euclaise/mathqa_programs huggingface dataset:
Problem: ( 500 + 200 + 100 ) ã — 4 ã — ( 3 + 4 ) = ?
Options: a ) 52000 , b ) 32400 , c ) 22400 , d ) 22800 , e ) 24200
Rationale: "( 500 + 200 + 100 ) ã — 4 ã — ( 3 + 4 ) = ? or , ? = 800 ã — 4 ã — 7 = 22400 answer c"
Answer: c
Python program:
a = 4 + 1 
b = 4 * a
c = b / 2
d = 500 - 1
e = d * 500
f = e / 2
g = c - f
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent e ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . e = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Python program:
a = 100 - 80
b = a - 10
c = 10 / b
d = c * 100
Problem: if the wheel is 10 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 16.8 , b ) 26 , c ) 14 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 10 * x = 1056 = > x = 16.8 answer : a"
Answer: a
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 10
h = 1056 / g
Problem: the perimeter of a semi circle is 126 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 98 , d ) 24.5 , e ) 13
Rationale: "36 / 7 r = 126 = > r = 24.5 answer : d"
Answer: d
Python program:
a = 2 + math.pi 
b = 126 / a
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 15 kmph . what time will they take to be 50 km apart ?
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: "to be ( 10 + 15 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 25 * 50 = 2 hrs answer is b"
Answer: b
Python program:
a = 10 + 15 
b = 50 / a
Problem: r is the set of positive even integers less than 101 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 101 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , 36 , 64 , and 100 are even integers ( less than 101 ) that are in both sets . solution : five answer : d"
Answer: d
Python program:
a = 4 - 1
Problem: a fill pipe can fill 1 / 4 of cistern in 16 minutes in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 48 min , b ) 36 min , c ) 25 min , d ) 30 min , e ) 50 min
Rationale: "1 / 4 of the cistern can fill in 16 min 3 / 4 of the cistern can fill in = 16 * 4 * 3 / 4 = 48 min answer is a"
Answer: a
Python program:
a = 16 / 1
Problem: how many three digit numbers e are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples e - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Python program:
a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 35 % and its breadth is decreased by 21 % ?
Options: a ) 4.65 % increase , b ) 5.65 % increase , c ) 6.65 % increase , d ) 6.65 % decrease , e ) 7.65 % increase
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 35 % = 135 b decrease by 21 % = 79 135 * 79 = 10665 6.65 % increase answer : c"
Answer: c
Python program:
a = 100 + 35 
b = 100 - 21
c = a * b
d = 100 * 100
e = c - d
f = 100 * 100
g = e / f
h = g * 100
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 3 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 56.6 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 3 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 3 or 45 * 18 - 45 * x + 36 * x = 3 * 100 or 9 x = - 3 * 100 + 45 * 18 x = 510 / 9 = 56.6 % b"
Answer: b
Python program:
a = 18 / 100
b = 18 / 100
c = 18 * 2
d = b * c
e = 3 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: a and b began business with rs . 2000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 455 , e ) 361
Rationale: "( 2 * 8 + 1 * 4 ) : ( 4 * 8 + 5 * 4 ) 5 : 13 13 / 18 * 630 = 455 answer : d"
Answer: d
Python program:
a = 2000 * 8
b = 2000 - 1000
c = 12 - 8
d = b * c
e = a + d 
f = 4000 * 8
g = 4000 + 1000 
h = 12 - 8
i = g * h
j = f + i 
k = e + j 
l = 630 / k
m = 2000 * 8
n = 2000 - 1000
o = 12 - 8
p = n * o
q = m + p 
r = l * q
Problem: if 70 % of a number exceeds 28 % of it by 39.9 , then find the number ?
