euclaise/mathqa_programs huggingface dataset:
Problem: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 40 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 132 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 72 min b"
Answer: b
Python program:
a = 2 * 40
b = 2 * 40
c = 80 - b
d = a / c
e = 80 - 40
f = 40 / e
g = d - f
h = g * const_60
Problem: a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 53 , b ) 50 , c ) 99 , d ) 288 , e ) 12
Rationale: speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 8 ) km / hr . x - 8 = 45 = = > x = 53 km / hr . answer : a
Answer: a
Python program:
a = 8 * const_0_2778
b = a * 8
c = 125 - b
d = c / 8
e = d / const_0_2778
Problem: when tossed , a certain coin has an equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32
Rationale: "on the first toss , the coin will land on one side or the other . on the second toss , the probability of landing on the same side is 1 / 2 . on the third toss , the probability of landing on the same side is 1 / 2 . on the fourth toss , the probability of landing on the same side is 1 / 2 . on the fifth toss , the probability of landing on the same side is 1 / 2 . p ( same side all five times ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 . the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = a ** 5
c = 1 / 2
d = c ** 5
e = b + d
Problem: the closest approximation of d ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "d ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c"
Answer: c
Python program:
a = 0 / 4
b = a * 69
Problem: in a 1000 m race , a beats b by 200 meters or 25 seconds . find the speed of b ?
Options: a ) 5 m / s , b ) 8 m / s , c ) 9 m / s , d ) 4 m / s , e ) 2 m / s
Rationale: b 8 m / s since a beats b by 200 m or 25 seconds , i t implies that b covers 200 m in 25 seconds . hence speed of b = 200 / 25 = 8 m / s .
Answer: b
Python program:
a = 200 / 25
Problem: robert ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 new final salary = 150 % of ( 50 % of $ 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = $ 75 decrease = 25 % correct option is c"
Answer: c
Python program:
a = 100 * 100
b = 100 - 50
c = 100 + 50 
d = b * c
e = a - d
f = 100 * 100
g = e / f
h = g * 100
Problem: the average age of 10 members of a committee is the same as it was 4 years ago , because an old member has been replaced by a young member . find how much younger is the new member ?
Options: a ) 35 , b ) 15 , c ) 40 , d ) 52 , e ) 14
Rationale: c let the sum of nine member ( total ) = x and the age of old one = z so its average 4 yrs before = ( x + z ) / 10 . after 4 yrs let z be replaced by y . so now avg = ( x + 4 * 10 + y ) / 10 now ( x + z ) / 10 = ( x + 40 + y ) / 10 so after solving it found z = y + 40 . so old person is 40 yrs older than young one .
Answer: c
Python program:
a = 10 * 4
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 157 per kg , the price of the third variety per kg will be
Options: a ) rs . 179.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 180 , e ) none
Rationale: solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 157 / 22.50 = 1 = â € º x - 157 = 22.50 = â € º x = 179.50 . hence , price of the third variety = rs . 179.50 per kg . answer a
Answer: a
Python program:
a = 1 + 1 
b = a + 2 
c = 157 * b
d = 126 + 126 
e = c - d
f = e / 2
Problem: if 75 percent of 600 is 50 percent of x , then x = ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "0.75 * 600 = 0.5 * x x = 7.5 / 5 * 600 = 900"
Answer: b
Python program:
a = 75 * 600
b = a / 50
Problem: there were 35 students in a hostel . due to the admission of 7 new students , the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1 . what was the original expenditure of the mess ?
Options: a ) 400 , b ) 400 , c ) 445 , d ) 465 , e ) none of the above
Rationale: let the original average expenditure be ` x . then , 42 ( x – 1 ) – 35 x = 42 ⇔ 7 x = 84 ⇒ x = 12 . ∴ original expenditure = ( 35 × 12 ) = 420 . answer b
Answer: b
Python program:
a = 42 + 42 
b = 42 - 35
c = a / b
d = c * 35
e = 42 + 42 
f = 42 - 35
g = e / f
h = 42 - g
i = 42 + 42 
j = 42 - 35
k = i / j
l = h - k
m = l + 2 
n = d - m
Problem: a person can row at 10 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 2 kmph ?
