regisss/math_qa huggingface dataset:
Problem: if 3 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 5 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . b"
Answer: b
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 1000 , what is the least possible value of n ?
Options: a ) 12 , b ) 11 , c ) 14 , d ) 13 , e ) 15
Rationale: 1000 = 2 * 2 * 2 * 5 * 5 * 5 , so we need 3 factors of 2 and 3 factors of 5 . therefore , the smallest value of n is 15 , so the answer is e .
Answer: e
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 2 . in the subsequent n games , the ratio of the team ´ s wins to losses was 1 : 4 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 20 , b ) 9 : 23 , c ) 11 : 27 , d ) 23 : 54 , e ) 31 : 77
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 3 * 4 / 9 + 1 / 5 * 5 / 9 = 4 / 27 + 3 / 27 = 7 / 27 losses = 1 - 7 / 27 = 20 / 27 the ratio of wins to losses is 7 : 20 . the answer is a ."
Answer: a
Problem: in an it company , there are a total of 120 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 75
Rationale: "you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 75 . e"
Answer: e
Problem: a and b can do a piece of work in 6 days , b and c in 8 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 48 days , b ) 55 days , c ) 24 days , d ) 33 days , e ) 40 days
Rationale: "2 c = 1 / 8 + 1 / 12 – 1 / 6 = 1 / 24 c = 1 / 48 = > 48 days answer : a"
Answer: a
Problem: john can row at 5 kmph and still water . he takes 5 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 28 km , b ) 12 km , c ) 16 km , d ) 30 km , e ) 20 km
Rationale: let the distance between a and b be x km . total time = x / ( 5 + 1 ) + x / ( 5 - 1 ) = 5 = > x / 6 + x / 4 = 4 = > ( 2 x + 3 x ) / 12 = 5 = > x = 12 km . answer : b
Answer: b
Problem: a semicircle has a radius of 12 . what is the approximate perimeter of the semicircle ?
Options: a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 12 + 2 * 12 which is about 62 . the answer is b ."
Answer: b
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 64 , find the sum of money ?
Options: a ) 328 , b ) 262 , c ) 72 , d ) 205 , e ) 267
Rationale: a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 64 41 - - - - ? = > rs . 328 answer : a
Answer: a
Problem: sonika bought a v . c . r . at the list price of 18,400 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 19,872 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,400 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,400 = 8 ⁄ 100 × 18400 = 1472 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,400 + 1472 = 19,872 . answer a"
Answer: a
Problem: if x is equal to the sum of the integers from 60 to 80 , inclusive , and y is the number of even integers from 60 to 80 , inclusive , what is the value of x + y ?
Options: a ) 1361 , b ) 1481 , c ) 1601 , d ) 1721 , e ) 1841
Rationale: "x = 60 + 61 + . . . + 80 = 21 ( 70 ) = 1470 y = 11 x + y = 1481 the answer is b ."
Answer: b
Problem: a mixture contains alcohol and water in the ratio 2 : 5 . if 10 liters of water is added to the mixture , the ratio becomes 2 : 7 . find the quality of alcohol in the given mixture .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: let the quantity of alcohol and water be 2 x and 5 x 2 x / ( 5 x + 10 ) = 2 / 7 20 x = 4 ( 3 x + 5 ) x = 5 quantity of alcohol = 2 * 5 = 10 liters . answer is b
Answer: b
Problem: in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10800 petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000
Rationale: 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
Answer: c
Problem: if x is 11 percent greater than 80 , then x =
Options: a ) 88.8 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 80 = ( 80 * 0.11 ) = 8.8 11 % greater than 80 = 80 + 8.8 = 88.8 answer is clearly a ."
Answer: a
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1628 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 110 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1628 74 x = 1628 = > x = 22 5 x = 110 rs . answer : c"
Answer: c
Problem: 8 people decided to split the restaurant bill evenly . if the bill was $ 314.12 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 412 not divisible by a hence , we need to add 4 to this number for it to be divisible by 8 correct option : a"
Answer: a
Problem: the average ( arithmetic mean ) monthly income of 4 workers is $ 1000 . after one worker ’ s income increases by 50 percent the new average income is $ 1200 . what was the original income of the worker whose monthly income increased ?
