euclaise/mathqa_programs huggingface dataset:
Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is -
Options: a ) 8 / 13 , b ) 6 / 13 , c ) 3 / 13 , d ) 4 / 13 , e ) 1 / 13
Rationale: explanation : p ( s á ´ œ k ) = p ( s ) + p ( k ) - p ( s â ˆ © k ) , where s denotes spade and k denotes king . p ( s á ´ œ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : d
Answer: d
Python program:
a = 3 / const_52
b = const_52 / 4
c = b / const_52
d = a + c
Problem: a man swims downstream 30 km and upstream 18 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 2 , e ) 4
Rationale: "30 - - - 6 ds = 5 ? - - - - 1 18 - - - - 6 us = 3 ? - - - - 1 m = ? m = ( 5 + 3 ) / 2 = 4 answer : e"
Answer: e
Python program:
a = 18 / 6
b = 30 / 6
c = a + b 
d = c / 2
Problem: what is the least value of x . so that 23 x 59 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 9 = 19 + x least value of x may be 2 therefore 19 + 2 = 21 is divisible by 3 . answer : option a"
Answer: a
Python program:
a = math.lcm(23, 59)
b = a / 59
c = b / 4
d = c / 4
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 16 , what is the sum of the first 15 terms of the progression ?
Options: a ) 80 , b ) 100 , c ) 105 , d ) 120 , e ) 110
Rationale: "4 th term + 12 th term = 16 i . e . , ( a + 3 d ) + ( a + 11 d ) = 16 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 16 - - - - - - - - - - - - - - - from ( 1 ) = 120 answer : d"
Answer: d
Python program:
a = 15 / 2
b = a * 16
Problem: if x = 1 - 2 t and y = 2 t - 2 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 3 / 4 , d ) 2 / 5 , e ) 0
Rationale: "we are given x = 1 – 2 t and y = 2 t – 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 2 t for x and 2 t – 2 for y in the equation x = y . this gives us : 1 – 2 t = 2 t – 2 3 = 4 t 3 / 4 = t the answer is c ."
Answer: c
Python program:
a = 1 + 2 
b = 2 + 2 
c = a / b
Problem: pipes a and b can fill a tank in 6 and 4 hours . pipe c can empty it in 12 hours . if all pipes are opened together , then the tank will be filled in ?
Options: a ) 3 hr , b ) 2 hr , c ) 1 hr , d ) 9 / 7 hr , e ) 5 / 3 hr
Rationale: net part filled in 1 hour = 1 / 6 + 1 / 4 - 1 / 12 = 1 / 3 the tank will be full in 3 hr answer is a
Answer: a
Python program:
a = 1 / 6
b = 1 / 4
c = a + b 
d = 1 / 12
e = c - d
f = 1/(e)
Problem: hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :
Options: a ) 720
b ) 900
c ) 1200
d ) 1800
e ) 2100
Rationale: 2 ( 15 + 12 ) x h = 2 ( 15 x 12 ) h = 180 / 27 m = 20 / 3 m . volume = 15 x 12 x 20 / 3 m 3 answer : option c
Answer: c
Python program:
a = 15 * 12
b = 15 * 12
c = b * 2
d = 15 + 12 
e = d * 2
f = c / e
g = a * f
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2370 votes . how many votes were cast ?