Options: a ) 32 km , b ) 25 km , c ) 28 km , d ) 24 km , e ) 20 km
Rationale: let the distance between a and b be x km . total time = x / ( 10 + 2 ) + x / ( 10 - 2 ) = 5 = > x / 12 + x / 8 = 5 = > ( 2 x + 3 x ) / 24 = 5 = > x = 24 km . answer : d
Answer: d
Python program:
a = 10 - 2
b = 10 + 2 
c = a * b
d = c * 5
e = 10 + 2 
f = 10 - 2
g = e + f 
h = d / g
Problem: a tour group of 25 people paid a total of $ 945 for entrance to a museum . if this price included a 5 % sales tax , and all the tickets cost the same amount , what was the face value of each ticket price without the sales tax ? choices
Options: a ) $ 22 , b ) $ 23.94 , c ) $ 36 , d ) $ 25.20 , e ) $ 30
Rationale: soln : - 945 / 25 = x + 0.05 x 945 / 25 = 1.05 x x = 36 answer : c
Answer: c
Python program:
a = 945 / 25
b = 100 - 5
c = a * b
d = c / 100
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 8.55 each . one day , she bought 9 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 73.1025
Rationale: $ 8.55 * 9 = $ 73.1025 . answer is e .
Answer: e
Python program:
a = 9 * 8
b = math.floor(a)
Problem: what is the average of the first 10 multiples of 11 ?
Options: a ) 55.5 , b ) 61.5 , c ) 53.5 , d ) 78.5 , e ) 60.5
Rationale: "( 11 + 22 + . . . + 110 ) / 10 = 11 ( 1 + 2 + . . . + 10 ) / 10 = 11 ( 10 ) ( 11 ) / ( 10 * 2 ) = 121 / 2 = 60.5 option e"
Answer: e
Python program:
a = 10 + 1 
b = 10 * a
c = b / 2
d = c / 10
e = d * 11
Problem: the difference between the squares of two consecutive numbers is 37 . find the numbers .
Options: a ) 38 and 19 .
b ) 28 and 19 .
c ) 18 and 19 .
d ) 18 and 29 .
e ) none
Rationale: solution : if the difference between the squares of two consecutive numbers is x , then the numbers are ( x - 1 ) / 2 and ( x + 1 ) / 2 ( 37 - 1 ) / 2 and ( 37 + 1 ) / 2 36 / 2 and 38 / 2 therefore the required answer = 18 and 19 . answer c
Answer: c
Python program:
a = 37 + 1 
b = a / 2
Problem: a miniature roulette wheel is divided into 10 equal sectors , each bearing a distinct integer from 1 to 10 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun four times , approximately what is the probability that the product of the four winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 88 % , d ) 94 % , e ) 98 %
Rationale: "the only way to have an odd product is if all 4 integers are odd . p ( odd product ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 p ( even product ) = 1 - 1 / 16 = 15 / 16 which is about 94 % the answer is d ."
Answer: d
Python program:
a = 10 / 2
b = a / 10
c = b ** 2
d = 1 - c
e = d * 100
Problem: what is 120 % of 13 / 24 of 840 ?
Options: a ) 436 , b ) 478 , c ) 512 , d ) 546 , e ) 620
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 35 = 546 the answer is d ."
