40 B) 80 C) 70 D) 60 E) 50

<gadget id="calculator">100 - 20</gadget> <output>80</output> <result>B</result>

B

A person decided to build a house in 100 days. He employed 100 men in the beginning and 100 more after 20 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?

subtract(100, 20)

subtract(n0,n3)|

"200 men do the rest of the work in 100 - 20 = 80 days 100 men can do the rest of the work in 80 * 200 / 100 = 160 days required number of days = 160 - 80 = 80 days answer is b"

general

math_qa__bHNpbBhE9pQgP8z8

Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.1.50 a meter? Answers: A) 287 B) 132 C) 150.9 D) 158 E) 267

<gadget id="calculator">32 / 2</gadget> <output>16</output> <gadget id="calculator">2 * pi * 16</gadget> <output>32*pi = around 100.530965</output> <gadget id="calculator">(32*pi) * 1.5</gadget> <output>48.0*pi = around 150.796447</output> <result>C</result>

C

Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.1.50 a meter?

multiply(circumface(divide(32, const_2)), 1.50)

divide(n0,const_2)|circumface(#0)|multiply(n1,#1)|

"2 * 22 / 7 * 16 = 100.6 100.6 * 1 1 / 2 = rs . 150.9 answer : c"

physics

math_qa__HMqdTPG9p5L9t8I2

Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 5 minutes 20 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister? Choose the correct answer: A) 3 % B) 50 % C) 8 % D) 10 % E) 12 %

<gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">5 * 60</gadget> <output>300</output> <gadget id="calculator">300 + 20</gadget> <output>320</output> <gadget id="calculator">10 * 60</gadget> <output>600</output> <gadget id="calculator">600 + 40</gadget> <output>640</output> <gadget id="calculator">320 / 640</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 - (1/2)</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">100 * (1/2)</gadget> <output>50</output> <result>B</result>

B

Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 5 minutes 20 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?

multiply(multiply(10, 10), subtract(const_1, divide(add(multiply(5, const_60), 20), add(multiply(10, const_60), 40))))

multiply(n0,n0)|multiply(n2,const_60)|multiply(n0,const_60)|add(n3,#1)|add(n1,#2)|divide(#3,#4)|subtract(const_1,#5)|multiply(#0,#6)|

"bob ' s time = 640 secs . his sis ' time = 320 secs . percent increase needed = ( 640 - 320 / 640 ) * 100 = 320 / 640 * 100 = 50 % . ans ( b ) ."

physics

math_qa__V6ObozVy4jfdvDeg

How much time does a train 100 metres long running at 72 km/hr take to pass a pole? Choose the correct choice from the following answers: A) 7.9 s B) 2.5 s C) 5 s D) 7.6 s E) 7.4 s

<gadget id="calculator">100 / 1_000</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/10) / 72</gadget> <output>1/720 = around 0.001389</output> <gadget id="calculator">(1/720) * 3_600</gadget> <output>5</output> <result>C</result>

C

How much time does a train 100 metres long running at 72 km/hr take to pass a pole?

multiply(divide(divide(100, const_1000), 72), const_3600)

divide(n0,const_1000)|divide(#0,n1)|multiply(#1,const_3600)

explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 100 / t t = 5 s answer : c

general

math_qa__e6X2p2YZ5jJzmWwK

Sahil purchased a machine at Rs 12000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it. Choose the correct option A) rs . 22000 B) rs . 24000 C) rs . 26000 D) rs . 27000 E) none of these

<gadget id="calculator">12_000 + 5_000</gadget> <output>17_000</output> <gadget id="calculator">17_000 + 1_000</gadget> <output>18_000</output> <gadget id="calculator">18_000 / 100</gadget> <output>180</output> <gadget id="calculator">180 * 50</gadget> <output>9_000</output> <gadget id="calculator">18_000 + 9_000</gadget> <output>27_000</output> <result>D</result>

D

Sahil purchased a machine at Rs 12000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.

add(add(add(12000, 5000), 1000), multiply(divide(add(add(12000, 5000), 1000), const_100), 50))

add(n0,n1)|add(n2,#0)|divide(#1,const_100)|multiply(n3,#2)|add(#1,#3)|

"explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 12000 + 5000 + 1000 = 18000 150 % of 18000 = 150 / 100 * 18000 = 27000 option d"

gain

math_qa__Wqc7pLTv0D66ekMz

In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 49 as quotient. What is the correct quotient ? Choices A) 0 B) 12 C) 13 D) 20 E) 28

<gadget id="calculator">12 * 49</gadget> <output>588</output> <gadget id="calculator">588 / 21</gadget> <output>28</output> <result>E</result>

E

In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 49 as quotient. What is the correct quotient ?

divide(multiply(12, 49), 21)

multiply(n1,n3)|divide(#0,n2)|

"12 * 49 = 588 588 % 21 = 28 answer : e"

general

math_qa__yJpFclDtbRj0g9hR

UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 4:6. If 40% of the Toyota bought and 60% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? Choose the correct choice from the following choices: A) 66 % B) 64 % C) 68 % D) 69 % E) 52 %

<gadget id="calculator">4 * 6</gadget> <output>24</output> <gadget id="calculator">6 * 4</gadget> <output>24</output> <gadget id="calculator">24 + 24</gadget> <output>48</output> <gadget id="calculator">100 - 48</gadget> <output>52</output> <result>E</result>

E

UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 4:6. If 40% of the Toyota bought and 60% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase?

subtract(const_100, add(multiply(4, 6), multiply(6, 4)))

multiply(n0,n1)|add(#0,#0)|subtract(const_100,#1)|

"let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : e"

other

math_qa__onA5fGMPHi6ipAEE

The effective annual rate of interest corresponding to a nominal rate of 12% per annum payable half-yearly is? Select A) 16.06 % B) 16.07 % C) 12.36 % D) 6.09 % E) 6.19 %

<gadget id="calculator">12 / 2</gadget> <output>6</output> <gadget id="calculator">6 + 6</gadget> <output>12</output> <gadget id="calculator">6 * 6</gadget> <output>36</output> <gadget id="calculator">36 / 100</gadget> <output>9/25 = around 0.36</output> <gadget id="calculator">12 + (9/25)</gadget> <output>309/25 = around 12.36</output> <result>C</result>

C

The effective annual rate of interest corresponding to a nominal rate of 12% per annum payable half-yearly is?

add(add(divide(12, const_2), divide(12, const_2)), divide(multiply(divide(12, const_2), divide(12, const_2)), const_100))

divide(n0,const_2)|add(#0,#0)|multiply(#0,#0)|divide(#2,const_100)|add(#1,#3)|

"amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 6 / 100 ) 2 ] = rs . 112.36 effective rate = ( 112.36 - 100 ) = 12.36 % answer : c"

gain

math_qa__UysfuPjCGtCCUNU0

an association of mathematics teachers has 1600 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ? Choose the correct choice from the following: A) 75 % B) 58 % C) 42 % D) 14.5 % E) 19.6 %

