euclaise/mathqa_programs huggingface dataset:
Problem: before 2 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 54 , d ) 60 , e ) 64
Rationale: a - 2 = 4 ( b - 2 ) - - > a - 4 b = - 6 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 14 - - > a = 3 ( 18 ) = 50 a - b = 50 - 14 = 36 answer : a
Answer: a
Python program:
a = 4 * 3
b = a - 4
c = 4 * 2
d = c - 2
e = b + d 
f = 4 * e
g = 4 * 2
h = g - 2
i = f - h
j = 4 * 3
k = j - 4
l = 4 * 2
m = l - 2
n = k + m 
o = i - n
Problem: how many integers between 500 and 1000 are there such that their unit digit is even ?
Options: a ) 250 , b ) 150 , c ) 500 , d ) 100 , e ) 200
Rationale: 500 numbers between - 500 and 1000 out of which half would be even , half odd . number of even unit digit number = 250 . correct option is a
Answer: a
Python program:
a = 500 / 2
b = a + 1
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 50 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.5 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 50 % income the savings increased by 100 % . or s = . 5 i or s = 50 % of income c is the answer"
Answer: c
Python program:
a = 100 + 50 
b = a + 100 
c = 2 * 100
d = b - c
e = d / 100
f = e * 100
Problem: the cost price of 24 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let the cost price = y the cost price of 24 articles = 24 y the selling price of x articles = 1.20 y * x 1.20 y * x = 24 y x = 24 / 1.2 = 20 the answer is d ."
Answer: d
Python program:
a = 24 * 4
b = 4 + 1 
c = a / b
Problem: on increasing the number of lines in a page by 110 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 20 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 84.6 %
Rationale: "explanation : number of pages increased = 110 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 110 = 130 % increase in the number of pages in the book = 110 / 130 x 100 % = 84.6 % e"
Answer: e
Python program:
a = 240 - 110
b = 240 / a
c = b * 100
d = c - 100
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 18 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 350
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 18 gallons then 0.12 a + 0.16 ( 200 - a ) = 18 - - > a = 350 . answer : e ."
Answer: e
Python program:
a = 16 / 100
b = 200 * a
c = b - 18
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 40 percent off the suggested retail price . if , during a special sale , an additional 5 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 500 before any discount ?
Options: a ) $ 130.00 , b ) $ 285.00 , c ) $ 200.00 , d ) $ 258.00 , e ) $ 210.00
Rationale: "original price : 500 $ max first discount = - 40 % thus : 500 â ˆ — ( 1 â ˆ ’ 40 / 100 ) = 300 second discount on the discounted price = - 20 % thus : 300 â ˆ — ( 1 â ˆ ’ 5 / 100 ) = 285 answer b ."
Answer: b
Python program:
a = 40 + 5 
b = a / 100
c = 500 * b
Problem: what is the total number of d integers between 100 and 200 that are divisible by 3 ?
Options: a ) 33 , b ) 32 , c ) 31 , d ) 30 , e ) 29
Rationale: yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33
Answer: a
Python program:
a = 200 / 3
b = math.floor(a)
c = b * 3
d = 100 / 3
e = math.floor(d)
f = 3 * e
g = 3 + f 
h = c - g
i = h + 3 
j = i / 3
Problem: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 6 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) none of these
Rationale: explanation : 1 woman ' s 1 day ' s work = 1 / 70 1 child ' s 1 day ' s work = 1 / 140 5 women and 10 children 1 day work = ( 570 + 10140 ) = 17 so 5 women and 10 children will finish the work in 7 days answer : b
Answer: b
Python program:
a = 10 * 7
b = 5 / a
c = 10 * 14
d = 10 / c
e = b + d 
f = 1/(e)
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 38 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 7
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 38 kg joins the group , total weight of boys = 30 x + 38 so 30 x + 38 = 31 ( x + 1 ) = > x = 7 . answer : e"
Answer: e
Python program:
a = 30 + 1 
b = 38 - a
c = b + 1
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 20 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "let the output of a factory is 100 first , increased by 10 % = 110 due to holiday rush , it increase by 20 % = 110 + 22 = 132 132 - ( x / 100 * 132 ) = 100 24.24 answer : b"
Answer: b
Python program:
a = 100 + 10 
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = e - 1
g = 100 + 10 
h = g / 100
i = 100 + 20 
j = i / 100
k = h * j
l = f / k
m = l * 100
Problem: maria sold 10 kg of apples in her first hour at the market , but only 2 kg of apples in the second hour . on average , how many kg of apples did she sell in two hours at the market ?
