euclaise/mathqa_programs huggingface dataset:
Problem: a monkey ascends a greased pole 12 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: in 2 minutes , he ascends = 1 metre ∴ 10 metres , he ascends in 20 minutes . ∴ he reaches the top in 21 st minute . answer b
Answer: b
Python program:
a = 2 * 12
b = a - 1
Problem: what will be the remainder when 17 ^ 200 is divided by 18
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "17 ^ 200 % 18 ( 17 - 18 ) ^ 200 % 18 ( - 1 ) ^ 200 % 18 1 % 18 = 1 answer : a"
Answer: a
Python program:
a = 17 ** 17
Problem: sakshi invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?
Options: a ) rs . 4000 , b ) rs . 4500 , c ) rs . 5500 , d ) rs . 6000 , e ) rs . 6500
Rationale: let investment in 12 % stock be rs . x . then , investment in 15 % stock = rs . ( 12000 - x ) . 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x / 10 + 3 / 25 ( 12000 - x ) = 1360 5 x + 72000 - 6 x = 1360 x 50 x = 4000 . answer = a
Answer: a
Python program:
a = 15 / 125
b = a * 12000
c = 1360 - b
d = 12 / 120
e = 15 / 125
f = d - e
g = c / f
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 5 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 11 / 8 , b ) 3 / 80 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 5 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 5 ) * ( 1 / 2 ) * ( 3 / 8 ) = 3 / 80 . ans . b ."
Answer: b
Python program:
a = 1 / 5
b = 1 / 2
c = a * b
d = 5 / 8
e = 1 - d
f = c * e
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 400 girls , the total number of students in the college is
Options: a ) 1040 , b ) 920 , c ) 980 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 400 = > x = 80 total students = 8 x + 5 x = 13 x = 13 ( 80 ) = 1040 option a"
Answer: a
Python program:
a = 400 / 5
b = a * 8
c = 400 + b
Problem: the tax on a commodity is diminished by 18 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8.7 % , c ) 5.7 % , d ) 6.7 % , e ) 1 %
Rationale: "100 * 100 = 10000 82 * 115 = 9430 - - - - - - - - - - - 10000 - - - - - - - - - - - 570 100 - - - - - - - - - - - ? = > 5.7 % decrease answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1 + a 
c = 18 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: a can do a job in 10 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 15 days , e ) none of these
Rationale: "explanation : 1 / 10 + 1 / 30 = 4 / 30 = 2 / 15 15 / 2 = 15 / 2 * 2 = 15 days answer : d"
Answer: d
Python program:
a = 1 / 10
b = 1 / 30
c = a + b
Problem: if jamie ' s income is rs 20000 , calculate his savings given that his income and expenditure are in the ratio 7 : 5 . ?
Options: a ) rs 7500 , b ) rs 4000 , c ) rs 2000 , d ) rs 8000 , e ) rs 7000
Rationale: let the income and the expenditure of the person be rs . 7 x and rs . 7 x respectively . income , 7 x = 28000 = > x = 4000 savings = income - expenditure = 7 x - 5 x = 2 x so , savings = rs . 8000 answer : d
Answer: d
Python program:
a = 7 + 5 
b = 5 / a
c = b * 20000
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 5 years . what is the sum ?
Options: a ) 82762 , b ) 12877 , c ) 82882 , d ) 80925 , e ) 80325
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 5 ) = rs . 80325 . answer : e"
Answer: e
Python program:
a = 4016 * 25
b = a / 1
c = b / 5
Problem: on thrusday mabel handled 90 transactions . anthony handled 10 % more transaction than mabel , cal handled 2 / 3 rds of the transactions that anthony handled and jade handled 16 more transaction than cal . how much transaction did jade handled ?
Options: a ) 92 , b ) 80 , c ) 72 , d ) 82 , e ) 28
Rationale: mabel handled 90 transaction , anthony 10 % more transaction the mabel . anthony = 90 + 90 * 10 % , = 90 + 90 * 0.10 , = 90 + 9 , = 99 , cal handled 2 / 3 rds than anthony handled , cal = 2 / 3 * 99 = 66 , jade handled 16 more than cal . jade = 66 + 16 = 82 , jade handled = 82 tranasactions . correct answer : ( d )
Answer: d
Python program:
a = 90 / 10
b = 90 + a 
c = b * 2
d = c / 3
e = d + 16
Problem: jar x is 1 / 3 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 5 / 6 , b ) 5 / 12 , c ) 7 / 12 , d ) 7 / 18 , e ) 11 / 18
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 3 + p / 4 = 7 p / 12 the answer is c ."