<gadget id="calculator">525 * 60</gadget> <output>31_500</output> <gadget id="calculator">31_500 / 100</gadget> <output>315</output> <gadget id="calculator">315 * 100</gadget> <output>31_500</output> <gadget id="calculator">31_500 / 1_600</gadget> <output>315/16 = around 19.6875</output> <result>E</result>

E

an association of mathematics teachers has 1600 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?

divide(multiply(divide(multiply(525, 60), const_100), const_100), 1600)

multiply(n1,n2)|divide(#0,const_100)|multiply(#1,const_100)|divide(#2,n0)

total umber of members = 1600 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1600 ) * 100 = 19.6 % answer e

gain

math_qa__RgyTb8GS6kBiLZTK

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is John’s weekly allowance? Choose the correct choice A) $ 2.25 B) $ 3.00 C) $ 3.25 D) $ 3.65 E) $ 4.80

<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (3/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(1/3) * (2/5)</gadget> <output>2/15 = around 0.133333</output> <gadget id="calculator">(3/5) + (2/15)</gadget> <output>11/15 = around 0.733333</output> <gadget id="calculator">1 - (11/15)</gadget> <output>4/15 = around 0.266667</output> <gadget id="calculator">0.6 / (4/15)</gadget> <output>2.25</output> <result>A</result>

A

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is John’s weekly allowance?

divide(0.60, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))

divide(n0,n1)|divide(const_1,n0)|subtract(const_1,#0)|multiply(#1,#2)|add(#0,#3)|subtract(const_1,#4)|divide(n2,#5)|

"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 60 4 x / 15 = 60 x = 225 = $ 2.25 the answer is a ."

general

math_qa__bDgB2ZPvv9xGx1WH

In the year 1990 there are 5000 men 3000 women 2000 boys. In 1994 men are increased by 20% women are increased by ratio of boys and women? Choose the correct choice from the following answers A) 11000 B) 12000 C) 13000 D) 14000 E) 15000

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 + (1/5)</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">5_000 * (6/5)</gadget> <output>6_000</output> <gadget id="calculator">2_000 / 3_000</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">1 + (2/3)</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">3_000 * (5/3)</gadget> <output>5_000</output> <gadget id="calculator">6_000 + 5_000</gadget> <output>11_000</output> <gadget id="calculator">11_000 + 2_000</gadget> <output>13_000</output> <result>C</result>

C

In the year 1990 there are 5000 men 3000 women 2000 boys. In 1994 men are increased by 20% women are increased by ratio of boys and women?

add(add(multiply(5000, add(const_1, divide(20, const_100))), multiply(3000, add(const_1, divide(2000, 3000)))), 2000)

divide(n5,const_100)|divide(n3,n2)|add(#0,const_1)|add(#1,const_1)|multiply(n1,#2)|multiply(n2,#3)|add(#4,#5)|add(n3,#6)

total population in year 1990 = 5000 + 3000 + 2000 = 10000 total population in year 1994 = ( ( 5000 * 120 / 100 ) + ( 3000 + ( 3000 * 2 / 3 ) ) + ( 2000 ) ) = 13000 answer : c

other

math_qa__seHmCzNravIXxi2p

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B Choose the correct option A) 10 B) 8 C) 6 D) 5 E) 7

<gadget id="calculator">27 - 2</gadget> <output>25</output> <gadget id="calculator">25 * 2</gadget> <output>50</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">50 / 5</gadget> <output>10</output> <result>A</result>

A

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B

divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1))

add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)|

"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 . hence , b ' s age = 2 x = 10 years answer : a"

general

math_qa__Yoctv3DZukmee0ZK

What is the sum of the multiples of 4 between 13 and 125 inclusive? Choices: A) 1,890 B) 1,960 C) 2,200 D) 3,780 E) 4,400

<gadget id="calculator">125 - 3</gadget> <output>122</output> <gadget id="calculator">13 + 2</gadget> <output>15</output> <gadget id="calculator">122 + 15</gadget> <output>137</output> <gadget id="calculator">137 / 2</gadget> <output>137/2 = around 68.5</output> <gadget id="calculator">122 - 15</gadget> <output>107</output> <gadget id="calculator">107 / 4</gadget> <output>107/4 = around 26.75</output> <gadget id="calculator">(107/4) + 1</gadget> <output>111/4 = around 27.75</output> <gadget id="calculator">(137/2) * (111/4)</gadget> <output>15_207/8 = around 1_900.875</output> <result>B</result>

B

What is the sum of the multiples of 4 between 13 and 125 inclusive?

multiply(divide(add(subtract(125, const_3), add(13, const_2)), const_2), add(divide(subtract(subtract(125, const_3), add(13, const_2)), 4), const_1))

add(n1,const_2)|subtract(n2,const_3)|add(#0,#1)|subtract(#1,#0)|divide(#3,n0)|divide(#2,const_2)|add(#4,const_1)|multiply(#6,#5)|

"the first multiple of 12 between 13 and 125 is 16 while the last is 124 total number of terms is given by 124 = 16 + ( n - 1 ) 4 4 n - 4 = 108 n = 112 / 4 = 28 or , ( 124 - 16 ) / 4 + 1 = 28 so , we have 28 multiples of 12 between 13 and 125 sum = 14 ( 2 * 16 + ( 27 ) 4 ) = 14 ( 140 ) = 1960 answer : b"

general

math_qa__QqnkO841LB7ozvwJ

Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is: Choose the correct choice from the following: A) 1050 sq . m B) 3850 sq . m C) 950 sq . m D) 1075 sq . m E) 1065 sq . m

<gadget id="calculator">70 ** 2</gadget> <output>4_900</output> <gadget id="calculator">70 / 2</gadget> <output>35</output> <gadget id="calculator">pi * (35 ** 2)</gadget> <output>1225*pi = around 3_848.451001</output> <gadget id="calculator">4_900 - (1225*pi)</gadget> <output>4900 - 1225*pi = around 1_051.548999</output> <result>A</result>

A

Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:

subtract(square_area(70), circle_area(divide(70, const_2)))

divide(n1,const_2)|square_area(n1)|circle_area(#0)|subtract(#1,#2)

area ungrazed is given by total area - 4 * area grazed by each horse = 70 * 70 - 4 * ( 90 / 360 ) * pi * ( 70 / 2 ) ^ 2 as the angle made by the horse is 90 degree , so applying the area of the sector , = theta / 360 * pi * radius ^ 2 above = 70 * 70 - pi * ( 70 / 2 ) * ( 70 / 2 ) = 70 * 70 { 1 - pi / 4 } = 70 * 70 { 6 / ( 7 * 4 ) } , expanding pi = 22 / 7 = ( 70 * 70 * 6 ) / ( 7 * 4 ) = 1050 sq m answer : a

geometry

math_qa__IWcRaVt85nLodHSb

A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 38. Find the profit percentage? Choose the correct choice from the following: A) 80 % B) 90 % C) 59 % D) 40 % E) 53 %