Answer: d
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 120 * n
p = o / 100
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 5 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 45 , b ) 65 , c ) 77 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 5 = 73 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 73 + 4 = 77 c"
Answer: c
Python program:
a = 80 * 4
b = 79 * 4
c = 80 * 4
d = 84 * 5
e = c - d
f = 3 + 0 
g = b - f
h = a - g
Problem: at golds gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 48 , e ) 96
Rationale: we are given that golds gym class can be divided into 8 teams or 12 teams , with an equal number of players on each team . translating this into two mathematical expressions we can say , where g is the total number of students in the gym class , that : g / 8 = integer and g / 12 = integer this means that g is a multiple of both 8 and 12 . we are asked to determine the lowest number of students in the class , or the lowest value for variable “ g ” . because we know that g is a multiple of 8 and of 12 , we need to find the least common multiple of 8 and 12 . although there are technical ways for determining the least common multiple , the easiest method is to analyze the multiples of 8 and 12 until we find one in common . starting with 8 , we have : 8 , 16 , 24 , 32 for 12 , we have : 12 , 24 for the multiples of 12 , we stopped at 24 , because we see that 24 is also a multiple of 8 . thus , 24 is the least common multiple of 8 and 12 , and therefore we know that the lowest possible number of students in the gym class is 24 . answer b .
Answer: b
Python program:
a = math.lcm(8, 12)
Problem: how many internal diagonals does a hexagon ( 6 sided polygon ) have ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 6 no . of diagonals = 6 ( 6 - 3 ) / 2 = 9 ans d
Answer: d
Python program:
a = 6 - 3
b = 6 * a
c = b / 2
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 14.70 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 14.70 when c . p = ( 100 * 14.70 ) / 21 = 70 answer : e"
Answer: e
Python program:
a = 14 * 70
b = 25 + 100 
c = 30 + 100 
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1568 ?
Options: a ) 1000 , b ) 2777 , c ) 2889 , d ) 1400 , e ) 2771
Rationale: "1568 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1400 . answer : d"
Answer: d
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 1568 / f
Problem: the average ( arithmetic mean ) of the even integers from 0 to 200 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive ?
Options: a ) 10 , b ) 25 , c ) 50 , d ) 100 , e ) 200
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 200 is 200 / 2 = 100 the average of the even numbers from 0 to 100 is 100 / 2 = 50 the answer is c ."
Answer: c
Python program:
a = 100 + 0 
b = a / 2
c = 200 + 0 
d = c / 2
e = b - d
Problem: by selling 22 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 83 , b ) 63 , c ) 53 , d ) 33 , e ) 13
Rationale: "80 % - - - 22 120 % - - - ? 80 / 120 * 22 = 33 answer : d"
Answer: d
Python program:
a = 100 + 20 
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 22
Problem: solve the equation for x : 19 ( x + y ) + 17 = 19 ( - x + y ) - 21
Options: a ) 1 , b ) 2 , c ) - 1 , d ) - 3 , e ) - 4
Rationale: "c - 1 19 x + 19 y + 17 = - 19 x + 19 y - 21 38 x = - 38 = > x = - 1"
Answer: c
Python program:
a = 17 + 21 
b = 19 + 19 
c = a / b
Problem: how many seconds will a 700 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 23 sec , b ) 30 sec , c ) 27 sec , d ) 36 sec , e ) 42 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 700 * 3 / 50 = 42 sec . answer : e"
Answer: e
Python program:
a = 63 - 3
b = a * const_0_2778
c = 700 / b
Problem: two concentric circles form a ring . the inner and outer circumferences of ring are ( 352 / 7 ) m and ( 518 / 7 ) m respectively . find the width of the ring .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) none of them
Rationale: "let the inner and outer radii be r and r meters . then 2 ( 22 / 7 ) r = ( 352 / 7 ) = r = ( ( 352 / 7 ) x ( 7 / 22 ) x ( 1 / 2 ) ) = 8 m . 2 ( 22 / 7 ) r = ( 528 / 7 ) = r = ( ( 528 / 7 ) x ( 7 / 22 ) x ( 1 / 2 ) ) = 12 m . therefore , width of the ring = ( r - r ) = ( 12 - 8 ) m = 4 m . answer is b ."