Answer: c
Python program:
a = 1 / 3
b = 1 / 3
c = 1 / 3
d = b * c
e = a + d
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 4 of the mixture is water , and the remaining 10 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 36
Rationale: "let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 4 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 4 ) x = ( 5 / 12 ) x = 10 x = 24 then answer will be a = 24"
Answer: a
Python program:
a = 1 / 3
b = 1 / 4
c = a + b 
d = 1 - c
e = 10 / d
Problem: 0.01 is what percent of 0.1 ?
Options: a ) 1 % , b ) 10 % , c ) 100 % , d ) 50 % , e ) 25 %
Rationale: "required percentage = 0.01 * 100 / 0.1 = 100 / 10 = 10 % answer is b"
Answer: b
Python program:
a = 0 / 1
b = a * 100
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 26 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 150 m , c ) 289 m , d ) 299 m , e ) 219 m
Rationale: "speed = 300 / 26 = 150 / 13 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 150 / 13 = > x = 150 m . answer : b"
Answer: b
Python program:
a = speed * (
b = a - 39
Problem: 9 persons went to a hotel for taking their meals . 8 of them spent rs 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them ?
Options: a ) 117 , b ) 180 , c ) 150 , d ) 200 , e ) 250
Rationale: exp . let the total expenditure be x , then the average = x / 9 , 8 * 12 + [ x / 9 + 8 ] = x or [ x - x / 9 ] = 104 . 8 x / 9 = 104 , x = 104 * 9 / 8 = 117 . answer : a
Answer: a
Python program:
a = 8 * 12
b = a + 8 
c = 9 - 1
d = b / c
e = 9 * d
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 7 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 252 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 7 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 = sum of 7 terms in ap whose first term is 30 and last term is 42 = 7 / 2 [ 30 + 42 ] = 252 km . answer : c"
Answer: c
Python program:
a = 2 * 7
b = 30 + a 
c = b + 30 
d = c / 2
Problem: the average ( arithmetic mean ) of 4 positive integers is 40 . if the average of 2 of these integers is 45 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 69 , c ) 100 , d ) 109 , e ) 115
Rationale: a + b + c + d = 160 a + b = 90 c + d = 70 greatest possible = 69 ( just less than 1 ) answer = b
Answer: b
Python program:
a = 40 * 4
b = 45 * 2
c = a - b
Problem: what is the least number of square tiles required to pave the floor of a room 12 m 12 cm long and 1 m 20 cm broad ?
Options: a ) 1010 , b ) 804 , c ) 814 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1212 cm & 120 cm = 12 cm . area of each tile = ( 12 x 12 ) cm 2 ∴ required number of tiles = [ 1212 x 120 / 12 x 12 ] = 1010 . answer a"
Answer: a
Python program:
a = 1 * 100
b = a + 20 
c = 12 * 100
d = b * c
e = 20 ** 2
f = d / e
Problem: if 2 x = 3 √ 32 , then x is equal to :
Options: a ) 3 / 5 , b ) 5 / 3 , c ) 15 , d ) 25 , e ) none
Rationale: "sol . 2 x = 3 √ 32 ⇔ 2 x = ( 32 ) 1 / 3 = ( 25 ) 1 / 3 = 25 / 3 ⇔ x = 5 / 3 . answer b"
Answer: b
Python program:
a = 2 * 100
b = a / 2
c = b - 2
d = 2 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: a train running at the speed of 48 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 120 meter , b ) 299 meter , c ) 666 meter , d ) 155 meter , e ) 144 meter
Rationale: "speed = 48 * ( 5 / 18 ) m / sec = 40 / 3 m / sec length of train ( distance ) = speed * time ( 40 / 3 ) * 9 = 120 meter answer : a"
Answer: a
Python program:
a = 48 * 1000
b = a / 3600
c = b * 9
Problem: a cricket player whose bowling average was 20.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 101 , d ) 111 , e ) 128
Rationale: "average = total runs / total wickets total runs after last match = 20.5 w + 52 total wickets after last match = w + 5 ( 20.5 w + 52 ) / ( w + 5 ) = 20.5 - 0.5 = 20 w = 96 so total wickets aftr last match = w + 5 = 101 answer : c"
Answer: c
Python program:
a = 20 - 5
b = a * 5
c = b - 52
d = c / 0
Problem: if a trader sold two cars each at rs . 325475 and gains 11 % on the first and loses 11 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.21 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.24 %
Rationale: "sp of each car is rs . 325475 , he gains 11 % on first car and losses 11 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 11 ) ( 11 ) / 100 % = 1.21 % answer : a"
Answer: a
Python program:
a = 11 * 11
b = a / 100
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 36 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 15 days , b ) 18 days , c ) 21 days , d ) 24 days , e ) 27 days
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 36 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 36 / 60 oxen = 18 days the answer is b ."