<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">38 * 5</gadget> <output>190</output> <gadget id="calculator">25 * 4</gadget> <output>100</output> <gadget id="calculator">190 - 100</gadget> <output>90</output> <result>B</result>

B

A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 38. Find the profit percentage?

subtract(multiply(38, add(const_4, const_1)), multiply(25, const_4))

add(const_1,const_4)|multiply(n1,const_4)|multiply(n3,#0)|subtract(#2,#1)

l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 190 ( 30 * 5 ) profit percentage = ( 190 - 100 ) / 100 * 100 = 90 % answer : b

gain

math_qa__M1vgJH83UOl3YBLC

redo ’ s manufacturing costs for sets of horseshoes include a $ 10000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ? Choices: A) $ 4500 B) $ 3500 C) $ 5500 D) $ 5000 E) $ 6300

<gadget id="calculator">50 - 20</gadget> <output>30</output> <gadget id="calculator">30 * 500</gadget> <output>15_000</output> <gadget id="calculator">15_000 - 10_000</gadget> <output>5_000</output> <result>D</result>

D

redo ’ s manufacturing costs for sets of horseshoes include a $ 10000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?

subtract(multiply(subtract(50, 20), 500), 10000)

subtract(n2,n1)|multiply(n3,#0)|subtract(#1,n0)

total manufacturing cost = 10000 + 500 * 20 = 20000 total selling cost = 500 * 50 = 25000 profit = 25000 - 20000 = 5000 answer : d

gain

math_qa__rBT9Evs91PohI9Ms

What is the largest 4 digit number exactly divisible by 72? Choose the correct choice from the following options A) 4676 B) 4678 C) 8888 D) 9504 E) 9936

<gadget id="calculator">10 ** 4</gadget> <output>10_000</output> <gadget id="calculator">10_000 / 72</gadget> <output>1_250/9 = around 138.888889</output> <gadget id="calculator">floor(1_250/9)</gadget> <output>138</output> <gadget id="calculator">138 * 72</gadget> <output>9_936</output> <result>E</result>

E

What is the largest 4 digit number exactly divisible by 72?

multiply(floor(divide(power(const_10, 4), 72)), 72)

power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)|

"largest 4 digit number = 9999 9999 ÷ 72 = 138 , remainder = 63 hence largest 4 digit number exactly divisible by 88 = 9999 - 63 = 9936 answer : e"

general

math_qa__lxIN441t94FjWkNE

Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 360 and for 36kgs of Apples is 420 then the cost of first 25kgs of Apples is Choose the correct choice A) 100 B) 250 C) 125 D) 110 E) 115

<gadget id="calculator">33 - 30</gadget> <output>3</output> <gadget id="calculator">420 - 360</gadget> <output>60</output> <gadget id="calculator">36 - 33</gadget> <output>3</output> <gadget id="calculator">60 / 3</gadget> <output>20</output> <gadget id="calculator">3 * 20</gadget> <output>60</output> <gadget id="calculator">360 - 60</gadget> <output>300</output> <gadget id="calculator">300 / 30</gadget> <output>10</output> <gadget id="calculator">10 * 25</gadget> <output>250</output> <result>B</result>

B

Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 360 and for 36kgs of Apples is 420 then the cost of first 25kgs of Apples is

multiply(divide(subtract(360, multiply(subtract(33, 30), divide(subtract(420, 360), subtract(36, 33)))), 30), 25)

subtract(n4,n2)|subtract(n3,n1)|subtract(n1,n0)|divide(#0,#1)|multiply(#3,#2)|subtract(n2,#4)|divide(#5,n0)|multiply(n5,#6)|

"ans : by framing equations we get 30 l + 3 q = 360 30 l + 6 q = 420 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 10 cost of 10 kgs of apples = 25 x 10 = 250 answer : b"

other

math_qa__qhr1rMKxri6jZLQ6

The ratio of the radius of two circles is 3: 4, and then the ratio of their areas is? Pick one: A) 1 : 7 B) 9 : 16 C) 1 : 9 D) 3 : 7 E) 3 : 4

<gadget id="calculator">pi * (3 ** 2)</gadget> <output>9*pi = around 28.274334</output> <gadget id="calculator">pi * (4 ** 2)</gadget> <output>16*pi = around 50.265482</output> <gadget id="calculator">(9*pi) / (16*pi)</gadget> <output>9/16 = around 0.5625</output> <result>B</result>

B

The ratio of the radius of two circles is 3: 4, and then the ratio of their areas is?

divide(circle_area(3), circle_area(4))

circle_area(n0)|circle_area(n1)|divide(#0,#1)|

"r 1 : r 2 = 3 : 4 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 9 : 16 answer : b"

geometry

math_qa__npZz4q82KfsSGbDA

Evaluate: 30 - |-x + 6| for x = 10 Choose one. A) 16 B) 26 C) 36 D) 46 E) 56

<gadget id="calculator">-10</gadget> <output>-10</output> <gadget id="calculator">(-10) + 6</gadget> <output>-4</output> <gadget id="calculator">-(-4)</gadget> <output>4</output> <gadget id="calculator">30 - 4</gadget> <output>26</output> <result>B</result>

B

Evaluate: 30 - |-x + 6| for x = 10

subtract(30, negate(add(negate(10), 6)))

negate(n2)|add(n1,#0)|negate(#1)|subtract(n0,#2)

substitute x by 10 in the given expression and evaluate 30 - | - ( 10 ) + 6 | = 30 - | - 10 + 6 | = 30 - | - 4 | = 30 - 4 = 26 correct answer b ) 26

general

math_qa__CIz8UcPLblWvRj1A

in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300 Choose the correct choice from the following choices. A) 100 B) 200 C) 300 D) 400 E) none of these

<gadget id="calculator">6 * 3</gadget> <output>18</output> <gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">18 + 5</gadget> <output>23</output> <gadget id="calculator">1 / 23</gadget> <output>1/23 = around 0.043478</output> <gadget id="calculator">(1/23) * 2_300</gadget> <output>100</output> <result>A</result>

