euclaise/mathqa_programs huggingface dataset:
Problem: the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1512 respectively . what is the rate of interest ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "1512 - 1400 = 112 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 112 ) / ( 1400 ) = 8 % the answer is d ."
Answer: d
Python program:
a = 1512 - 1400
b = a * 100
c = b / 1400
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is
Options: a ) 86 , b ) 90 , c ) 92 , d ) 94 , e ) 96
Rationale: "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . a"
Answer: a
Python program:
a = 6 * 3
b = a + 2 
c = 6 * 3
d = c + 2 
e = d / 5
f = b * e
g = f + 6
Problem: a number when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 31
Options: a ) 5 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "explanation : p ÷ 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 option a"
Answer: a
Python program:
a = 44 * 432
b = a / 31
Problem: if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 250
Rationale: "120 amounts to 160 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 160 120 + 120 * ( r / 100 ) * ( 3 ) = 160 = > r = 100 / 9 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) 250 answer is e ."
Answer: e
Python program:
a = 150 * 6
b = 160 - 120
c = b * 120
d = c / 120
e = d / 3
f = a * e
g = f / 120
h = 150 + g
Problem: the population of a town increased from 1 , 33,400 to 1 , 93,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.5 % , b ) 5.5 % , c ) 6.5 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 193500 - 133400 ) = 60100 . increase % = ( 60100 / 133400 x 100 ) % = 45 % . required average = ( 45 / 10 ) % = 4.5 % . answer : option a"
Answer: a
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 1 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 1 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 60000 . find his total income ?
Options: a ) a ) 1200000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 60000 100 % = 60000 * 100 / 5 = $ 1200000 answer is a"
Answer: a
Python program:
a = 20 * 3
b = a + 30 
c = b + 5 
d = 100 - c
e = 60000 / d
f = e * 100
Problem: a = 5 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "a = 5 ^ 15 - 625 ^ 3 = > 5 ^ 15 - ( 5 ^ 4 ) ^ 3 = > 5 ^ 15 - 5 ^ 12 = 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 * 124 124 = 31 * 4 a / x is integer for condition of 2 < p < x only 5 and 31 satisfies this hence answer is c"
Answer: c
Python program:
a = 3 * 4
b = 15 - a
Problem: a car takes 6 hours to cover a distance of 360 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 360 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 360 / 9 = 40 kmph answer c ."
Answer: c
Python program:
a = 6 * 3
b = a / 2
c = 360 / b
Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Rationale: "if we are to select 4 people from 7 couples without any restriction , how many ways can we make the selection ? 14 ! / 4 ! 10 ! = 1001 if we are to select 4 people from 7 couples with restriction that no married couple can both make it to the group , only a representative ? 7 ! / 4 ! 3 ! = 35 but we know that to select a person from each couple , take 2 possibilities 35 * 2 * 2 * 2 * 2 = 560 probability = desired / all possibilities = 560 / 1001 = 47 / 84 answer : e"
Answer: e
Python program:
a = 7 * 2
b = 7 * 2
c = a / b
d = 4 * 4
e = 7 * 2
f = e - 1
g = d / f
h = c * g
i = 4 * 4
j = i - 2
k = 4 * 4
l = j / k
m = h * l
n = 4 * 4
o = n - 2
p = o - 2
q = 4 * 4
r = q - 1
s = p / r
t = m * s
Problem: a shopkeeper has 100 kg of apples . he sells 50 % of these at 25 % profit and remaining 50 % at 30 % profit . find his % profit on total .
Options: a ) 27.5 % , b ) 25.6 % , c ) 31.5 % , d ) 35.9 % , e ) 29.5 %
Rationale: "total number of apples = 100 let the cost price be x selling price at 25 % profit = 1.25 x selling price at 30 % profit = 1.3 x profit % = ( ( sp - cp ) / cp ) * 100 profit % = ( ( 1 / 2 ) * 100 * 1.25 x + ( 1 / 2 ) * 100 * 1.3 x - 100 x ) / 100 x * 100 = ( 255 - 200 ) / 2 = 27.5 % answer is a"
Answer: a
Python program:
a = 100 * 50
b = a / 100
c = 100 + 25 
d = c / 100
e = b * d
f = 100 * 50
g = f / 100
h = 100 + 30 
i = h / 100
j = g * i
k = e + j 
l = k - 100
m = l * 100
n = m / 100
Problem: a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 6 points if you must draw exactly 4 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 5 ! / 4 ! which represents ( 5 * 4 * 3 * 2 * 1 ) / ( 4 * 3 * 2 * 1 ) which simplifies to just 5 , giving you answer e ."
Answer: e
Python program:
a = 4 * 4
b = a * 2
c = b * 1
d = 4 * 2
e = d * 1
f = c / e
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 970 gm . for a kg . his gain is … % .
Options: a ) 3.09 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 %
Rationale: "his percentage gain is 100 * 30 / 970 as he is gaining 30 units for his purchase of 970 units . so 3.09 % . answer : a"
Answer: a
Python program:
a = 4 + 1 
b = a * 2
c = b * 100
d = 970 / c
e = 1/(d)
f = e - 1
g = f * 100
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 6 ) , what is the value of w ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 6 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 6 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 18 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 18 w = 18 the answer is c ."