Answer: b
Python program:
a = 24 / 4
b = a * 3
c = 15 + b 
d = 8 / 2
e = d * 3
f = c + e 
g = 36 * f
h = 15 + 15 
i = 24 + 40 
j = i / 4
k = j * 3
l = h + k 
m = 8 / 2
n = m * 3
o = l + n 
p = g / o
Problem: for any non - zero a and b that satisfy | ab | = ab and | a | = a | b - 4 | + | ab - b | = ?
Options: a ) ab - 4 , b ) 2 b - ab - 4 , c ) ab + 4 , d ) ab - 2 b + 4 , e ) 4 - ab
Rationale: | ab | = ab and | a | = - a = > b is also negative . so | b - 4 | + | ab - b | = ( b - 4 ) + ab - b ( as ab is positive and - b is positive , so expression is totally positive ) = b - 4 + ab - b = ab - 4 answer - a
Answer: a
Python program:
a = 1 - 1
b = a - 4
Problem: p software has coding line 5 % more than n , n software has coding line 1 / 3 more than m . m software has 90 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 126 , d ) 109 , e ) 110
Rationale: m s / w has 90 line of code n s / w has = 90 + 90 * 1 / 3 = 120 line of code p s / w 5 % more n ' code 120 + 6 = 126 answer : c
Answer: c
Python program:
a = 90 / 3
b = 90 + a
Problem: a and b go around a circular track of length 1800 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 360 sec
Rationale: time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1800 / ( 36 * 5 / 18 ) , 1800 / ( 54 * 5 / 18 ) } = lcm ( 180 , 120 ) = 360 sec . answer : e
Answer: e
Python program:
a = 54 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 1800 / c
Problem: the greatest common divisor of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . what is the value of b ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 9 , e ) 6
Rationale: gcd of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . find x . best way to find n is substitute each of the answer and find out the correct one . only option d gave the correct answer . option d : 9 and find gcd or 7 ! , 10 ! and 13 ! . 7 ! itself is 5040 and 7 ! which is contained in the other two factorials . this satisfies the condition , hence answer is 9 . answer is d .
Answer: d
Python program:
a = 4 + 4 
b = a + 1
Problem: the length of a side of a hexagon is 10 inches . what is the perimeter ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 60
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 10 ) = 60 inches answer e"
Answer: e
Python program:
a = 3 * 2
b = 10 * a
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent s of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march s = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Python program:
a = 40 / 100
b = 25 / 100
c = 40 / 100
d = b * c
e = a - d
f = 25 / 100
g = 40 / 100
h = f * g
i = 1 - h
j = e / i
k = j * 100
Problem: if a : b = 1 : 4 , b : c = 13 : 9 , c : d = 5 : 13 , find a : d ?
Options: a ) 5 / 46 , b ) 7 / 36 , c ) 1 / 36 , d ) 5 / 36 , e ) 5 / 37
Rationale: a / d = ( 1 / 4 ) * ( 13 / 9 ) * ( 5 / 13 ) = > 5 / 36 answer : d
Answer: d
Python program:
a = 1 * 13
b = a * 5
c = 4 * 9
d = c * 13
e = b / d
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 5 , 1 ) , ( 1 , 1 ) , ( 1 , - 4 ) and ( - 5 , - 4 ) ?
Options: a ) 20
b ) 30
c ) 40
d ) 55
e ) 48
Rationale: length of side 1 = 5 + 1 = 6 length of side 2 = 4 + 1 = 5 area of rectangle = 6 * 5 = 30 b is the answer
Answer: b
Python program:
a = 5 + 1 
b = 1 + 4 
c = a * b
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 30 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 971750 , c ) 980241 , d ) 2356677 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 30 / 100 ) = 971750 b"
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1000000 * h
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 90 ?
Options: a ) 180 , b ) 160 , c ) 140 , d ) 150 , e ) 120
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 90 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 90 = ( 2 ^ 2 * 5 ^ 2 ) ^ 90 = 2 ^ 180 * 5 ^ 180 answer : a"
Answer: a
Python program:
a = 100 / 90
b = 2 ** a
c = b - 1
d = 100 - c
Problem: alex takes a loan of $ 9,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 810 , c ) 800 , d ) 730 , e ) 750
Rationale: from the details given in the problem principle = p = $ 9,000 and r = 9 % or 0.09 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 9,000 x 1 x 0.09 = 810.00 annual interest to be paid = $ 810 answer : b
Answer: b
Python program:
a = 9 * 100
b = math.sqrt(100)
c = a * b
d = c * 9
e = d / 100
Problem: last month , john rejected 0.7 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 0.7 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.7 x = 0.05 / 0.1 x = 1 / 2 therefore the answer is b : 1 / 2 ."