A

in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300

multiply(inverse(add(multiply(6, 3), add(const_1, const_4))), 2300)

add(const_1,const_4)|multiply(n1,n5)|add(#0,#1)|inverse(#2)|multiply(n8,#3)

remaining capital = 1 - ( 1 ⁄ 6 + 1 ⁄ 3 ) = 1 ⁄ 2 ratio of their profit = 1 ⁄ 6 × [ 1 ⁄ 6 × 12 ] : 1 ⁄ 3 × [ 1 ⁄ 3 × 12 ] : 1 ⁄ 2 × 12 = 1 ⁄ 3 : 4 ⁄ 3 : 6 = 1 : 4 : 18 ∴ a ' s share = 1 / 1 + 4 + 18 × 2300 = 100 answer a

gain

math_qa__I3gjHJb3DJtSAolP

Car X began traveling at an average speed of 35 miles per hour. After 48 minutes, car Y began traveling at an average speed of 39 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped? Choose the correct choice from the following. A) 105 B) 140 C) 175 D) 210 E) 245

<gadget id="calculator">48 / 60</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(4/5) * 35</gadget> <output>28</output> <gadget id="calculator">39 - 35</gadget> <output>4</output> <gadget id="calculator">28 / 4</gadget> <output>7</output> <gadget id="calculator">35 * 7</gadget> <output>245</output> <result>E</result>

E

Car X began traveling at an average speed of 35 miles per hour. After 48 minutes, car Y began traveling at an average speed of 39 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

multiply(35, divide(multiply(divide(48, const_60), 35), subtract(39, 35)))

divide(n1,const_60)|subtract(n2,n0)|multiply(n0,#0)|divide(#2,#1)|multiply(n0,#3)|

"in 48 minutes , car x travels 28 miles . car y gains 4 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is e ."

physics

math_qa__1ALbmoLJQLYuSETy

benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ? Choose the correct choice from the following A) 8 B) 9 C) 5 D) 7 E) 10

<gadget id="calculator">360 / 4</gadget> <output>90</output> <gadget id="calculator">9 * 2</gadget> <output>18</output> <gadget id="calculator">90 / 18</gadget> <output>5</output> <result>C</result>

C

benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ?

divide(divide(360, 4), multiply(9, const_2))

divide(n1,n2)|multiply(n0,const_2)|divide(#0,#1)

cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5

general

math_qa__2FQuuzlz39Pmvfyn

It takes nine minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth? Select A) 13.58 B) 13.87 C) 14.24 D) 14.59 E) 14.85

<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">5 + 4</gadget> <output>9</output> <gadget id="calculator">9 * 60</gadget> <output>540</output> <gadget id="calculator">1 / 540</gadget> <output>1/540 = around 0.001852</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 + 3</gadget> <output>15</output> <gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">(1/540) + (1/15)</gadget> <output>37/540 = around 0.068519</output> <gadget id="calculator">1 / (37/540)</gadget> <output>540/37 = around 14.594595</output> <gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">16 * 3</gadget> <output>48</output> <gadget id="calculator">48 - 2</gadget> <output>46</output> <gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">46 / 10_000</gadget> <output>23/5_000 = around 0.0046</output> <gadget id="calculator">(540/37) - (23/5_000)</gadget> <output>2_699_149/185_000 = around 14.589995</output> <result>D</result>

D

It takes nine minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth?

subtract(inverse(add(inverse(multiply(add(add(const_2, const_3), const_4), const_60)), inverse(add(multiply(const_3, const_4), const_3)))), divide(subtract(multiply(multiply(const_4, const_4), const_3), const_2), multiply(const_100, const_100)))

add(const_2,const_3)|multiply(const_3,const_4)|multiply(const_4,const_4)|multiply(const_100,const_100)|add(#0,const_4)|add(#1,const_3)|multiply(#2,const_3)|inverse(#5)|multiply(#4,const_60)|subtract(#6,const_2)|divide(#9,#3)|inverse(#8)|add(#11,#7)|inverse(#12)|subtract(#13,#10)

the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 9 ) = 1 / 540 of the video per second . the combined rate is 1 / 15 + 1 / 540 = 37 / 540 of the video per second . the time required to load the video is 540 / 37 = 14.59 seconds . the answer is d .

physics

math_qa__dAMaJwYbzGJqjsGT

A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 820 in 4 years. The rate on interest per annum is. Choose the most appropriate option. A) 0.4 % B) 5.0 % C) 2.5 % D) 7 % E) 8 %

<gadget id="calculator">820 - 800</gadget> <output>20</output> <gadget id="calculator">100 * 20</gadget> <output>2_000</output> <gadget id="calculator">2_000 / 800</gadget> <output>5/2 = around 2.5</output> <result>C</result>

C

A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 820 in 4 years. The rate on interest per annum is.

divide(multiply(const_100, subtract(820, 800)), 800)

subtract(n2,n0)|multiply(#0,const_100)|divide(#1,n0)

explanation : s . i . on rs 800 for 1 year = 20 rate = ( 100 * 20 ) / ( 800 * 1 ) = 2.5 % answer : c

gain

math_qa__FtfgssJK1cA1p2yO

Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually Pick one: A) rs 312 B) rs 412 C) rs 512 D) rs 612 E) none of these

<gadget id="calculator">7_500 * 4</gadget> <output>30_000</output> <gadget id="calculator">30_000 / 100</gadget> <output>300</output> <gadget id="calculator">7_500 + 300</gadget> <output>7_800</output> <gadget id="calculator">7_800 * 4</gadget> <output>31_200</output> <gadget id="calculator">31_200 / 100</gadget> <output>312</output> <gadget id="calculator">7_800 + 312</gadget> <output>8_112</output> <gadget id="calculator">8_112 - 7_500</gadget> <output>612</output> <result>D</result>

D

Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually

subtract(add(add(7500, divide(multiply(7500, const_4), const_100)), divide(multiply(add(7500, divide(multiply(7500, const_4), const_100)), 4), const_100)), 7500)

multiply(n0,const_4)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|add(#2,#4)|subtract(#5,n0)

explanation : please apply the formula amount = p ( 1 + r 100 ) nc . i . = amount - p answer : d

gain

math_qa__WLuZZ0EeRxSKQhxU

LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number is Answers A) 269 B) 285 C) 300 D) 275 E) none of these

<gadget id="calculator">7_700 * 11</gadget> <output>84_700</output> <gadget id="calculator">84_700 / 308</gadget> <output>275</output> <result>D</result>

D

LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number is

divide(multiply(7700, 11), 308)

multiply(n0,n1)|divide(#0,n2)

option d

physics

math_qa__kHkdisDtUMwmTmoF

The radius of a cylindrical vessel is 7cm and height is 2cm. Find the whole surface of the cylinder? Choose the correct choice from the following options A) 281 B) 396 C) 440 D) 767 E) 1981

<gadget id="calculator">2 * pi * 7 * (7 + 2)</gadget> <output>126*pi = around 395.840674</output> <result>B</result>

B

The radius of a cylindrical vessel is 7cm and height is 2cm. Find the whole surface of the cylinder?