Answer: b
Python program:
a = 518 / 7
b = a / 2
c = b / math.pi
d = 352 / 7
e = d / 2
f = e / math.pi
g = c - f
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 25 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 7 , b ) 5 , c ) 2 , d ) 3 , e ) 1
Rationale: "200 men do the rest of the work in 100 - 25 = 75 days 100 men can do the rest of the work in 75 * 200 / 100 = 75 days required number of days = 75 - 80 = 5 days answer is b"
Answer: b
Python program:
a = 100 - 25
Problem: the initial price of an article is rs . 4000 which increases 40 % increse in its price in the first year , a 20 % decrease in the second year and a 20 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 2928 , b ) rs . 5928 , c ) rs . 3928 , d ) rs . r 4928 , e ) rs . 6928
Rationale: "the initial price of the article is rs . 4000 . in the 1 st year , price of the article = 4000 + 1600 = rs . 5600 . in the 2 nd year , price = 5600 - 20 % of 5600 = 5600 - 1120 = rs . 4480 . in the 3 rd year , price = 4480 + 10 % of 4480 = 4480 + 448 = rs . 4928 required price = = rs . 4928 . answer : d"
Answer: d
Python program:
a = 4000 * 20
b = a / 100
c = 4000 - b
d = 4000 * 20
e = d / 100
f = 4000 - e
g = f * 20
h = g / 100
i = c + h
Problem: if 3 men or 4 women can reap a field in 10 days how long will 5 men and 6 women take to reap it ?
Options: a ) 19 / 60 , b ) 9 / 60 , c ) 2 / 3 , d ) 5 / 18 , e ) 6 / 24
Rationale: explanation : 3 men reap 1 / 10 field in 1 day 1 man reap 1 / ( 3 x 10 ) 4 women reap 1 / 10 field in 1 day 1 woman reap 1 / ( 10 x 4 ) 5 men and 6 women reap ( 5 / ( 3 x 10 ) + 6 / ( 4 x 10 ) ) = 19 / 60 in 1 day 5 men and 6 women will reap the field in 19 / 60 days answer : option a
Answer: a
Python program:
a = 10 / 3
b = 5 * a
c = 10 / 4
d = 6 * c
e = b + d 
f = 10 / e
Problem: qames can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ?
Options: a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes .
Rationale: rate = output / time qames rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min
Answer: c
Python program:
a = 25 / const_60
b = 25 / 20
c = a + b 
d = 150 / c
e = 3 / 2
f = d / e
g = const_60 / f
Problem: ajay and balu together can do a piece of work in 12 days . balu and charan together can do the same work in 16 days . after ajay has been working at it for 5 days and balu for 7 days , charan finishes it in 13 days . in how many days will charan alone be able to do the work ?
Options: a ) 16 days , b ) 24 days , c ) 36 days , d ) 48 days , e ) 58 days
Rationale: let the total work be 48 units . ajay and balu ’ s one day work = 48 / 12 = 4 units . balu and charan ’ s one day work = 48 / 16 = 3 units . ajay ’ s one day work = 4 - balu ’ s one day work . balu ’ s one day work = 3 - charan ’ s one day work . therefore , ajay ’ s one day work = 1 + charan ’ s one day work . also given , 5 x ajay ’ s one day work + 7 x balu ’ s one day work + 13 x charan ’ s one day work = 48 equating all the equations formed , we get charan ’ s one day work is 2 units . hence , charan can finish the whole work in 48 / 2 = 24 days . answer : b
Answer: b
Python program:
a = 1/(12)
b = 5 * a
c = 1 - b
d = 7 - 5
e = 1/(16)
f = d * e
g = c - f
h = 1/(g)
i = 13 - 2
j = h * i
Problem: city a to city b , john drove for 1 hour at 40 mph and for 3 hours at 60 mph . what was the average speed for the whole trip ?
Options: a ) 57 , b ) 57.5 , c ) 58.2 , d ) 59 , e ) 55
Rationale: the total distance is 1 × 40 + 3 × 60 = 220 and the total time is 4 hours . hence , average speed = ( total distance / total time ) = 220 / 4 = 55 answer : e
Answer: e
Python program:
a = 1 * 40
b = 3 * 60
c = a + b 
d = 1 + 3 
e = c / d
Problem: if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 720 , b ) 830 , c ) 940 , d ) 1050 , e ) 1160
Rationale: 6 ! = 720 the answer is a .
Answer: a
Python program:
a = math.factorial(6)
Problem: find the average of all prime numbers between 12 and 24 .