Options: a ) 65 , b ) 67 , c ) 100 , d ) 95 , e ) 33
Rationale: "use the elimination method to find the correct option . of all the options only 95 fits 70 % of 95 = 66.5 28 % of 95 = 26.6 66.5 - 26.6 = 39.9 required number is 95 . answer : d"
Answer: d
Python program:
a = 70 - 28
b = a / 100
c = 39 / 9
d = c + 28
Problem: 40 onions on a scale weigh 7.68 kg . when 5 onions are removed from the scale , the average weight of the 35 onions is 190 grams . what is the average weight ( in grams ) of the 5 onions which were removed ?
Options: a ) 200 , b ) 202 , c ) 204 , d ) 206 , e ) 208
Rationale: "35 * 190 = 6650 . the other 5 onions weigh a total of 1030 grams . the average weight is 1030 / 5 = 206 grams . the answer is d ."
Answer: d
Python program:
a = 7 * 68
b = 35 * 190
c = a - b
d = c / 5
Problem: evaluate : 6402.5 + 640.25 + 64.025 + 6.4025 + 0.64025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 7113.81775 , e ) 6891.59775
Rationale: "6402.5 640.25 64.025 6.4025 + 0.64025 - - - - - - - - - - - - - - - 7113.81775 answer is d ."
Answer: d
Python program:
a = 640 * 25
b = a * 6
c = 6402 - 5
Problem: mudit ' s age 16 years hence will be thrice his age 4 years ago . find mudit ' s present age ?
Options: a ) 14 , b ) 19 , c ) 27 , d ) 18 , e ) 15
Rationale: explanation : let mudit ' s present age be ' m ' years . m + 16 = 3 ( m - 4 ) = > 2 m = 28 = > m = 14 years . answer : a
Answer: a
Python program:
a = 3 * 4
b = 16 + a 
c = b / 2
Problem: the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1540 respectively . what is the rate of interest ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: 1540 - 1400 = 140 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 140 ) / ( 1400 ) = 10 % the answer is e .
Answer: e
Python program:
a = 1540 - 1400
b = a * 100
c = b / 1400
Problem: on a certain planet where people usually tend to live for more than a century , the ratio of present ages of father and son is 7 : 4 . 10 years later , the ratio of their ages will be 5 : 3 . what is the sum of their present ages ?
Options: a ) 220 , b ) 200 , c ) 140 , d ) 80 , e ) 60
Rationale: the ratio of present ages of father and son is 7 : 4 , so suppose the present ages are 7 x and 4 x , respectively . 10 years later , the ages of father and son , respectively , shall be 7 x + 10 and 4 x + 10 . the ratio of ages 10 years later is given to be 5 : 3 . this means ( 7 x + 10 ) / ( 4 x + 10 ) = 5 / 3 solving we get x = 20 . so present age of father is 7 x = 140 and present age of son is 4 x = 80 . the sum of present ages is thus 220 . ans a
Answer: a
Python program:
a = 5 * 10
b = 3 * 10
c = a - b
d = 7 * c
e = 5 * 10
f = 3 * 10
g = e - f
h = 4 * g
i = d + h
Problem: a certain candy manufacturer reduced the weight of candy bar m by 40 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?
Options: a ) 66.66 , b ) 62.5 , c ) 58 , d ) 60 , e ) 62
Rationale: "assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.6 oz new price of candy = 1 / 0.6 = 1.6666 price increase 66.66 % a"
Answer: a
Python program:
a = 40 / 100
b = 1 - a
c = 1 / b
d = c * 100
e = d - 100
Problem: weights of two friends ram and shyam are in the ratio 1 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: solution : given ratio of ram and shayam ' s weight = 1 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 1 / 5 or , x = 16 % . answer : option d
Answer: d
Python program:
a = 15 - 10
b = 1 / 5
c = a * b
d = 15 + c
Problem: the average of first 20 prime numbers is ?
Options: a ) 9.5 , b ) 8.6 , c ) 9.3 , d ) 9.6 , e ) 9.8
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 / 8 = 77 / 8 = 9.6 ( approx ) answer is d"
Answer: d
Python program:
a = 20 + 1
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = − 2 , y = 1 , and z = 4 ?