surface_cylinder(7, 2)

surface_cylinder(n0,n1)|

"r = 7 h = 2 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 9 ) = 396 answer : b"

geometry

math_qa__prgyC9954wCgfAeA

A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number R of tickets sold by the male members of the association Pick one: A) 50 B) 56 C) 58 D) 62 E) 66

<gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">66 * 3</gadget> <output>198</output> <gadget id="calculator">70 * 2</gadget> <output>140</output> <gadget id="calculator">198 - 140</gadget> <output>58</output> <result>C</result>

C

A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number R of tickets sold by the male members of the association

subtract(multiply(66, add(1, 2)), multiply(70, 2))

add(n2,n3)|multiply(n1,n3)|multiply(n0,#0)|subtract(#2,#1)|

"given that , total average r sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."

general

math_qa__MZzwkgJiiTFaYUzV

If x is less than y by 50% then y exceed x by: Choose the most appropriate option A) 33.33 % B) 100 % C) 75 % D) 66.66 % E) none of these

<gadget id="calculator">100 - 50</gadget> <output>50</output> <gadget id="calculator">100 / 50</gadget> <output>2</output> <gadget id="calculator">2 - 1</gadget> <output>1</output> <gadget id="calculator">1 * 100</gadget> <output>100</output> <result>B</result>

B

If x is less than y by 50% then y exceed x by:

multiply(subtract(divide(const_100, subtract(const_100, 50)), const_1), const_100)

subtract(const_100,n0)|divide(const_100,#0)|subtract(#1,const_1)|multiply(#2,const_100)|

"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b"

general

math_qa__6BjKOg2DdwlHK0Kn

Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit? Choose the correct choice from the following answers. A) 66.3 B) 76.3 C) 86.3 D) 16.3 E) 36.3

<gadget id="calculator">30 * 11.5</gadget> <output>345</output> <gadget id="calculator">20 * 14.25</gadget> <output>285</output> <gadget id="calculator">345 + 285</gadget> <output>630</output> <gadget id="calculator">630 / 100</gadget> <output>63/10 = around 6.3</output> <gadget id="calculator">(63/10) * 30</gadget> <output>189</output> <gadget id="calculator">630 + 189</gadget> <output>819</output> <gadget id="calculator">30 + 20</gadget> <output>50</output> <gadget id="calculator">819 / 50</gadget> <output>819/50 = around 16.38</output> <result>D</result>

D

Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?

divide(add(add(multiply(30, 11.50), multiply(20, 14.25)), multiply(divide(add(multiply(30, 11.50), multiply(20, 14.25)), const_100), 30)), add(30, 20))

add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,const_100)|multiply(n4,#4)|add(#3,#5)|divide(#6,#0)|

"explanation : c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 130 % of rs . 630 = 130 / 100 * 630 = rs . 819 . s . p . per kg = 819 / 50 = rs . 16.38 = 16.30 . answer : d"

gain

math_qa__uVsB1sDaSEJAtw3j

What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? Choose the correct choice A) 6200 B) 3000 C) 3000 D) 2000 E) 1000

<gadget id="calculator">5 * 10</gadget> <output>50</output> <gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 - (1/2)</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">3_100 / (1/2)</gadget> <output>6_200</output> <result>A</result>

A

What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent?

divide(3100, subtract(const_1, divide(multiply(5, 10), const_100)))

multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)|

"p - 2336 = ( p * 10 * 5 ) / 100 p = 6200 answer : a"

gain

math_qa__1qWxXMmyl3at1nis

The list price of an article is Rs.68. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? Options A) 3.23 % B) 4.23 % C) 5.23 % D) 7.23 % E) 8.23 %

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">68 * (1/10)</gadget> <output>34/5 = around 6.8</output> <gadget id="calculator">68 - (34/5)</gadget> <output>306/5 = around 61.2</output> <gadget id="calculator">(306/5) - 56.16</gadget> <output>5.04</output> <gadget id="calculator">5.04 / (306/5)</gadget> <output>0.082353</output> <gadget id="calculator">0.082353 * 100</gadget> <output>8.2353</output> <result>E</result>

E

The list price of an article is Rs.68. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?

multiply(divide(subtract(subtract(68, multiply(68, divide(10, const_100))), 56.16), subtract(68, multiply(68, divide(10, const_100)))), const_100)

divide(n2,const_100)|multiply(n0,#0)|subtract(n0,#1)|subtract(#2,n1)|divide(#3,#2)|multiply(#4,const_100)|

"68 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 8.23 % answer : e"

gain

math_qa__TtLFcx6A2bgasuFx

The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side. Choose the correct choice from the following answers: A) rs . 850 B) rs . 860 C) rs . 876 D) rs . 886 E) none of these

<gadget id="calculator">6 * (8 ** 2)</gadget> <output>384</output> <gadget id="calculator">384 / 16</gadget> <output>24</output> <gadget id="calculator">24 * 36.5</gadget> <output>876</output> <result>C</result>

C

The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side.

multiply(divide(surface_cube(8), 16), 36.50)

surface_cube(n3)|divide(#0,n2)|multiply(n0,#1)|

"explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 ∗ 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 ∗ 24 = rs . 876 option c"

geometry

math_qa__T49ITlbkAs2GSOIT

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many W hours will it take if Jim types the report and Mary edits it immediately after he is done? Select A) 41.4 B) 34.1 C) 13.4 D) 12.4 E) 10.8

<gadget id="calculator">1 / 12.5</gadget> <output>0.08</output> <gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">0.08 - (1/30)</gadget> <output>0.046667</output> <gadget id="calculator">1 / 0.046667</gadget> <output>21.428418</output> <gadget id="calculator">1 / 7.5</gadget> <output>0.133333</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">0.133333 - (1/12)</gadget> <output>0.05</output> <gadget id="calculator">1 / 0.05</gadget> <output>20</output> <gadget id="calculator">21.428418 + 20</gadget> <output>41.428418</output> <result>A</result>

A

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many W hours will it take if Jim types the report and Mary edits it immediately after he is done?

add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12))))

divide(const_1,n0)|divide(const_1,n2)|divide(const_1,n1)|divide(const_1,n3)|subtract(#0,#1)|subtract(#2,#3)|inverse(#4)|inverse(#5)|add(#6,#7)|

"break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many w hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."

physics

math_qa__YAhfRsPgDq43FmRI

A scuba diver descends at a rate of 35 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3500feet below the sea level..how long will he take to reach the ship? Choose the correct choice from the following. A) 160 minutes B) 120 minutes C) 100 minutes D) 76 minutes E) 77 minutes

<gadget id="calculator">3_500 / 35</gadget> <output>100</output> <result>C</result>

C

A scuba diver descends at a rate of 35 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3500feet below the sea level..how long will he take to reach the ship?