Options: a ) $ 1,800 , b ) $ 1,500 , c ) $ 1,300 , d ) $ 1,600 , e ) $ 1,100
Rationale: increase in total income was 200 * 4 = $ 800 , we know that this increase was 50 % ( 1 / 2 ) of the workers original income , thus his / her original income was 800 * 2 = $ 1,600 . answer : d
Answer: d
Problem: if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction .
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 , e ) none of them
Rationale: "let the original fraction be x / y . then ( 115 % of x ) / ( 92 % of y ) = 15 / 16 = > ( 115 x / 92 y ) = 15 / 16 = ( ( 15 / 16 ) * ( 92 / 115 ) ) = 3 / 4 answer is a ."
Answer: a
Problem: in town x , 72 percent of the population are employed , and 36 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 50 %
Rationale: "total employed people 72 % , out of which 36 are employed males , hence 36 % are employed females . ( employed females ) / ( total employed people ) = 36 / 72 = 1 / 2 = 50 % answer : e ."
Answer: e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 100 resolutions .
Options: a ) 140 m , b ) 141 m , c ) 142 m , d ) 143 m , e ) 144 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 22.4 = 14100 cm = 141 m answer : b"
Answer: b
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 92 hours , b ) 24 hours , c ) 84 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 3 kmph ; speed downstream = 9 kmph . ∴ total time taken = [ 210 / 3 + 210 / 9 ] hours = 84 hours . answer c"
Answer: c
Problem: a cistern 9 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 68.5 m 2 , e ) 57 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 9 x 1.25 ) + 9 x 4 ] m 2 = 68.5 m 2 . answer : option d"
Answer: d
Problem: at a contest with 2,500 participants , 1 / 2 of the people are aged 10 to 12 . next year , the number of people aged 10 to 12 will increase by 1 / 5 . after this change , what percentage of the total 2,500 people will the 10 - to 12 - year - olds represent ?
Options: a ) 55 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 66 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 5 , we are multiplying it by 1 + 1 / 5 = 6 / 5 , so the answer here must be ( 1 / 2 ) * ( 6 / 5 ) = 3 / 5 = 60 % . answer : b"
Answer: b
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 140 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 140 km time taken = distance / speed = 140 / 28 = 5 hours answer : option c"
Answer: c
Problem: there are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 90 , b ) 85 , c ) 75 , d ) 95 , e ) 82
Rationale: first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 10 and for second = 9 so total methods = 10 * 9 = 90 answer : a
Answer: a
Problem: a large box contains 17 small boxes and each small box contains 26 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 442 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 690
Rationale: the only thing you have to do is a simple multiply we have : 17 * 26 = 442 correct answer is : a ) 442
Answer: a
Problem: find out the ratio of milk to that of water , if a mixture is formed after mixing milk and water of 3 different vessels containning the mixture of milk to that of water in the proportion 3 : 2 , 7 : 3 , 9 : 2 respectively .
Options: a ) 233 : 97 , b ) 235 : 98 , c ) 236 : 97 , d ) 265 : 98 , e ) 234 : 97
Rationale: 3 + 2 = 57 + 3 = 109 + 2 = 11 now , 3 / 5 + 7 / 10 + 9 / 11 : 2 / 5 + 3 / 10 + 2 / 11 = > 233 / 110 : 97 / 110 = > 233 : 97 answer : a
Answer: a
Problem: a student scored an average of 85 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 16 , c ) 76 , d ) 65 , e ) 26
Rationale: given m + p + c = 85 * 3 = 255 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 255 = 65 answer : d
Answer: d
Problem: if you write down all the numbers from 1 to 100 , then how many times do you write 2 ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22
Rationale: "explanation : clearly , from 1 to 100 , there are ten numbers with 2 as the unit ' s digit - 2 , 12 , 22 , 32 , 42 , 52 , 62 , 72 , 82 , 92 ; and ten numbers with 2 as the ten ' s digit - 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 . so , required number = 10 + 10 = 20 . answer : c"
Answer: c
Problem: abce is an isosceles trapezoid and acde is a rectangle . ab = 10 and ec = 20 . what is the length of ae .