Options: a ) 7500 , b ) 7900 , c ) 2665 , d ) 2888 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2370 100 % - - - - - - - - - ? = > 7900 answer : b"
Answer: b
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 2370 / d
Problem: sonika bought a v . c . r . at the list price of 18,500 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 19,980 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: sol . list price of v . c . r . = 18,500 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,500 = 8 ⁄ 100 × 18500 = 1480 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,500 + 1480 = 19,980 . answer a
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = b + 8 
d = c * 100
e = 1 + 4 
f = e * 2
g = d * f
h = 1 + 4 
i = h * 100
j = g + i 
k = 100 + 8 
l = j * k
m = l / 100
n = 1 + 4 
o = n * 100
p = o * 2
q = m / p
r = math.floor(q)
Problem: a cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the west surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55 m 2 , e ) none of these
Rationale: "solution area of the west surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 × 1.25 + 6 × 1.25 ) + 6 × 4 ] m 2 = 49 m 2 . answer a"
Answer: a
Python program:
a = 25 / 100
b = a + 1 
c = b * 4
d = 25 / 100
e = d + 1 
f = e * 6
g = c + f 
h = 2 * g
i = 4 * 6
j = h + i
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 220 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,218
Rationale: "i can buy 9 250 - pack for rs 22.95 * 9 = $ 206.55 now , i can buy 5 20 - pack for 3.05 * 5 = $ 15.25 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2218 e"
Answer: e
Python program:
a = 220 / 22
b = a * 250
Problem: if ( n + 2 ) ! / n ! = 90 , n = ?
Options: a ) 2 / 131 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 90 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 132 from here , we might just test the answer choices . since ( 10 ) ( 9 ) = 90 , we can see that n = 8 b"
Answer: b
Python program:
a = 4 + 4 
b = a - 1
Problem: abcd is a square . f and e are the midpoints of sides ad and cd , respectively . the area of triangle fed is 2 square inches . what is the area of square abcd ( in square inches ) ?
Options: a ) 4
b ) 8
c ) 16
d ) 32
e ) 64
Rationale: area of fed = 2 sq inches = 1 / 2 * de * fd = 1 / 2 * de ^ 2 because the sides of a square are equal , hence half of the sides will also be equal . de ^ 2 = 4 de = fd = 2 hence the side of the square = 4 area if the square = 4 * 4 = 16 correct option : c
Answer: c
Python program:
a = 2 * 2
b = a * 4
Problem: the triplicate ratio of 1 : 7 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 343 , d ) 1 : 1 , e ) 1 : 2
Rationale: "1 ^ 3 : 7 ^ 3 = 1 : 343 answer : c"
Answer: c
Python program:
a = 1 ** 7
b = 7 ** 7
c = a / b
Problem: what profit percent is made by selling an article at a certain price , if by selling at 3 / 4 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 29 % , c ) 7 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 3 / 4 sp 1 cp = 100 sp 2 = 80 3 / 4 sp 1 = 80 sp 1 = 107 100 - - - 107 = > 7 % answer : c"
Answer: c
Python program:
a = 100 - 20
b = 3 / 4
c = a / b
d = c - 100
Problem: 275.124 x 16.98 ã · 5.001 + 22.22 = ?
Options: a ) 983.578 , b ) 659.121 , c ) 957.641 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 275.124 x 16.98 ã · 5.001 + 22.22 = ? â ‰ ˆ ( 275.124 x 17 / 5 ) + 22.22 â ‰ ˆ 935.421 + 22.22 â ‰ ˆ 957.641 answer : option c"
Answer: c
Python program:
a = 16 ** 98
b = 275 * 124
Problem: a clock store sold a certain clock to a collector for 30 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 60 percent of what the collector had paid . the shop then sold the clock again at a profit of 90 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 150 , for how much did the shop sell the clock the second time ?
Options: a ) $ 1010.46 , b ) $ 505.23 , c ) $ 2020.92 , d ) $ 800.46 , e ) $ 1515.69
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 30 % profit . this means the clocks ' selling price was c ( 1.3 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 60 % the price at which the collector bought it . thus , you get = 1.3 * 0.6 * c = 0.78 c furthermore , the store sells the clock for the second time for 90 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.9 = 1.9 * 0.78 c finally given that c - 0.78 c = 150 - - - - > c = 681.82 $ thus , the cost of the clock the second time around = 1.9 * 0.78 c = 1.9 * 0.78 * 681.82 = 1010.46 $ . hence a is the correct answer ."