Options: a ) 20 , b ) 24 , c ) 30 , d ) 32 , e ) 48
Rationale: "4 * 1 * 4 - ( - 2 * 1 * 16 ) = 16 + 32 = 48 ans : e"
Answer: e
Python program:
a = negate * (
b = a * 1
c = b * 4
Problem: a train of 35 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 9 , e ) 3.6
Rationale: "d = 35 * 60 + 1500 = 3600 m t = 3600 / 60 * 18 / 5 = 216 sec = 3.6 mins answer : e"
Answer: e
Python program:
a = 35 + 1 
b = a * 60
c = b / 1000
d = c + 1
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent q of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before q = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Python program:
a = 10 * 10
Problem: the difference of two numbers is 11 and one - fifth of their sum is 9 . find the numbers
Options: a ) 28,22 , b ) 28,17 , c ) 27,17 , d ) 26,17 , e ) 28,19
Rationale: if two numbers are x , y x - y = 11 - - ( i ) & ( x + y ) / 5 = 9 - - ( ii ) solving ( i ) & ( ii ) , x = 28 , y = 17 answer : b
Answer: b
Python program:
a = 10 / 2
b = a * 9
c = 10 / 2
d = c * 9
e = 11 + d 
f = e / 2
g = b - f
h = 10 / 2
i = g + h
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 18000 left with him . find salary . .
Options: a ) $ 10800 , b ) $ 18000 , c ) $ 180000 , d ) $ 1800 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 18000 , = [ 1 - 9 / 10 ] * total salary = $ 18000 , total salary = $ 18000 * 10 = $ 180000 , correct answer ( c )"
Answer: c
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 3 / 5
e = c + d 
f = 1 - e
g = 18000 / f
Problem: bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 12 left in his pocket . what was the value of n ?
Options: a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer b if he had 44 , then he spent 11 at hardware store now he was left with 33 $ he spent 9 dollars on cleaning , thus he remained with 24 $ he then spent 1 / 2 of 24 , or 12 , and was left with 12 . hence , the only option that can be right is b"
Answer: b
Python program:
a = 1 / 4
b = 1 - a
c = 1/(b)
d = 9 / 2
e = d + 12 
f = c * e
g = f * 2
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 3520 cm is ?
Options: a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 40
Rationale: "2 * 22 / 7 * 14 * x = 3520 = > x = 40 answer : e"
Answer: e
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 3520 / g
Problem: what will be the compound interest on a sum of rs . 15000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.22 , b ) s . 5823.20 , c ) s . 9123.20 , d ) s . 7256.20 , e ) s . 6073.92
Rationale: "explanation : amount = [ 15000 * ( 1 + 12 / 100 ) 3 ] = 15000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 35123.20 - 15000 ) = rs . 6073.92 answer : e"
Answer: e
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: if 13 = 13 w / ( 1 - w ) , then ( w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: 13 - 13 w = 13 w 26 w = 13 w = 1 / 2 2 w * 2 = 1 / 2 * 2 = 1 answer : c
Answer: c
Python program:
a = 13 + 13 
b = 13 / a
c = b * 2
Problem: on dividing 15968 by a certain number , the quotient is 89 and the remainder is 37 . find the divisor .
Options: a ) 170 , b ) 179 , c ) 37 , d ) 67 , e ) 32
Rationale: "divisor = ( dividend – remainder / quotient ) = ( 15968 - 37 ) / 89 = 179 answer b 179"
Answer: b
Python program:
a = 15968 - 37
b = a / 89
Problem: 58 , 52 , 46 , 40 , 34 , . . . ?