Options: a ) 5 , b ) 10 , c ) 12 , d ) 15 , e ) 20
Rationale: as abce is an isosceles trapezoid and ec is twice times ab , we can consider the given trapezoid as half of a regular hexagon ( as length of diagonal in regular hexagon is always double the side ) . thus , sides ab = ae = bc . = > ae = 10 . answer : b
Answer: b
Problem: evaluate 24.39 + 562.093 + 35.96
Options: a ) 631.344 , b ) 622.443 , c ) 623.434 , d ) 632.423 , e ) 632.443
Rationale: "24.39 + 562.093 + 35.96 = 622.443 option b"
Answer: b
Problem: rs 3400 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 1800 , c ) s 800 , d ) s 500 , e ) s 1300
Rationale: "explanation : average rate = ( 144 / 3400 ) * 100 = 4.24 ratio = 7.65 : 12.35 so , first part = ( 7.65 / 20 ) * 3400 = rs 1300 . answer : e"
Answer: e
Problem: at a certain college , 40 percent of the total number of students are freshmen . if 50 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %
Rationale: "let ' s say there is a total of 100 students at this college . 40 percent of the total number of students are freshmen . # of freshmen = 40 % of 100 = 40 50 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 50 % of 40 = 20 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 20 = 10 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 10 / 100 = 10 % answer : a"
Answer: a
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 40 % of the total school population of x students , what is x ?
Options: a ) 125 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = ( x / 100 ) * ( # boys ) # boys = . 4 x substitute and solve : 90 = ( x / 100 ) * ( . 4 x ) 9000 = . 4 ( x ^ 2 ) 25000 = x ^ 2 x = 150 answer : b"
Answer: b
Problem: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "c 25 x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 40 = 25 * 3 = 75 . in x game of 100 points , y gives ( 100 - 75 ) = 25 points to c ."
Answer: c
Problem: 3500 – ( 1000 ÷ 20.50 ) is equal to :
Options: a ) 3451.21 , b ) 3029.0 , c ) 2993.03 , d ) 2984.36 , e ) none of these
Rationale: explanation : given exp . = 3500 - ( ( 1000 ÷ 2050 ) * 100 ) = 3451.21 answer a
Answer: a
Problem: a man swims downstream 60 km and upstream 40 km taking 4 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 2.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 60 - - - 4 ds = 15 ? - - - - 1 40 - - - - 4 us = 10 ? - - - - 1 s = ? s = ( 15 - 10 ) / 2 = 2.5 answer : option b"
Answer: b
Problem: two trains of equal length 120 metres move in the same direction . the faster train completely overtakes the slower one in 15 seconds . if the slower train were to move at half its speed , the over taking would take in 10 seconds . at what speeds are the 2 trains moving ( faster and slower respectively in m / s )
Options: a ) 24 , 22 , b ) 32 , 16 , c ) 30 , 18 , d ) 28 , 14 , e ) none of these
Rationale: the total distance covered for over taking = length of the two trains = 120 + 120 = 240 speed of faster train be x m / s and slower train be y m / s in the first case relative speed = x - y relative speed = distance / time taken = x - y = 240 / 15 = 16 m / s … … … ( 1 ) in the second case , the slower train moves at half its speed relative speed = x - 0.5 y = 240 / 10 = 24 m / s … … … … … … … . . ( 2 ) solving equation 1 & 2 we get x = 32 and y = 16 . : . the speed of the faster and slower trains are 32 m / s and 16 m / s respectively answer : b
Answer: b
Problem: present ages of abi and suji are in the ratio of 5 : 4 respectively . 3 years hence , the ratio of their ages will become 11 : 9 respectively . what is suji ' s present age in years ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: present ages = 5 x : 4 x three hence = 5 x + 3 : 4 x + 3 5 x + 3 : 4 x + 3 = 11 : 9 weget x = 6 suji age is = 4 x = 4 * 6 = 24 answer : e
Answer: e
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 8 , b ) 8 / 11 , c ) 8 / 13 , d ) 8 / 15 , e ) none
Rationale: a ' s 1 day ' s work = 1 ; 15 b ' s 1 day ' s work = 1 ; 20 ( a + b ) ' s 1 day ' s work = ( 1 + 1 ) = 7 . 15 20 60 ( a + b ) ' s 4 day ' s work = ( 7 x 4 ) = 7 . 60 15 therefore , remaining work = ( 1 - 7 ) = 8 . 15 15 option d
Answer: d
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 7 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 7 , b ) - 1 , c ) 0 , d ) 1 , e ) 7
Rationale: "when x = 1 and when x = - 7 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 7 ) f ( 0 ) = - 7 the answer is a ."
Answer: a
Problem: the ratio of flour to water to sugar in a recipe is 8 : 4 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "the ratio of flour to water is 16 : 4 = 4 : 1 . the ratio of flour to sugar is 4 : 3 . the new ratio of flour to water to sugar is 4 : 1 : 3 if we need 2 cups of water , then we need 6 cups of sugar . the answer is a ."