Options: a ) 6 kg , b ) 5 kg , c ) 12 kg , d ) 24 kg , e ) 20 kg
Rationale: ( 10 kg + 2 kg ) / 2 = 6 kg correct answer is : a
Answer: a
Python program:
a = 2 * 2
b = 10 - a
Problem: a can finish a piece of work in 15 days . b can do it in 30 days . they work together for 6 days and then a goes away . in how many days will b finish the work ?
Options: a ) 11 days , b ) 12 days , c ) 14 days , d ) 10 days , e ) 15 days
Rationale: "6 / 15 + ( 6 + x ) / 30 = 1 = > x = 12 days answer : b"
Answer: b
Python program:
a = 1 / 4
b = a * 2
c = 1 / 30
d = c * 2
e = b + d 
f = 1 - e
g = 1 / 30
h = f / g
Problem: find the largest 5 digit number which is exactly divisible by 88 ?
Options: a ) 98765 , b ) 98907 , c ) 99944 , d ) 99954 , e ) 99968
Rationale: "largest 5 digit number is 99999 after doing 99999 ÷ 88 we get remainder 31 hence largest 5 digit number exactly divisible by 88 = 99999 - 31 = 99968 e"
Answer: e
Python program:
a = 100 * 100
b = 100 * 10
c = a + b 
d = 100 * 3
e = c + d 
f = 5 * 10
g = e + f 
h = g + 3 
i = h * 88
Problem: a club wants to mix 15 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 15 * 8 + 5 * w ) / ( 15 + w ) = > 90 + 6 w = 120 + 5 w = > w = 30 answer b"
Answer: b
Python program:
a = 15 * 8
b = 6 * 0
c = a - b
Problem: 300 + 5 × 8 = ?
Options: a ) 820 , b ) 340 , c ) 420 , d ) 209 , e ) none of these
Rationale: 300 + 5 × 8 = ? or , ? = 300 + 40 = 340 answer b
Answer: b
Python program:
a = 5 * 8
b = a + 300
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 18 kmph , b ) 17 kmph , c ) 24 kmph , d ) 19 kmph , e ) 12 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 3 x / ( x / 8 ) = 24 kmph answer : c"
Answer: c
Python program:
a = 40 * 3
b = 40 / 40
c = 2 * 40
d = c / 20
e = b + d 
f = a / e
Problem: the avg weight of a , b & c is 70 kg . if d joins the group , the avg weight of the group becomes 70 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 68 kg . what is the weight of a ?
Options: a ) 81 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 70 = 210 a + b + c + d = 4 * 70 = 280 - - - - ( i ) so , d = 70 & e = 70 + 3 = 73 b + c + d + e = 68 * 4 = 272 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 280 – 272 = 8 a = e + 8 = 73 + 8 = 81 answer : a"
Answer: a
Python program:
a = 70 * 4
b = 68 * 4
c = 70 * 4
d = 70 * 3
e = c - d
f = 3 + e 
g = b - f
h = a - g
Problem: john paid a sum of money for purchasing 30 pens , which he recovered in full when he sold 20 of them . what was his percentage of profit or loss per pen ?