Options: a ) 20 , b ) 22 , c ) 28 , d ) 27 , e ) 32
Rationale: "each number is 6 less than the previous number . 58 - 6 = 52 52 - 6 = 46 46 - 6 = 40 40 - 6 = 34 34 - 6 = 28 answer : c"
Answer: c
Python program:
a = negate - (
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 4 times , what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 1 / 16 , e ) 1 / 32
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 16 answer : d
Answer: d
Python program:
a = 2 ** 4
b = 1/(a)
Problem: if rs . 460 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) rs . 575 , b ) rs . 595 , c ) rs . 590 , d ) rs . 580 , e ) rs . 585
Rationale: "80 = ( 460 * 4 * r ) / 100 r = 4.34 % i = ( 460 * 6 * 4.34 ) / 100 = 120 460 + 120 = 580 answer : d"
Answer: d
Python program:
a = 540 - 460
b = a * 6
c = 540 - 460
d = b - c
Problem: a train passes a station platform in 50 sec and a man standing on the platform in 15 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 500 , c ) 550 , d ) 525 , e ) 171
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 15 = 225 m . let the length of the platform be x m . then , ( x + 225 ) / 50 = 15 = > x = 525 m . answer : d"
Answer: d
Python program:
a = 54 * const_0_2778
b = 15 * a
Problem: a trained covered x km at 70 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 ) 22.25 , b ) 99 , c ) 26.25 , d ) 66 , e ) 887
Rationale: "total time taken = x / 70 + 2 x / 20 hours = 4 x / 35 hours average speed = 3 x / ( 4 x / 35 ) = 26.25 kmph answer : c"
Answer: c
Python program:
a = 70 * 3
b = 70 / 70
c = 2 * 70
d = c / 20
e = b + d 
f = a / e
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 420 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "3 x = 420 x = 140 therefore , the salesman sold 140 kg in the morning and 2 ⋅ 140 = 280 kg in the afternoon . so answer is d ."
Answer: d
Python program:
a = 420 / 3
b = a * 2
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1000 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 20625 , e ) none of these
Rationale: solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1000 × 20.625 ) = 20625 . answer d
Answer: d
Python program:
a = 5 * 5
b = 1000 * a
Problem: the probability that a can solve the problem is 2 / 3 and b can solve it is 3 / 4 . if both of them attemp the problem , then what is the probability that the problem get solved ?
Options: a ) 9 / 12 , b ) 10 / 12 , c ) 11 / 12 , d ) 1 , e ) 2
Rationale: explanation : the event is defined as : a solves the problem and b does not solve the problem or a does n ' t solve the problem and b solves the problem or a solves the problem and b solves the problem numerically this is equivalent to : ( 2 / 3 ) x ( 1 / 4 ) + ( 1 / 3 ) x ( 3 / 4 ) + ( 2 / 3 ) x ( 3 / 4 ) = 11 / 12 answer : c
Answer: c
Python program:
a = 2 / 3
b = 1 - a
c = 3 / 4
d = 1 - c
e = b * d
f = 1 - e
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 11 days . c alone will finish the job in
Options: a ) 41.25 days , b ) 30.25 days , c ) 60.25 days , d ) 71.25 days , e ) 51.25 days
Rationale: explanation : 11 = ( 15 * x ) / ( 15 + x ) 165 + 11 x = 15 x 4 x = 165 x = 41.25 answer : option a
Answer: a
Python program:
a = 11 * 15
b = 15 - 11
c = a / b
Problem: on a map , 1 inch represents 28 miles . how many x xxinches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "x inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Python program:
a = 383 / 6
Problem: tim has 13 10 - dollar bills , 11 5 - dollar bills , and 17 one - dollar bills . if tim needs to pay exactly $ 128 , what is the least number of bills he will need to use ?