Answer: a
Problem: a train 165 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 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 8 , e ) 5
Rationale: "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 = [ 165 * 3 / 55 ] sec = 9 sec answer : c"
Answer: c
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 12100 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 5 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 12100 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 121 so we have 1 , 3 , 9 , 27 . . . . . 12100 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r 121 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 121 x - 2 = 1 - 3 ^ n - 242 = 1 - 3 ^ n - 243 = - 3 ^ n 243 = 3 ^ n ( negatives cancel out ) 243 can also be re written as 3 ^ 5 therefore ; 3 ^ 5 = 3 ^ n thus n = 5 ( d )"
Answer: d
Problem: the diagonals of two squares are in the ratio of 2 : 5 . find the ratio of their areas .
Options: a ) 4 : 25
b ) 4 : 15
c ) 3 : 25
d ) 3 : 15
e ) none of these
Rationale: explanation : let the diagonals of the squares be 2 x and 5 x . then ratio of their areas will be area of square = 1 / 2 ∗ diagonal 2 1 / 2 ∗ 2 x 2 : 1 / 2 ∗ 5 x 2 4 x 2 : 25 x 2 = 4 : 25 option a
Answer: a
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits q are in s ( 99 ) ?
Options: a ) q = 350 , b ) q = 353 , c ) q = 354 , d ) q = 356 , e ) 357
Rationale: focus on the points where the number of digits q in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b
Answer: b
Problem: bhanu spends 30 % of his income on petrol on scooter 30 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 210 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 30 % ( 700 ) = rs . 210 answer : d"
Answer: d
Problem: the slant height of a right circular cone is 10 m and its height is 8 m . find the area of its curved surface .
Options: a ) 30 pi m ^ 2
b ) 40 pi m ^ 2
c ) 60 pi m ^ 2
d ) 80 pi m ^ 2
e ) 100 pi m ^ 2
Rationale: l = 10 m h = 8 m r = root ( i ^ 2 - h ^ 2 ) = root ( 10 ^ 2 - 8 ^ 2 ) = 6 m curved surface area = pi ri = 60 pi m ^ 2 answer c
Answer: c
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 150 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 150 male associates implies 60 female associates which means the remaining 30 females must be managers d . 30"
Answer: d
Problem: the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 181.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b"
Answer: b
Problem: 65 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 66 , e ) 21
Rationale: "65 + 5 * 12 / ( 180 / 3 ) = 65 + 5 * 12 / ( 60 ) = 65 + ( 5 * 12 ) / 60 = 65 + 1 = 66 . answer : d"
Answer: d
Problem: what is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other ?
Options: a ) 3 : 6 , b ) 1.5 : 1 , c ) 3 : 1.5 , d ) 2 : 1 , e ) 3 : 2
Rationale: "d = 1.5 d d = d a √ 2 = 1.5 d a √ 2 = d a = 1.5 d / √ 2 a = d / √ 2 = > 1.5 : 1 answer : b"
Answer: b
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 6 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 12
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 6 ( pir ^ 2 ) pir ^ 2 = 12 pir r = 12 answer : e"
Answer: e
Problem: what is the 28 th digit to the right of the decimal point in the decimal form of 4 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "4 / 11 = 0.363636 . . . the even numbered positions in the decimal expansion are all 6 . the answer is d ."
Answer: d
Problem: the radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 125 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 140 cm . then , circumference of wheel = 2 ï € r = 280 ï € = 880 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 880 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 880 = 125 answer a"
Answer: a
Problem: a can finish a work in 15 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 15 * 1 / 3 ) = 5 days . correct option : a"
Answer: a
Problem: in the county of veenapaniville , there are a total of 50 high schools , of 3 kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . these 50 schools are divided between 3 districts : a , b , and c . district a has 18 high schools total . district b has 17 high schools total , and only two of those are private independent schools . if district c has an equal number of each of the 3 kinds of schools , how many private independent schools are there in district a ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: “ in the county of veenapaniville , there are a total of 50 high schools , of three kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . ” “ district a has 18 high schools total . ” “ district b has 17 high schools total , and only two of those are private independent schools . ” “ district c has an equal number of each of the three kinds of schools . ” hmm . that ’ s not a simple number . let ’ s put that on hold for a moment . so far , from the matrix it looks like we could figure out the missing number in the “ totals ” row . that number must be 15 , because 18 + 17 + 15 = 50 . now , go back to that last fact : “ district c has an equal number of each of the three kinds of schools . ” now that makes sense . district c has 15 schools , so it must have 5 of each kind : the question is asking : “ how many private independent schools are there in district a ? ” well , now that ’ s just a matter of adding across the “ private independent ” row . we know 2 + 2 + 5 = 9 , so the missing number must be 2 . there ’ s still a good deal of information we can ’ t figure out from the information given in the question , but we are able to answer the specific question asked here . there are 2 private independent schools in district a , so the answer = ( a ) .