Options: a ) 50 % , b ) 60 % , c ) 40 % , d ) 30 % , e ) 45 %
Rationale: "a 50 % if the sum he paid whilst purchasing 30 pens = a , then the cost price of each pen = a / 30 . since the amount he got whilst selling 20 pens is also = a then the selling price of each pen = a / 20 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 20 - a / 30 = a / 60 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 60 ) / ( a / 30 ) x 100 = 50 %"
Answer: a
Python program:
a = 30 - 20
b = a / 20
c = b * 100
Problem: 1 / 0.025 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 40 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.025 = ( 1 * 1000 ) / 25 = 1000 / 25 = 40 option c"
Answer: c
Python program:
a = 1 / 0
Problem: a train covers a distance of 18 km in 3 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 370 , b ) 380 , c ) 390 , d ) 400 , e ) 410
Rationale: "speed = ( 18 / 3 * 60 ) km / hr = ( 360 * 5 / 18 ) m / sec = 100 m / sec . length of the train = 100 * 4 = 400 m . answer : option d"
Answer: d
Python program:
a = 18 / 3
b = a - 4
c = 18 / b
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 25 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 56.25 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 25 % profit ) x = 1.25 / . 8 * c x = 12.5 / 8 c original selling price is 1.5625 c which is 56.25 % profit answer c"
Answer: c
Python program:
a = 100 - 20
b = a - 25
c = 100 - b
Problem: evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | =
Options: a ) 49 , b ) 55 , c ) 69 , d ) 70 , e ) 82
Rationale: "according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70"
Answer: d
Python program:
a = 3 - 12
b = 8 * a
c = 4 - b
d = 5 - 11
e = c - negate
Problem: how much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 50 sec , b ) 26 sec , c ) 80 sec , d ) 82 sec , e ) 81 sec
Rationale: the distance to be covered = sum of their lengths = 200 + 300 = 500 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 500 / 10 = 50 sec . answer : a
Answer: a
Python program:
a = 200 + 300 
b = 72 - 36
c = b * const_0_2778
d = a / c
Problem: a train covers a distance of 36 km in 12 min . if it takes 7 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
Rationale: "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 7 = 350 m . answer : option c"
Answer: c
Python program:
a = 36 / 12
b = a - 7
c = 36 / b
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3146 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 30 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 726 100 - - - ? = > 30 % answer : option b"
Answer: b
Python program:
a = 3146 - 2420
b = a / 2420
c = b * 100
Problem: the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 800 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 800 x = ( 2 ^ 5 * 25 ) / 2 ^ 9 = 25 / 16 the answer is d .
Answer: d
Python program:
a = const_60 / 2
b = a + const_60 
c = b / 10
d = c - 1
e = 2 ** d
f = 800 / e
g = f / 2
Problem: if i equals the sum of the even integers from 2 to 224 , inclusive , and k equals the sum of the even integers from 8 to 80 , inclusive , what is the value of i - k ?
Options: a ) 11028 , b ) 14172 , c ) 14284 , d ) 14015 , e ) 14397
Rationale: use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 224 - 2 ) / 2 ] + 1 = 112 and [ ( 80 - 8 ) / 2 ] + 1 = 37 mean of integers = ( 224 + 2 ) / 2 = 113 and ( 80 + 8 ) / 2 = 44 sum of integers = ( 112 * 113 ) = 12656 and ( 37 * 44 ) = 1628 thus their difference ( i - k ) = 12656 - 1628 = 11028 answer : a
Answer: a
Python program:
a = 80 + 2 
b = a + 224 
c = 80 + 2 
d = 224 - c
e = d / 2
f = b * e
g = 80 + 2 
h = g + 224 
i = f + h 
j = i / 2
k = 2 + 2 
l = k + 8 
m = j + l
Problem: if 25 % of x is 15 less than 12 % of 1500 , then x is ?
Options: a ) 660 , b ) 738 , c ) 837 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 12 % of 1500 = 12 / 100 * 1500 = 180 given that , x / 4 = 180 - 15 = > x / 4 = 165 = > x = 660 . answer : a"
Answer: a
Python program:
a = 12 / 100
b = 1500 * a
c = b - 15
d = 25 / 100
e = c / d
Problem: evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = . . . .
Options: a ) 3 , b ) 33 , c ) 43 , d ) 23 , e ) 13
Rationale: according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer is e ) 13
Answer: e
Python program:
a = 6 * 4
b = a / 3
c = b - 4
d = math.sqrt(c)
e = 11 + d
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 800,000 ?
Options: a ) 60 , b ) 100 , c ) 160 , d ) 240 , e ) 300
Rationale: "the first digit and last digit are the same so the only possibility is 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 1 * 10 * 10 = 100 the answer is b ."
Answer: b
Python program:
a = 6 - 4
b = a * 10
c = b * 10
Problem: a trader sold an item at a loss of 18 % . if he had increased the price by $ 25 he would have made a gain of 5 % . what is the cost price of the item ?
Options: a ) $ 414.78 , b ) $ 424.78 , c ) $ 534.78 , d ) $ 434.78 , e ) $ 435.78
Rationale: let c . p . be $ x then 105 % of x - 82 % of x = 100 23 % of x = 100 23 / 100 * x = 100 23 x = 10000 x = 434.78 answer is d
Answer: d
Python program:
a = 25 * 100
b = 5 / 100
c = 1 + b 
d = 18 / 100
e = 1 - d
f = c - e
g = f * 100
h = a / g
Problem: if 3 women can color 180 m long cloth in 2 days , then 5 women can color 300 m long cloth in ?
Options: a ) 2 days , b ) 3 days , c ) 5 days , d ) 1 day , e ) 4 days
Rationale: "the length of cloth painted by one woman in one day = 180 / 3 × 2 = 30 m no . of days required to paint 300 m cloth by 5 women = 300 / 5 × 30 = 2 days answer : a"
Answer: a
Python program:
a = 3 * 2
b = 180 / a
c = 5 * b
d = 300 / c
Problem: if $ 5,000 is invested in an account that earns 6 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 6 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "ans a solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.06 / 2 ) ^ 2 = 5406 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 8 / 100 ) = 5400 difference = 5406 - 5400 = 6 $ a"
Answer: a
Python program:
a = 6 * 1
Problem: a train with 1200 m crosses a tree in 120 sec , how much time will i take to pass a platform 700 m long ?
Options: a ) 150 sec , b ) 130 sec , c ) 190 sec , d ) 200 sec , e ) 100 sec
Rationale: s = 1200 / 120 s - 10 m / sec total length = 1900 m t = d / s t = 1900 / 10 t = 190 sec answer c
Answer: c
Python program:
a = 1200 + 700 
b = 1200 / 120
c = a / b
Problem: the area of a circle is added to its diameter , and the circumference is then subtracted from this total , the result is 10 . what is the radius of the circle ?
Options: a ) 2 * pi
b ) pi
c ) 2
d ) 4 * pi
e ) 4
Rationale: the equation is ; diameter + area - circumference = d + a - c = d + pi * r ^ 2 - 2 * pi * r = 2 r + pi * r ( r - 2 ) . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : e
Answer: e
Python program:
a = 1 - math.pi
b = a * 2
c = b / math.pi
d = c ** 2
e = 10 / math.pi
f = 4 * negate
g = d - f
h = math.sqrt(g)
Problem: a man can row upstream at 5 kmph and downstream at 25 kmph , and then find the speed of the man in still water ?
Options: a ) 15 , b ) 77 , c ) 30 , d ) 88 , e ) 34
Rationale: "us = 5 ds = 25 m = ( 5 + 25 ) / 2 = 15 answer : a"
Answer: a
Python program:
a = 5 + 25 
b = a / 2
Problem: sum of 49 odd numbers is ?
Options: a ) 2398 , b ) 2399 , c ) 2400 , d ) 2401 , e ) 2402
Rationale: sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 49 odd numbers = 49 ^ 2 = 2401 answer : d
Answer: d
Python program:
a = 49 * 2
b = 49 / 2
c = a * b
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 40 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 40 = 30 x = 3600 km answer is d"
Answer: d
Python program:
a = 30 * 40
Problem: the product of x and y is a constant . if the value of x is increased by 20 % , by what percentage must the value of y be decreased ?