Answer: a
Python program:
a = 150 + 90 
b = 150 + 30 
c = b / 2
d = a * c
e = d / 150
f = 150 * e
g = 150 + 30 
h = g / 2
i = h - 30
j = f / i
Problem: a certain junior class has 1000 students and a certain senior class has 900 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 2 / 30000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 60 / 1000 first then we can only pick 1 other pair from the 800 so total will be 60 / 900 * 1000 simplify and you get 2 / 30000 answer is b"
Answer: b
Python program:
a = 1 / 3
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 3 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.86
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 3 / 100 ) = 350 â † ’ t = 4.86 answer e
Answer: e
Python program:
a = 3 * 1000
b = a / 100
c = 1400 * 3
d = c / 100
e = b + d 
f = 350 / e
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 400 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.58 % , b ) 1.98 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 400 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 400 ) / 100 + ( 1.8 * 700 ) / 100 = 15.8 gms % of liquid x in resultant mixture = ( 15.8 / 1000 ) * 100 = 1.58 % a"
Answer: a
Python program:
a = 400 * 0
b = 700 * 1
c = a + b 
d = c / 1000
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 21 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 4 , d ) 6 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 21 - 9 = 12 ab = 6 . answer is d ."
Answer: d
Python program:
a = 3 ** 2
b = 21 - a
c = b / 2
Problem: out of 460 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 90
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 460 - 50 = 410 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 410 = 90 . answer is e"
Answer: e
Python program:
a = 175 + 325 
b = 460 - 50
c = a - b
Problem: in a 8 x 8 chess board what is the total number of squares .
Options: a ) 238 , b ) 204 , c ) 678 , d ) 169 , e ) 161
Rationale: ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares ' ' i . e . , n ( n + 1 ) ( 2 n + 1 ) 6 n ( n + 1 ) ( 2 n + 1 ) 6 so substituting 8 in the above formula we get 204 answer : b
Answer: b
Python program:
a = 8 + 1 
b = 8 * a
c = 8 * 2
d = c + 1 
e = b * d
f = 8 - 2
g = e / f
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 ) 1 / 4 , b ) 1 / 10 , c ) 7 / 15 , d ) 8 / 15 , e ) 9 / 15
Rationale: "explanation : a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 4 day ' s work = 7 / 60 x 4 = 7 / 15 therefore , remaining work = 1 - 7 / 15 = 8 / 15 answer is d"
Answer: d
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = c * 4
e = 1 - d
Problem: rakesh credits 15 % of his salary in his fixed deposit account and spends 30 % of the remaining amount on groceries . if the cash in hand is rs . 2380 , what is his salary ?
Options: a ) rs . 3500 , b ) rs . 4000 , c ) rs . 4500 , d ) rs . 5000 , e ) none
Rationale: explanation : let salary be rs . x . then , x - 15 % of x - 30 % of 85 % of x = 2380 or x - 15 x / 100 − 30 × 85 × x / 100 × 100 = 2380 or 200 x - 30 x - 51 x = 2380 × 2002380 × 200 or 119 x = 2380 × 2002380 × 200 or x 2380 × 200 / 119 = 4000 correct option : b
Answer: b
Python program:
a = 100 - 15
b = a / 100
c = 100 - 30
d = c / 100
e = b * d
f = 2380 / e
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth
Options: a ) 12000 , b ) 14000 , c ) 15000 , d ) 20000 , e ) 60000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer a"
Answer: a
Python program:
a = 5 * 4
b = a - 12
Problem: if a light flashes every 6 seconds , how many times will it flash in ¾ of an hour ?