divide(3500, 35)

divide(n1,n0)|

"time taken to reach = 3500 / 35 = 100 minutes answer : c"

gain

math_qa__R192tHxtjEdYzzZw

A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall? Choose the correct choice. A) 20 B) 26 C) 32 D) 39 E) 51

<gadget id="calculator">42 - 4</gadget> <output>38</output> <result>D</result>

D

A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?

subtract(42, 4)

subtract(n0,n1)|

"total transaction in two days = 4 - 2 = 2 feet in 38 days it will climb 38 feet on the 39 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 39 d"

physics

math_qa__rH2ep58tPLlWyxfu

At what rate percent on simple interest will Rs.900 amount to Rs.950 in 5 years? Choices: A) 1.11 % B) 5.93 % C) 4.33 % D) 5.33 % E) 6.33 %

<gadget id="calculator">950 - 900</gadget> <output>50</output> <gadget id="calculator">50 / 900</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">(1/18) / 5</gadget> <output>1/90 = around 0.011111</output> <gadget id="calculator">(1/90) * 100</gadget> <output>10/9 = around 1.111111</output> <result>A</result>

A

At what rate percent on simple interest will Rs.900 amount to Rs.950 in 5 years?

multiply(divide(divide(subtract(950, 900), 900), 5), const_100)

subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)|

"50 = ( 900 * 5 * r ) / 100 r = 1.11 % answer : a"

gain

math_qa__tcbtqZXw2b3osY8A

If the price of sugar rises from Rs.10 per kg to Rs. 12 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by Choose one: A) 17 % B) 20 % C) 25 % D) 30 % E) none

<gadget id="calculator">1 * 10</gadget> <output>10</output> <gadget id="calculator">10 / 12</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">1 - (5/6)</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/6) * 100</gadget> <output>50/3 = around 16.666667</output> <result>A</result>

A

If the price of sugar rises from Rs.10 per kg to Rs. 12 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by

multiply(subtract(const_1, divide(multiply(const_1, 10), 12)), const_100)

multiply(n0,const_1)|divide(#0,n1)|subtract(const_1,#1)|multiply(#2,const_100)|

"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 12 = x = 83 kg . ∴ reduction in consumption = 17 % . answer a"

general

math_qa__AKnM6cXbof0Mi3xx

Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many E women are currently in the room? Choose the correct choice from the following choices. A) 12 B) 14 C) 15 D) 24 E) 36

<gadget id="calculator">14 - 2</gadget> <output>12</output> <gadget id="calculator">5 * 12</gadget> <output>60</output> <gadget id="calculator">60 / 4</gadget> <output>15</output> <gadget id="calculator">15 - 3</gadget> <output>12</output> <gadget id="calculator">2 * 12</gadget> <output>24</output> <result>D</result>

D

Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many E women are currently in the room?

multiply(2, subtract(divide(multiply(5, subtract(14, 2)), 4), 3))

subtract(n4,n2)|multiply(n1,#0)|divide(#1,n0)|subtract(#2,n3)|multiply(n2,#3)|

"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"

other

math_qa__KAf8vVtlHzeJshBp

In a neighborhood having 90 households, 11 did not have either a car or a bike. If 16 households had a both a car and a bike and 44 had a car, how many had bike only? Choices: A) 30 B) 35 C) 20 D) 18 E) 10

<gadget id="calculator">90 - 11</gadget> <output>79</output> <gadget id="calculator">79 + 16</gadget> <output>95</output> <gadget id="calculator">95 - 44</gadget> <output>51</output> <gadget id="calculator">51 - 16</gadget> <output>35</output> <result>B</result>

B

In a neighborhood having 90 households, 11 did not have either a car or a bike. If 16 households had a both a car and a bike and 44 had a car, how many had bike only?

subtract(subtract(add(subtract(90, 11), 16), 44), 16)

subtract(n0,n1)|add(n2,#0)|subtract(#1,n3)|subtract(#2,n2)|

"{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 16 + 11 - - > { bike } = 51 - - > # those who have bike only is { bike } - { both } = 51 - 16 = 35 . answer : b ."

other

math_qa__ITQtZJFE4VcJTG3J

A bag marked at $150 is sold for $120. The rate of discount is? Pick: A) 10 % B) 25 % C) 20 % D) 50 % E) 45 %

<gadget id="calculator">150 - 120</gadget> <output>30</output> <gadget id="calculator">30 / 150</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <result>C</result>

C

A bag marked at $150 is sold for $120. The rate of discount is?

multiply(divide(subtract(150, 120), 150), const_100)

subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|

"rate of discount = 30 / 150 * 100 = 20 % answer is c"

gain

math_qa__bzEeOhbjjjBGT0Ps

If an object travels at three feet per second, how many feet does it travel in one hour? Answers: A) 3488 B) 10800 C) 12788 D) 1800 E) 2881

<gadget id="calculator">3 * 60</gadget> <output>180</output> <gadget id="calculator">180 * 60</gadget> <output>10_800</output> <result>B</result>

B

If an object travels at three feet per second, how many feet does it travel in one hour?

multiply(multiply(const_3, const_60), const_60)

multiply(const_3,const_60)|multiply(#0,const_60)

explanation : if an object travels at 2 feet per second it covers 3 x 60 feet in one minute , and 3 x 60 x 60 feet in one hour . answer = 10800 answer : b ) 10800

physics

math_qa__C4dcq9qae53nAFli

A cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water. If the water is then used to fill several smaller cylinders (2 meters radius and 5 meters height), how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty? Choose the correct choice from the following answers. A) 5 B) 4 C) 3 D) 2 E) 1

<gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">pi * (3 ** 2) * 8</gadget> <output>72*pi = around 226.194671</output> <gadget id="calculator">pi * (2 ** 2) * 5</gadget> <output>20*pi = around 62.831853</output> <gadget id="calculator">(72*pi) / (20*pi)</gadget> <output>18/5 = around 3.6</output> <gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">6 / 10</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(18/5) - (3/5)</gadget> <output>3</output> <result>C</result>

C

A cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water. If the water is then used to fill several smaller cylinders (2 meters radius and 5 meters height), how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty?

subtract(divide(volume_cylinder(divide(6, const_2), 8), volume_cylinder(2, 5)), divide(add(const_4, const_2), const_10))

add(const_2,const_4)|divide(n0,const_2)|volume_cylinder(n2,n3)|divide(#0,const_10)|volume_cylinder(#1,n1)|divide(#4,#2)|subtract(#5,#3)

calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 226.19 smaller cylinder volume = 62.83 therefore the number of smaller cylinders can be filled to capacity = 226.19 / 62.83 = 3.6 answer is c only 3 smaller cylinders can be filled to capacity .

geometry

math_qa__2Qh32Jh8sisMJjvz

four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is Choose one A) 12 B) 32 C) 42 D) 52 E) 58