Options: a ) 16.66 % , b ) 33.33 % , c ) 44.44 % , d ) 55.55 % , e ) 19.92 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.2 x ( 120 ) i . e . 120 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 120 = 83.33 i . e . y decreases from 100 to 83.33 i . e . decrease of 16.66 % answer : option a"
Answer: a
Python program:
a = 100 + 20 
b = 100 / a
c = 1 - b
d = c * 100
Problem: if 12 men or 20 women can do a piece of work in 27 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 27 days . so , 27 women can do it in ( 20 * 27 ) / 27 = 20 days ."
Answer: c
Python program:
a = 12 * 27
b = 9 / a
c = 20 * 27
d = 12 / c
e = b + d 
f = 1/(e)
Problem: how many trucks are there if each truck carrying 70 packages and total of 490 packages ?
Options: a ) a ) 7 , b ) b ) 6 , c ) c ) 9 , d ) d ) 11 , e ) e ) none of the above
Rationale: sol . total packages 490 each truck carries 70 packages = 490 / 70 = 7 answer : a
Answer: a
Python program:
a = 490 / 70
Problem: calculate 42120 ÷ ? = 195
Options: a ) 212 , b ) 219 , c ) 217 , d ) 213 , e ) 216
Rationale: "answer let 42120 / x = 195 then x = 42120 / 195 = 216 option : e"
Answer: e
Python program:
a = 42120 * 195
Problem: the average of 6 observations is 14 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 84 + x ) / 7 = 13 = > x = 7 . hence , the seventh observation is 7 . answer : e"
Answer: e
Python program:
a = 14 - 1
b = 6 + 1 
c = a * b
d = 14 * 6
e = c - d
Problem: find the value of ( 50 + 20 / 90 ) × 90
Options: a ) 2520 , b ) 3520 , c ) 4520 , d ) 1520 , e ) 1750
Rationale: "( 4500 + 20 ) / 90 * 90 = 4520 answer : c"
Answer: c
Python program:
a = 20 / 90
b = a + 50 
c = b * 90
Problem: if a and b are positive real numbers , and a ^ 3 + b ^ 3 = 20 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a > 3 , then a ^ 3 + b ^ 3 > 20 . the answer is a ."
Answer: a
Python program:
a = 1 / 3
b = 20 ** a
Problem: the ages of 2 persons differ by 32 years . if 9 years ago the elder one be 5 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 42.5 , c ) 45 , d ) 49 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 32 5 ( x - 9 ) = x + 32 - 9 x = 17 age of elder person = 17 + 32 = 49 answer is d"
Answer: d
Python program:
a = 2 * 32
b = 32 - 1
c = a / b
d = c + 32 
e = d - 2
Problem: what is the greatest possible length which can be used to measure exactly the lengths 18 m , 40 m and 6 m 50 cm ?
Options: a ) 20 cm , b ) 23 cm , c ) 25 cm , d ) 10 cm , e ) 28 cm
Rationale: "required length = hcf of 1800 cm , 4000 cm , 650 cm = 50 cm answer is d"
Answer: d
Python program:
a = 50 * 4
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 5 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 43
Rationale: "soln : - 5 x = 45 - - > 21 / 20 * x = 45 - - > x = 45 * 20 / 21 = 300 / 7 = ~ 43 . answer : e ."
Answer: e
Python program:
a = 100 + 5 
b = 100 / a
c = b * 45
Problem: the number which exceeds 16 % of it by 42 is :
Options: a ) 50 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 42 x - 16 / 100 x = 42 x - 4 / 25 x = 42 21 / 25 x = 42 x = ( 42 x 25 / 21 ) = 50 answer a"
Answer: a
Python program:
a = 42 * 100
b = 100 - 16
c = a / b