Options: a ) 451 times , b ) 638 times , c ) 838 times , d ) 436 times , e ) 435 times
Rationale: there are 60 minutes in an hour . in ¾ of an hour there are ( 60 * ¾ ) minutes = 45 minutes . in ¾ of an hour there are ( 60 * 45 ) seconds = 2700 seconds . light flashed for every 6 seconds . in 2700 seconds 2700 / 6 = 450 times . the count start after the first flash , the light will flashes 451 times in ¾ of an hour . answer : a
Answer: a
Python program:
a = 3600 / 4
b = a * 3
c = b / 6
Problem: by selling an article at rs . 400 , a profit of 60 % is made . find its cost price ?
Options: a ) 228 , b ) 267 , c ) 287 , d ) 250 , e ) 811
Rationale: "sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 60 ) ] = 400 * [ 100 / 160 ] = rs . 250 answer : d"
Answer: d
Python program:
a = 400 * 100
b = 100 + 60 
c = a / b
Problem: while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 3 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 1.6 , b ) 1.8 , c ) 2 , d ) 2.2 , e ) 2.4
Rationale: "both computers together process files at a rate of 240 / 12 + 240 / 3 = 20 + 80 = 100 files per hour . the time required to process 240 files is 240 / 100 = 2.4 hours the answer is e ."
Answer: e
Python program:
a = 240 / 12
b = 240 / 3
c = a + b 
d = 240 / c
Problem: on dividing a number by 357 , we get 39 as remainder . on dividing the same number 17 , what will be the remainder ?
Options: a ) 10 , b ) 12 , c ) 5 , d ) 25 , e ) 85
Rationale: "explanation : let x be the number and y be the quotient . then , x = 357 x y + 39 = ( 17 x 21 x y ) + ( 17 x 2 ) + 5 = 17 x ( 21 y + 2 ) + 5 ) required remainder = 5 . c )"
Answer: c
Python program:
a = 39 ** 2
b = a / 357
c = 39 ** 2
d = c / 357
e = math.floor(d)
f = b - e
g = f * 357
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team r . if team a ' s average speed was 5 mph greater than team r ' s , what was team r ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team r ' s speed was s . then team r ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team r . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team r is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Python program:
a = 300 / 5
b = a / 3
Problem: the average marks of a class of 24 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 53.5 , e ) 52.1
Rationale: "sum of the marks for the class of 24 students = 24 * 40 = 960 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 74 students = 960 + 3000 = 3960 average marks of all the students = 3960 / 74 = 53.5 answer : d"
Answer: d
Python program:
a = 24 * 40
b = 50 * 60
c = a + b 
d = 24 + 50 
e = c / d
Problem: each month a retailer sells 100 identical items . on each item he makes a profit of $ 30 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 30 sell price = $ 300 + $ 30 thus , the sell price is $ 330 for each item . selling all 100 items gives the retailer . . . 100 ( $ 30 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 330 ) = $ 16.5 discount $ 313.5 = $ 300 + $ 13.5 now , the retailer makes a profit of just $ 13.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 13.5 ( x ) = $ 2,000 x = 2,000 / 13.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Python program:
a = 100 * 30
b = 100 * 30
c = b / 10
d = c + 30 
e = d * 5
f = e / 100
g = 30 - f
h = a / g
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 555 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 150 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 555 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 55 3.7 z = 555 , z = 150 answer : . d"
Answer: d
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / 100
d = 1 + c 
e = b * d
f = 20 / 100
g = 1 + f 
h = e + g 
i = h + 1 
j = 555 / i
Problem: for integers x , y , and z , if ( 3 ^ x ) ( 4 ^ y ) ( 5 ^ z ) = 13107 , 200000 and x + y + z = 16 , what is the value of xy / z ?
Options: a ) undefined , b ) 0 , c ) 3 , d ) 5 , e ) 7
Rationale: the number 13,107 , 200,000 is not divisible by 3 . ( we can verify this by adding the digits of the number to see that the sum is not a multiple of 3 . ) thus x = 0 and xy / z = 0 . the answer is b .