<gadget id="calculator">7 * 2</gadget> <output>14</output> <gadget id="calculator">14 ** 2</gadget> <output>196</output> <gadget id="calculator">7 ** 2</gadget> <output>49</output> <gadget id="calculator">49 * pi</gadget> <output>49*pi = around 153.93804</output> <gadget id="calculator">196 - (49*pi)</gadget> <output>196 - 49*pi = around 42.06196</output> <result>C</result>

C

four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is

subtract(power(multiply(7, const_2), const_2), multiply(power(7, const_2), const_pi))

multiply(n0,const_2)|power(n0,const_2)|multiply(#1,const_pi)|power(#0,const_2)|subtract(#3,#2)

required area = 14 * 14 - ( 4 * 1 / 4 * 22 / 7 * 7 * 7 ) sq cm = 196 - 154 = 42 sq cm . answer : c

geometry

math_qa__6xsxuyxYzcL32piB

The roof of an apartment building is rectangular and its length is 5 times longer than its width. If the area of the roof is 720 feet squared, what is the difference between the length and the width of the roof? Choose the correct choice from the following answers A) 38 . B) 40 . C) 42 . D) 44 . E) 48 .

<gadget id="calculator">720 / 5</gadget> <output>144</output> <gadget id="calculator">144 ** (1/2)</gadget> <output>12</output> <gadget id="calculator">12 * 5</gadget> <output>60</output> <gadget id="calculator">60 - 12</gadget> <output>48</output> <result>E</result>

E

The roof of an apartment building is rectangular and its length is 5 times longer than its width. If the area of the roof is 720 feet squared, what is the difference between the length and the width of the roof?

subtract(multiply(sqrt(divide(720, 5)), 5), sqrt(divide(720, 5)))

divide(n1,n0)|sqrt(#0)|multiply(#1,n0)|subtract(#2,#1)|

"answer is e : 48 let w be the width , so length is 5 w . therefore : w * 5 w = 720 , solving for , w = 12 , so 5 w - w = 4 w = 4 * 12 = 48"

geometry

math_qa__NiedqY2Yrei62Mit

Jaclyn buys $10 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter Choose one A) 237.5 B) 234 C) 289.5 D) 345 E) none of these

<gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">10_000 * 9.5</gadget> <output>95_000</output> <gadget id="calculator">95_000 / 100</gadget> <output>950</output> <gadget id="calculator">950 / 4</gadget> <output>475/2 = around 237.5</output> <result>A</result>

A

Jaclyn buys $10 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter

divide(divide(multiply(multiply(const_100, const_100), 9.5), const_100), const_4)

multiply(const_100,const_100)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_4)

explanation : i = ( p x r x t ) / 100 = 10000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 237.5 answer : a

gain

math_qa__jBwazObcIc4qlPsg

At garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale? Pick: A) 33 B) 34 C) 35 D) 39 E) 37

<gadget id="calculator">15 + 25</gadget> <output>40</output> <gadget id="calculator">40 - 1</gadget> <output>39</output> <result>D</result>

D

At garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale?

subtract(add(15, 25), const_1)

add(n0,n1)|subtract(#0,const_1)|

"14 + 24 + 1 = 39 answer : d"

other

math_qa__JyWBoqoENP3bvUx0

In a division sum, the quotient is 20, the divisor 66 and the remainder 55, find the dividend? Choose the correct choice from the following answers: A) 1375 B) 1376 C) 1875 D) 1365 E) 1345

<gadget id="calculator">20 * 66</gadget> <output>1_320</output> <gadget id="calculator">1_320 + 55</gadget> <output>1_375</output> <result>A</result>

A

In a division sum, the quotient is 20, the divisor 66 and the remainder 55, find the dividend?

add(multiply(20, 66), 55)

multiply(n0,n1)|add(n2,#0)|

"explanation : 20 * 66 + 55 = 1375 answer : a"

general

math_qa__aMD1DMGM4kQydSoS

A and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? Pick: A) 66 / 5 B) 13 C) 17 D) 21 E) 23

<gadget id="calculator">6 + 3</gadget> <output>9</output> <gadget id="calculator">9 + 2</gadget> <output>11</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">11 * 3</gadget> <output>33</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">2 + (1/2)</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">33 / (5/2)</gadget> <output>66/5 = around 13.2</output> <result>A</result>

A

A and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?

divide(multiply(add(add(6, const_3), const_2), divide(6, const_2)), add(const_2, divide(const_1, const_2)))

add(n0,const_3)|divide(n0,const_2)|divide(const_1,const_2)|add(#0,const_2)|add(#2,const_2)|multiply(#3,#1)|divide(#5,#4)

let bucket a be a and bucket b be b scenario 1 a - 6 = 1 / 3 ( b + 6 ) - - - - > 3 a - 18 = b + 6 scenario 2 b - 6 = 1 / 2 ( a + 6 ) - - - - - > 2 b - 12 = a + 6 from scenario 1 , b = 3 a - 24 substitute b with this information in stmt 2 2 ( 3 a - 24 ) - 12 = a + 6 - - - - - - > 6 a - 48 - 12 = a + 6 - - - - - - > 6 a - a = 60 + 6 - - - > 5 a = 66 a = 66 / 5 , answer choice a

general

math_qa__mDnlCGvKVjy0XcQm

What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? Select the correct option: A) $ 3.36 B) $ 6.85 C) $ 8.46 D) $ 10.08 E) $ 12.46

<gadget id="calculator">2 * 2.49</gadget> <output>4.98</output> <gadget id="calculator">4 * 1.87</gadget> <output>7.48</output> <gadget id="calculator">4.98 + 7.48</gadget> <output>12.46</output> <result>E</result>

E

What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each?

add(multiply(2, 2.49), multiply(4, 1.87))

multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|

"answer = e 2 * 2.49 + 4 * 1.87 = 2 ( 2.50 - 0.01 ) + 4 ( 2.00 - 0.13 ) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46"

general

math_qa__CNn0hibnjlX2yAxG

After a storm deposits 110 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 220 billion gallons, the reservoir was approximately what percentage full before the storm? Choose the correct option. A) 40 % B) 48 % C) 54 % D) 58 % E) 65 %

<gadget id="calculator">110 + 220</gadget> <output>330</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">330 / (3/5)</gadget> <output>550</output> <gadget id="calculator">220 / 550</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 100</gadget> <output>40</output> <result>A</result>

A

After a storm deposits 110 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 220 billion gallons, the reservoir was approximately what percentage full before the storm?