Answer: a
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 120 meters , c ) 1777 meters , d ) 60 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 12 seconds distance = speed * time 36000 * 12 / 3600 = 120 meters . b is the answer ."
Answer: b
Problem: how many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 17 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 , 6 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 , 18 - > the number = 5 , 8 , 11 , 14 , 17 , 20 - - > 6 numbers when a = 2 , b = 1 , 2,3 , 4,5 , 6 - > . . . . - - > 6 numbers when a = 3 , b = 1,2 , 3,4 , 5 - - > . . . . - - > 5 numbers total number is already 17 . look at the answer there is no number greater than 17 - - > we dont need to try any more answer must be a"
Answer: a
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.4 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 3 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.4 - 19 x 15 ) kg = 3 kg . correct option : b"
Answer: b
Problem: a , b , c can complete a piece of work in 21 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 84 / 25
Rationale: "a + b + c 1 day work = 1 / 21 + 1 / 6 + 1 / 12 = 25 / 84 a , b , c together will complete the job in 84 / 25 days answer is e"
Answer: e
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : option b"
Answer: b
Problem: a new model car was not selling as expected and the base retail price was lowered by 5 % to increase sales . a customer haggled on the price and negotiated a final agreed price of 90 % of the retail price . how much did the customer save off the retail price ?
Options: a ) 10.5 % , b ) 11.5 % , c ) 12.5 % , d ) 13.5 % , e ) 14.5 %
Rationale: quantity x rate = price 1 x 1 = 1 0.9 x 0.95 = 0.855 decrease in price = ( 0.145 / 1 ) ã — 100 = 14.5 % answer = option e
Answer: e
Problem: a machine , working at a constant rate , manufactures 40 pencils in 30 minutes . how many pencils does it make in 1 hr 30 min ?
Options: a ) 120 , b ) 125 , c ) 110 , d ) 115 , e ) 121
Rationale: "change 1 hr 30 min to 90 min . for this , we need to set up a simple proportion of pensils per time 40 / 30 = s / 90 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can and can ’ t cancel in a proportion , seethis post . we can cancel the factor of 10 in the 40 and 30 . 4 / 3 = s / 90 we can cancel the common factor of 3 in the two denominators . 4 / 1 = s / 30 . now that the fraction is entirely simplified , we can cross - multiply . s = 4 * 30 = 120 the machine would be 120 pencils in 1 hr 30 min . answer : a"
Answer: a
Problem: sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1320 , what is the gain percent ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "selling price / total cost = 1320 / 1200 = 1.1 the gain percent is 10 % . the answer is e ."
Answer: e
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 8 m wide at the top and 2 m wide at the bottom and the area of cross - section is 770 sq m , the depth of cannel is ?
Options: a ) 150 , b ) 152 , c ) 154 , d ) 156 , e ) 158
Rationale: "1 / 2 * d ( 8 + 2 ) = 770 d = 154 answer : c"
Answer: c
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 80 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 800 meters , d ) 1822 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 80 seconds distance = speed * time 36000 * 80 / 3600 = 800 meters . c is the answer ."
Answer: c
Problem: if 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 287 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) men \ : 8 : 36 \ \ days \ : 24 : 30 \ end { matrix } \ right \ } : 80 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn 8 \ times 24 \ times x = 36 \ times 30 \ times 80 \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 30 \ times 80 } { 8 \ times 24 } \ inline \ fn _ jvn \ leftrightarrow x = 450 answer : d"
Answer: d
Problem: 1 / 4 of all married couples have more than one child . 1 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) b . 1 / 4 , c ) 1 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 1 / 4 of 100 couples have more than one child = 25 couples . 1 / 5 of 100 couples have more than 3 kids = 20 couples . this implies that 20 couples are a subset of 25 couples and the complement of 25 couples within those 100 couples , which equals 75 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 25 - 20 = 5 . fraction will be 5 / 100 = 1 / 20 . option c"
Answer: c
Problem: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order r ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . r = 12.5 * 6 = 75 . e
Answer: e
Problem: a man can row downstream at the rate of 26 kmph and upstream at 12 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 8.0 , c ) 9.5 , d ) 7.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 26 + 12 ) = 19 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 26 - 12 ) = 1 / 2 ( 14 ) = 7 kmph answer is d ."