Options: a ) 68 , b ) 66 , c ) 565 , d ) 16 , e ) 35
Rationale: 128 is the total sum of money . as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128 - 120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 ( use only 1 5 dollar bill ) = 3 so we can get 3 from using 3 $ 1 bills . hence 16 ( 12 + 1 + 3 ) answer is d
Answer: d
Python program:
a = 13 - 1
b = a + 1 
c = b + 3
Problem: if in a race of 130 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 26 m , c ) 11 m , d ) 10 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 130 * 5 ) / 25 = 26 m hence , a beats b by 26 m . answer b"
Answer: b
Python program:
a = 25 - 20
b = a / 25
c = b * 130
Problem: the average of 10 consecutive integers is 25 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 19 , b ) 19.5 , c ) 20 , d ) 20.5 , e ) 21
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Python program:
a = 10 * 25
b = 4 + 1 
c = b * 9
d = a - c
e = d / 10
Problem: if 0.75 : x : : 5 : 11 , then x is equal to :
Options: a ) 1.12 , b ) 1.65 , c ) 1.2 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 11 ) x = 8.25 / 5 = 1.65 answer : b"
Answer: b
Python program:
a = 0 * 75
b = a / 5
Problem: an empty fuel tank is filled with brand z gasoline . when the tank is 3 / 4 empty , it is filled with brand x gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand x gasoline . at this time , what percent of the gasoline in the tank is brand z ?
Options: a ) 41 % , b ) 42 % , c ) 43 % , d ) 43.75 % , e ) 44 %
Rationale: "work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 2 3 rd step : brand z is ( 3 / 4 ) * ( 1 / 2 ) + 1 / 2 = 7 / 8 4 th step : brand z is ( 1 / 2 ) * ( 7 / 8 ) = 7 / 16 = 43.75 % answer ( d )"
Answer: d
Python program:
a = 3 / 4
b = a * 100
c = 100 - b
d = c / 2
e = 100 - d
f = e / 2
Problem: there are 9 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 24 , b ) 25 , c ) 28 , d ) 32 , e ) 36
Rationale: "9 c 2 = 36 the answer is e"
Answer: e
Python program:
a = 9 - 1
b = 9 * a
c = b / 2
Problem: in how many years rs 160 will produce the same interest at 8 % as rs . 500 produce in 4 years at 8 %
Options: a ) 13 , b ) 13.5 , c ) 11.5 , d ) 12.5 , e ) 12
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 500 , time 4 years and rate 8 % , it will be rs . 160 then we can get the time as time = ( 100 * 160 ) / ( 160 * 8 ) = 12.5 option d"
Answer: d
Python program:
a = 500 * 8
b = a / 100
c = b * 4
d = 8 / 100
e = d * 160
f = c / e
Problem: of 15 applicants for a job , 7 had at least 4 years ' experience , 9 had degrees , and 1 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 2
Rationale: "15 - 1 = 14 14 - 7 - 9 = - 2 then 2 are in the intersection between 4 years experience and degree . answer : e"
Answer: e
Python program:
a = 7 + 9 
b = 15 - 1
c = a - b
d = 9 - 7
e = c + d
Problem: simple interest on a certain sum of money for 5 years at 8 % per annum is half the compound interest on rs . 8000 for 2 years at 15 % per annum . the sum placed on simple interest is
Options: a ) rs . 3225 , b ) rs . 2580 , c ) rs . 8000 , d ) rs . 1290 , e ) none
Rationale: solution c . i . = rs [ 8000 x ( 1 + 15 / 100 ) â ² - 8000 ] rs . ( 8000 x 115 / 100 x 115 / 100 - 8000 ) = rs . 2580 . sum = rs . [ 1290 x 100 / 5 x 8 ] = rs . 3225 . answer a
Answer: a
Python program:
a = 8000 * 15
b = a / 100
c = 8000 * 15
d = c / 100
e = 8000 + d 
f = e * 15
g = f / 100
h = b + g 
i = h / 2
j = i / 5
k = j * 100
l = k / 8
Problem: for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 80 color copies at print shop y than at print shop x ?
Options: a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140
Rationale: "the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 80 * $ 1.50 = $ 120 the answer is a ."
Answer: a
Python program:
a = 2 * 75
b = 1 * 25
c = a - b