multiply(divide(220, divide(add(110, 220), divide(60, const_100))), const_100)

add(n0,n2)|divide(n1,const_100)|divide(#0,#1)|divide(n2,#2)|multiply(#3,const_100)

when the storm deposited 110 billion gallons , volume of water in the reservoir = 220 + 110 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 330 / 0.6 = 550 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 550 ) * 100 = 40 % option a

general

math_qa__JTg7H2Ws9Ld7Aijx

A fill pipe can fill 1/2 of cistern in 20 minutes. In how many minutes, it can fill 1/2 of the cistern? Choose the correct answer A) 5 min B) 10 min C) 15 min D) 20 min E) 25 min

<gadget id="calculator">20 / 1</gadget> <output>20</output> <result>D</result>

D

A fill pipe can fill 1/2 of cistern in 20 minutes. In how many minutes, it can fill 1/2 of the cistern?

divide(20, 1)

divide(n2,n0)

required time = 20 * 2 * 1 / 2 = 20 minutes answer is d

physics

math_qa__ZbdI6Ceb8qtiR2rL

What is the average of 120, 130, 140, 510, 520, 530, 1115, 1120, and 1125? Choose the correct choice from the following options: A) 419 B) 551 C) 601 D) 590 E) 721

<gadget id="calculator">1_115 + 130</gadget> <output>1_245</output> <gadget id="calculator">1_245 + 140</gadget> <output>1_385</output> <gadget id="calculator">1_385 + 510</gadget> <output>1_895</output> <gadget id="calculator">1_895 + 520</gadget> <output>2_415</output> <gadget id="calculator">2_415 + 530</gadget> <output>2_945</output> <gadget id="calculator">2_945 + 1_115</gadget> <output>4_060</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">4_060 / 7</gadget> <output>580</output> <result>D</result>

D

What is the average of 120, 130, 140, 510, 520, 530, 1115, 1120, and 1125?

divide(add(add(add(add(add(add(1115, 130), 140), 510), 520), 530), 1115), add(const_3, const_4))

add(n6,n1)|add(const_3,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|add(n5,#4)|add(n6,#5)|divide(#6,#1)|

"add 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 5310 5310 / 9 = 590 . d"

general

math_qa__uK11nJkqarZhXefg

A bus travels from town A to town B. If the bus's speed is 50 km/hr, it will arrive in town B 42 min later than scheduled. If the bus increases its speed by 509509 m/sec, it will arrive in town B 30 min earlier than scheduled. Find: A) The distance between the two towns; B) The bus's scheduled time of arrival in B; C) The speed of the bus when it's on schedule. Select the correct option A) 60 B) 37 C) 26 D) 28 E) 11

<gadget id="calculator">30 / 60</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">509_509 * 36</gadget> <output>18_342_324</output> <gadget id="calculator">(1/2) * 18_342_324</gadget> <output>9_171_162</output> <gadget id="calculator">42 / 60</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">50 * (7/10)</gadget> <output>35</output> <gadget id="calculator">9_171_162 - 35</gadget> <output>9_171_127</output> <gadget id="calculator">18_342_324 - 50</gadget> <output>18_342_274</output> <gadget id="calculator">9_171_127 / 18_342_274</gadget> <output>9_171_127/18_342_274 = around 0.499999</output> <gadget id="calculator">(9_171_127/18_342_274) + (7/10)</gadget> <output>55_026_797/45_855_685 = around 1.199999</output> <gadget id="calculator">50 * (55_026_797/45_855_685)</gadget> <output>550_267_970/9_171_137 = around 59.999973</output> <result>A</result>

A

A bus travels from town A to town B. If the bus's speed is 50 km/hr, it will arrive in town B 42 min later than scheduled. If the bus increases its speed by 509509 m/sec, it will arrive in town B 30 min earlier than scheduled. Find: A) The distance between the two towns; B) The bus's scheduled time of arrival in B; C) The speed of the bus when it's on schedule.

multiply(50, add(divide(subtract(multiply(divide(30, const_60), multiply(509509, const_3_6)), multiply(50, divide(42, const_60))), subtract(multiply(509509, const_3_6), 50)), divide(42, const_60)))

divide(n3,const_60)|divide(n1,const_60)|multiply(n2,const_3_6)|multiply(#0,#2)|multiply(n0,#1)|subtract(#2,n0)|subtract(#3,#4)|divide(#6,#5)|add(#7,#1)|multiply(n0,#8)

first we will determine the speed of the bus following its increase . the speed is increased by 509509 m / sec = 50 ⋅ 60 ⋅ 6091000 = 50 ⋅ 60 ⋅ 6091000 km / hr = 20 = 20 km / hr . therefore , the new speed is v = 50 + 20 = 70 v = 50 + 20 = 70 km / hr . if xx is the number of hours according to the schedule , then at the speed of 50 km / hr the bus travels from a to b within ( x + 4260 ) ( x + 4260 ) hr . when the speed of the bus is v = 70 v = 70 km / hr , the travel time is x − 3060 x − 3060 hr . then 50 ( x + 4260 ) = 70 ( x − 3060 ) 50 ( x + 4260 ) = 70 ( x − 3060 ) 5 ( x + 710 ) = 7 ( x − 12 ) 5 ( x + 710 ) = 7 ( x − 12 ) 72 + 72 = 7 x − 5 x 72 + 72 = 7 x − 5 x 2 x = 72 x = 7 x = 72 x = 72 hr . so , the bus is scheduled to make the trip in 33 hr 3030 min . the distance between the two towns is 70 ( 72 − 12 ) = 70 ⋅ 3 = 21070 ( 72 − 12 ) = 70 ⋅ 3 = 210 km and the scheduled speed is 210 / 7 / 2 = 60 km / hr . answer : a

physics

math_qa__30q3Q72G7n789OMW

How many numbers from 10 to 100000 are exactly divisible by 9? Choices A) 900 B) 11110 C) 1100 D) 1200 E) 1400

<gadget id="calculator">100_000 / 9</gadget> <output>100_000/9 = around 11_111.111111</output> <gadget id="calculator">floor(100_000/9)</gadget> <output>11_111</output> <gadget id="calculator">11_111 * 9</gadget> <output>99_999</output> <gadget id="calculator">10 / 9</gadget> <output>10/9 = around 1.111111</output> <gadget id="calculator">floor(10/9)</gadget> <output>1</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 * 9</gadget> <output>18</output> <gadget id="calculator">99_999 - 18</gadget> <output>99_981</output> <gadget id="calculator">99_981 / 9</gadget> <output>11_109</output> <gadget id="calculator">11_109 + 1</gadget> <output>11_110</output> <result>B</result>

B

How many numbers from 10 to 100000 are exactly divisible by 9?

add(divide(subtract(multiply(floor(divide(100000, 9)), 9), multiply(add(floor(divide(10, 9)), const_1), 9)), 9), const_1)

divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)|

"10 / 9 = 1 and 100000 / 9 = 11111 = = > 11111 - 1 = 11110 . answer : b"

general