Answer: d
Problem: the perimeter of a rectangle is equal to the perimeter of aright - angled triangle of height 12 cm . if the base of the triangle is equal to the breadth of the rectangle , what is the length of the rectangle ”
Options: a ) 18 cm
b ) 24 cm
c ) 22 cm
d ) data inadequate
e ) none of these
Rationale: p = 2 ( l + b ) = l + b + h = l + b + 12 . data inadequate . answer d
Answer: d
Problem: in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 6 persons are added ( 7 - 1 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"
Answer: e
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 45 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 43 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 5 * 2 x = 50 x dollars ; we know that harry also earned the same 50 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 20 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 20 x / 1.5 x = 13 additional hours , so harry worked for total of 30 + 13 = 43 hours . answer : d ."
Answer: d
Problem: a certain cube floating in a bucket of water has between 60 and 85 percent of its volume below the surface of the water . if between 9 and 26 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 60 % = 205.8 , 85 % = 291.55 so vol above water , between 137.2 and 51.45 - - > too big if side are 4 , vol = 64 60 % = 38.4 , 85 % = 54.4 vol above water between 25.6 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 60 % = 75 , . 85 % = 106.25 vol above water between 18.75 - 50 ( sides are 4 cubic centimeters ) a"
Answer: a
Problem: how long does a train 150 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 14.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 13.1 sec , e ) 12.15 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 150 + 132 = 282 m . required time = 282 / 20 = 14.1 sec . answer : a"
Answer: a
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 800 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.44 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 800 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 800 * 2 * ( 4 / 5 ) = 1280 2160 + 1280 = 3440 solving for units gives us 3.44 so the answer is c"
Answer: c
Problem: what is the unit ’ s digit of 7 ^ 7
Options: a ) 9 , b ) 5 , c ) 3 , d ) 7 , e ) 1
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 7 = 3 answer c"
Answer: c
Problem: the list price of an article is rs . 70 . a customer pays rs . 61.11 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 3 % , e ) 4 %
Rationale: "explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 61.11 x = 3 % d"
Answer: d
Problem: a train is 300 meter long is running at a speed of 35 km / hour . in what time will it pass a bridge of 115 meter length ?
Options: a ) 29 , b ) 23 , c ) 47.119 , d ) 44.586 , e ) 42.686
Rationale: "speed = 35 km / hr = 35 * ( 5 / 18 ) m / sec = 175 / 18 m / sec total distance = 300 + 115 = 415 meter time = distance / speed = 415 * ( 18 / 175 ) = 42.686 seconds . answer : e"
Answer: e
Problem: the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70 , then how long is the base of isosceles triangle ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "the base of the isosceles triangle is 70 - 20 - 20 = 30 units the answer is d ."
Answer: d
Problem: the ratio of male to female in a class is 2 : 7 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two - third of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 192 degree
e ) e ) 213 degree
Rationale: here is my approach = > males = > 2 x and females = 7 x = > total = 9 x now 9 x = > 360 therefore 16 x / 3 = > 213 degree . p . s = > 16 x / 3 is nothing but total number of students with the given preference answer e
Answer: e
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 28 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "28 % is 3 % - points above 25 % and 12 % - points below 40 % . thus the ratio of mixture y to mixture x is 4 : 1 . the percent of mixture x is 1 / 5 = 20 % . the answer is b ."
Answer: b
Problem: which is the smallest number divides 2800 and gives a perfect square .
Options: a ) 5
b ) 6
c ) 7
d ) 8
e ) 9
Rationale: 7 is the smallest number which divides 2800 and gives a perfect square . as 2800 = 2 * 2 * 2 * 2 * 5 * 5 * 7 and 7 is not in a pair which gives 400 ( a perfect square of 20 ) on dividing 2800 . answer : c
Answer: c
Problem: if a light flashes every 6 seconds , how many times will it flash in 1 / 5 of an hour ?