Options: a ) 30 , b ) 33.6 , c ) 18 , d ) 20 , e ) none
Rationale: "sol . there are five prime numbers between 12 and 24 . they are 13 , 17 , 19 , 23 â ˆ ´ required average = [ 13 + 17 + 19 + 23 / 4 ] = 72 / 4 = 18 answer c"
Answer: c
Python program:
a = 12 + 1 
b = 12 + 1 
c = b + 2 
d = a + c 
e = 24 - 12
f = 24 - 2
g = e + f 
h = d + g 
i = h / 12
Problem: a ’ s speed is 20 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 19 , b ) 3 / 19 , c ) 1 / 10 , d ) 1 / 20 , e ) 3 / 10
Rationale: "let d be the full distance . let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 20 v / 19 ) = xd / v ( 19 / 20 ) * d / v = x * d / v x = 19 / 20 b should have a head start of 1 / 20 of the full distance . the answer is d ."
Answer: d
Python program:
a = 20 - 19
b = a / 20
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 504 per week . how much does she earn in dollars per hour ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 14 , e ) 24
Rationale: explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 504 . hourly wage = 504 / 36 = 14 answer : d
Answer: d
Python program:
a = 8 * 3
b = 6 * 2
c = a + b 
d = 504 / c
Problem: if 1 = 6 , 2 = 12 , 3 = 18 , 4 = 24 , 5 = 30 , then 6 = ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 7 , e ) 9
Rationale: solution : 1 as stated 1 = 6 = > 6 = 1 answer c
Answer: c
Python program:
a = 2 - 1
Problem: 3 partners a , b , c start a business . twice a ’ s capital is equal to thrice b ’ s capital and b ’ s capital is 4 times c ’ s capital . out of a total profit of rs . 16500 at the end of the year , b ’ share is :
Options: a ) 2000 , b ) 4000 , c ) 5000 , d ) 6000 , e ) none
Rationale: sol . let c = x . then , b = 4 x and 2 a = 3 * 4 x = 12 x or a = 6 x . ∴ a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so , b ’ s capital = rs . [ 16500 * 4 / 11 ] = rs . 6000 . answer d
Answer: d
Python program:
a = 3 / 2
b = a + 1 
c = 1 / 4
d = b + c 
e = 16500 / d
Problem: a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 25 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 47.5 % , b ) 44 % , c ) 50 % , d ) 35 % , e ) 38 %
Rationale: suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.25 = 150 increase in 1993 from 1991 = 150 - 100 = 50 answer : c
Answer: c
Python program:
a = 100 + 20 
b = 100 + 25 
c = b / 100
d = a * c
e = d - 100
Problem: a is three times as fast as b . if b alone can do a piece of work in 12 days , in what time can a and b together complete the work ?
Options: a ) 5 , b ) 8 , c ) 3 , d ) 2 , e ) 12
Rationale: "a can do the work in 12 / 3 i . e . , 4 days . a and b ' s one day ' s work = 1 / 4 + 1 / 12 = ( 3 + 1 ) / 12 = 1 / 3 so a and b together can do the work in 3 days . answer : c"
Answer: c
Python program:
a = 12 / 4
b = 1/(a)
c = 1/(12)
d = b + c 
e = 1/(d)
Problem: by selling 10 pencils for a rupee a man loses 15 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 8.39 , b ) 6.39 , c ) 7.39 , d ) 9.39 , e ) 2.39
Rationale: 85 % - - - 10 115 % - - - ? 85 / 115 * 10 = 7.39 answer : c
Answer: c
Python program:
a = 100 + 15 
b = 100 - 15
c = 1 / b
d = a * c
e = 1 / d
f = e * 10
Problem: a trader bought a car at 20 % discount on its original price . he sold it at a 100 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 18 % , b ) 13 % , c ) 60 % , d ) 40 % , e ) 15 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 200 / 100 ) = 160 100 - 160 = 60 % answer : c"
Answer: c
Python program:
a = 100 - 20
b = 100 + 100 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100