Answer: b
Python program:
a = 0 - 75
b = 0 - 8
c = a / b
Problem: if the average ( arithmetic mean ) of x and y is 60 , and z – x = 80 , what is the average of y and z ?
Options: a ) 100 , b ) 120 , c ) 125 , d ) 115 , e ) 90
Rationale: "x + y / 2 = 60 = > x + y = 120 x = z - 80 . . . sub this value z - 80 + y = 120 = > z + y = 200 = > z + y / 2 = 100 answer : a"
Answer: a
Python program:
a = 80 * 2
b = 60 * 2
c = a - b
Problem: what is the smallest integer z for which 27 ^ z > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ z > 3 ^ 24 converting into the same bases : 27 ^ z > 27 ^ 8 therefore for the equation to hold true , z > 8 or z = 9 option c"
Answer: c
Python program:
a = 24 / 3
b = math.floor(a)
c = b + 1
Problem: a is twice as good a work man as b and together they finish the work in 8 days . in how many days a alone can finish the work ?
Options: a ) 23 , b ) 12 , c ) 77 , d ) 92 , e ) 61
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 = > x = 1 / 24 2 x = 1 / 12 a can do the work in 12 days . answer : b"
Answer: b
Python program:
a = 1/(8)
b = 2 + 1 
c = a / b
d = 1/(c)
Problem: the sum of two numbers is 21 and the sum of their squares is 527 . find the product of the numbers .
Options: a ) 48 , b ) 41 , c ) 46 , d ) 43 , e ) 96
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 21 a ^ 2 + b ^ 2 = 527 so , 21 ^ 2 = 527 + 2 ab 2 ab = 527 - 441 2 ab = 86 ab = 43 ans d
Answer: d
Python program:
a = 21 ** 2
b = 527 - a
c = b / 2
Problem: thabo owns exactly 280 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 55
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 280 3 x + 60 + x = 280 x = 55 answer ( e . )"
Answer: e
Python program:
a = 280 + 20 
b = a / 4
c = b - 20
Problem: in the number 100 ab , a and b represent the tens and units digits , respectively . if 110 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d
Answer: d
Python program:
a = 110 / 10
b = 55 / a
c = 110 / 10
d = 55 / c
e = d - 2
f = b * e
Problem: a train 350 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 88 sec , e ) 20 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 350 * 2 / 35 = 20 sec answer : e"
Answer: e
Python program:
a = 63 * 1000
b = 350 / a
c = b * 3600
Problem: a car travelling with 5 / 7 km of its actual speed covers 42 km in 1 hr 40 min 48 sec find the actual speed of the car ?
Options: a ) 78 kmph , b ) 85 kmph , c ) 35 kmph , d ) 24 kmph , e ) 74 kmph
Rationale: time taken = 1 hr 40 min 48 sec = 126 / 75 hrs let the actual speed be x kmph then 5 / 7 x * 126 / 75 = 42 x = ( 42 * 7 * 75 ) / 5 * 126 = 35 kmph answer ( c )
Answer: c
Python program:
a = 40 * const_60
b = a + 48 
c = b / 3600
d = 1 + c 
e = 42 / d
f = e * 7
g = f / 5
Problem: compare the rates of two trains , one travelling at 90 km / hr and other is at 50 m / s ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 1 : 3 , d ) 3 : 1 , e ) 2 : 3
Rationale: speed of the 1 st train = 90 km / hr speed of the 2 nd train = 50 m / s = 50 * 18 / 5 = 180 km / hr ratio of the speeds of the train = 90 : 180 = 1 : 2 answer is b
Answer: b
Python program:
a = 50 / 1000
b = a * 3600
c = 90 / b
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 10,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 1000 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 122 , b ) 112 , c ) 134 , d ) 108 , e ) 101
Rationale: "$ 10000 is a fixed cost each component is $ 102 ( $ 100 to produce , $ 2 to ship ) manufacturer will be producing and selling 1000 components so therefore the equation to find price would be 1000 * p = 10000 + ( 1000 * 100 ) + ( 1000 * 2 ) p = ( 10000 + 100000 + 2000 ) / 1000 p = 112 answer : b"
Answer: b
Python program:
a = 4 * 4
b = a * 1000
c = 2 * 100
d = b + c 
e = 100 + 2 
f = e * 1000
g = d + f 
h = g / 1000
Problem: sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 08 : 00 and starts climbing at a constant pace . ken starts climbing only at 10 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: "both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 10 : 00 , in 5 hrs , the time will be 15 : 00 answer ( d )"
Answer: d
Python program:
a = 700 + 50 
b = 700 / 2
c = 500 - b
d = a / c
e = d + 10