Options: a ) 81 , b ) 101 , c ) 121 , d ) 141 , e ) 161
Rationale: "in 1 / 5 of an hour there are 12 * 60 = 720 seconds the number of 6 - second intervals = 720 / 6 = 120 after the first flash , there will be 120 more flashes for a total of 121 . the answer is c ."
Answer: c
Problem: in how many ways can the integer 800 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 7 , c ) 5 , d ) 4 , e ) 2
Rationale: "800 = ( 2 ^ 5 ) * ( 5 ^ 2 ) since 800 is not a perfect square , no of ways = 7 answer b"
Answer: b
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 15 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 103.5 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 20 % = 90 * 1.15 = 103.5 thus ratio = 103.5 / 100 = 1.03 ( in % terms = 103 % ) . thus b is the correct answer ."
Answer: b
Problem: d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 144 : 25 and de = 13 cm , then find the length of bc .
Options: a ) 5
b ) 13
c ) 14
d ) 11
e ) 15
Rationale: abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 25 / 169 side of abc / side of ade = 5 / 13 so the length of bc = 5 answer - a
Answer: a
Problem: at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 15 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 28 , c ) 50 , d ) 68 , e ) 70
Rationale: the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 15 are males , so remaining 90 - 15 = 75 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 75 , 100 % = 75 * 100 / 60 = 125 . . ans 40 % of 125 = 50 c
Answer: c
Problem: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 34 inches and the width of the wall is 54 inches , what is the length of the wall , in inches ?
Options: a ) 22.8 , b ) 33.8 , c ) 42.8 , d ) 63.8 , e ) 56.8
Rationale: "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 34 ^ 2 = 1156 . area of rectangle is double of that 2 * 1156 = 2312 . now a = lw and we need find w so a / l = w ; 2312 / 54 = 42.8 answer ! answer is c"
Answer: c
Problem: how many positive integers less than 100 have a remainder of 11 when divided by 13 ?
Options: a ) 11 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have to include 11 also . as 13 * 0 + 11 = 11 if somebody says to divide 11 by 13 , we will be telling we have 0 quotient and remainder as 11 . answer is a"
Answer: a
Problem: last year elaine spent 20 % of her annual earnings on rent . this year she earned 25 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 182.5 , b ) 184.5 , c ) 167.5 , d ) 172.5 , e ) 187.5
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 25 % more , or $ 125 . she would ' ve spent 30 % of this on rent , or $ 37.5 do $ 37.5 / $ 20 this will give you 187.5 % e is the correct answer ."
Answer: e
Problem: how much time does a train 150 metres long running at 90 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 6 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s
Rationale: "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 150 / t t = 6 s answer : b"
Answer: b
Problem: a dog takes 4 leaps for every 5 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 12 : 5 , b ) 4 : 3 , c ) 9 : 5 , d ) 9 : 1 , e ) 9 : 2
Rationale: "explanation : dog : hare = ( 4 * 3 ) leaps of hare : 5 leaps of hare = 12 : 5 . answer : a ) 12 : 5"
Answer: a
Problem: if an article is sold at 19 % profit instead of 12 % profit , then the profit would be rs . 105 more . what is the cost price ?
Options: a ) 1890 , b ) 2790 , c ) 1990 , d ) 1500 , e ) 1701
Rationale: "let the cost price of an article be rs . x . ( 19 % of x ) - ( 12 % of x ) = 105 19 x / 100 - 12 x / 100 = 105 = > 7 x = 105 * 100 = > x = 1500 cost price = rs . 1500 answer : c"
Answer: c
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 130 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 260 , b ) 620 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 130 ) = 2 + 2 ( extra ) = > 2 x - 260 = x = > x = 260 . answer : a"
Answer: a
Problem: an intern wants to label folders with numbers using digit stickers only . if the intern uses 999 stickers , how many folders have been numbered ? ( the numbers of the folders are consecutive and the number of the first folder is 1 ) .
Options: a ) 287 , b ) 369 , c ) 370 , d ) 371 , e ) 430
Rationale: for the first 9 folders we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 folders we need 3 stickers each . the first 99 folders correspond to 189 stickers . subtract 189 from the total number of stickers ( 999 ) . this leaves 810 stickers for folders that use 3 stickers each . so , divide 810 by 3 to get 270 folders . add 99 folders to 270 folders to get the total number of folders , 369 . answer : b
Answer: b