Answer: b
Python program:
a = 4 - 3
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 972 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 972 3 b 2 = 972 b 2 = 324 b = 18 m . answer : option c"
Answer: c
Python program:
a = 972 / 3
b = math.sqrt(a)
Problem: the mean of 15 observations was 25 . it was found later that an observation 40 was wrongly taken as 25 . the corrected new mean is
Options: a ) 20 , b ) 30 , c ) 15 , d ) 18 , e ) 26
Rationale: "explanation : correct sum = ( 25 * 15 + 40 - 25 ) = 390 correct mean = = 390 / 15 = 26 answer : e"
Answer: e
Python program:
a = 25 * 15
b = 15 - 2
c = b - 25
d = a + c 
e = d / 15
Problem: what is the area of a square field whose diagonal of length 24 m ?
Options: a ) 240 sq m , b ) 250 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m
Rationale: "d 2 / 2 = ( 24 * 24 ) / 2 = 240 answer : a"
Answer: a
Python program:
a = square_area / (
Problem: if 40 % of a number is equal to two - thirds of another number , what is the ratio of the first number to the second ?
Options: a ) 7 : 3 , b ) 3 : 7 , c ) 2 : 5 , d ) 5 : 3 , e ) none of these
Rationale: "suppose the first number is x and the second numbery . therefore , 40 % of x = 2 ⁄ 3 of y ∴ x ⁄ y = 2 ⁄ 3 × 100 ⁄ 40 = 5 ⁄ 3 answer d"
Answer: d
Python program:
a = 1 / 4
b = 40 / 100
c = a / b
Problem: ( x ) + 3612 + 16125 - 6149 = 90189 . calculate the value of x
Options: a ) 76601 , b ) 76600 , c ) 76655 , d ) 76313 , e ) 76723
Rationale: "x + 3612 + 16125 - 6149 = 90189 = x + 3612 + 16125 = 90189 + 6149 = x + 19737 = 96338 = x = 96338 - 19737 = 76601 answer is a"
Answer: a
Python program:
a = 90189 + 6149 
b = a - 16125
c = b - 3612
d = const_60 / 2
e = c * d
Problem: if the radius of a circle is increased by 12 % , then the area of the circle
Options: a ) decreases by 25.44 %
b ) increases by 25.44 %
c ) no change in area
d ) decreases by 12 %
e ) none
Rationale: a 1 = pi ( 100 ) ^ 2 a 2 = pi ( 112 ) ^ 2 so ( a 2 - a 1 ) / a 1 * 100 = 25.44 answer : b
Answer: b
Python program:
a = 12 / 100
b = a + 1 
c = b ** 2
d = c - 1
e = d * 100
Problem: a grocer has a sale of rs . 2500 , rs . 6500 , rs . 9855 , rs . 7230 and rs . 7000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) s . 49180 , b ) s . 49910 , c ) s . 11915 , d ) s 6997 , e ) s . 5000
Rationale: total sale for 5 months = rs . ( 2500 + 6500 + 9855 + 7230 + 7000 ) = rs . 33085 . required sale = rs . [ ( 7500 x 6 ) - 33085 ] = rs . ( 45000 - 33085 ) = rs . 11915 . c
Answer: c
Python program:
a = 5 + 1 
b = a * 7500
c = 2500 + 6500 
d = c + 9855 
e = d + 7230 
f = e + 7000 
g = b - f
Problem: a cyclist bikes x distance at 20 miles per hour and returns over the same path at 16 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 17.6 , b ) 17.3 , c ) 8.6 , d ) 17.2 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 20 miles per hour time = t 1 = distance / speed = x / 20 2 . going from b to a distance = d 2 = x miles speed = s 2 = 16 miles per hour time = t 2 = distance / speed = x / 16 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 20 + x / 16 = 9 x / 80 speed = 2 x / ( 9 x / 80 ) = 160 / 9 = 17.6 answer : a"
Answer: a
Python program:
a = 20 + 16 
b = a / 2