Answer: c
Python program:
a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
Problem: tom traveled the entire 20 miles trip . if he did the first 10 miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 12.45 mph , b ) 11.25 mph , c ) 10.95 mph , d ) 10.91 mph , e ) 10.56 mph
Rationale: avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 10 + 10 ) / ( ( 10 / 12 ) + ( 10 / 10 ) = 120 / 11 = 10.91 mph d
Answer: d
Python program:
a = 20 - 10
b = 10 / a
c = 10 / 12
d = b + c 
e = 20 / d
Problem: a , b are positive integers . the remainder of a to be divided by 8 is 3 and the remainder of b to be divided by 6 is 5 . which is possible to be the remainder of a * b to be divided by 48
Options: a ) a ) 2 , b ) b ) 6 , c ) c ) 8 , d ) d ) 15 , e ) e ) 20
Rationale: two ways to do it . . . a = 8 x + 3 . . b = 6 y + 5 . . 1 ) convenient way . . take x and y as 0 , and you will get a * b as 3 * 5 = 15 answer : d
Answer: d
Python program:
a = 3 * 5
Problem: one pipe can fill a pool 1.25 times faster than a second pipe . when both pipes are opened , they fill the pool in five hours . how long would it take to fill the pool if only the faster pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 7.2 , e ) 9
Rationale: say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.25 r = 5 r / 4 . since when both pipes are opened , they fill the pool in five hours , then their combined rate is 1 / 5 pool / hour . thus we have that r + 5 r / 4 = 1 / 5 - - > r = 4 / 45 pool / hour , faster pipe fills at 1.25 r which is 5 / 4 * 4 / 45 = 1 / 9 - - > time is reciprocal of rate thus it ' s 9 / 1 = 9 hours . answer : e .
Answer: e
Python program:
a = 3 + 2 
b = 1/(a)
c = 1 + 1 
d = b / c
e = 1/(d)
f = e / 1
Problem: the revenue from sales items in 1996 increases by x percent , compared in 1995 and the revenue in 1997 decreases by x percent , compared in 1996 . if the revenue from sales items in 1997 decreases by 4 percent , compared in 1995 , what is the value of x ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 35
Rationale: 1995 - let the value be z 1996 - x % increase - z ( 1 + x / 100 ) 1997 - x % decrease - z ( 1 + x / 100 ) ( 1 - x / 100 ) from 95 to 97 decrease is 4 % hence , [ z - { z ( 1 + x / 100 ) ( 1 - x / 100 ) } ] / z = 4 / 100 solving x = 20 % c is the answer
Answer: c
Python program:
a = 4 * 100
b = math.sqrt(a)
Problem: peter has $ 642986 in his savings account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among his 9 children ?
Options: a ) $ 642986 , b ) $ 642987 , c ) $ 642988 , d ) $ 642989 , e ) $ 642990
Rationale: to find the least amount the man should add to his saving account to split the money evenly among his 9 children , he needs to make the total divisible by 9 simply add the individual digits of the total = 6 + 4 + 2 + 9 + 8 + 6 = 35 if you add 1 , the number is divisible by 9 ( 35 + 1 ) correct option : b
Answer: b
Python program:
a = 9 / 9
b = 642986 + a
Problem: the measurement of a rectangular box with lid is 25 cmx 4 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 11.12 , b ) 10.11 , c ) 72 , d ) 10.66 , e ) 9.2
Rationale: "d = 4 , r = 2 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 2 * 2 * 2 = 10.66 π cm 3 answer : d"
Answer: d
Python program:
a = 4 / 3
b = 3 ** 3
c = a * b
Problem: a car travels at a speed of 60 miles per hour . how far will it travel in 5 hours ?
Options: a ) 425 miles , b ) 625 miles , c ) 300 miles , d ) 225 miles , e ) 625 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 60 + 60 + 60 + 60 + 60 = 5 * 65 = 300 miles correct answer c"
Answer: c
Python program:
a = 60 * 5
Problem: find the distance covered by a man walking for 72 min at a speed of 10 km / hr ?
Options: a ) 12 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 72 / 60 = 12 km answer is a"
Answer: a
Python program:
a = 10 * 1000
b = a / const_60
c = 72 * b
d = c / 1000
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is
Options: a ) 276 , b ) 299 , c ) 312 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer d"
Answer: d
Python program:
a = 23 * 14
Problem: what percent is 2 gm of 1 kg ?
Options: a ) 0.5 % , b ) 0.2 % , c ) 1.5 % , d ) 2 % , e ) 3 %
Rationale: "1 kg = 1000 gm 2 / 1000 × 100 = 200 / 1000 = 1 / 5 = 0.2 % b )"
Answer: b
Python program:
a = 2 / 1
b = a * 100
Problem: a car travels first 160 km at 75 km / hr and the next 160 km at 70 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 72.4 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 70 km / hr time taken to travel next 160 km = distancespeed = 160 / 70 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 75 + 160 / 70 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 70 ) = 72.4 km / hr answer : c"
Answer: c
Python program:
a = 160 / 75
b = 160 / 70
c = a + b 
d = 1 / c
e = 320 * d
Problem: a train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . what is the length of the train ?
Options: a ) 62 m , b ) 54 m , c ) 50 m , d ) 55 m , e ) 56 m
Rationale: explanation : let x is the length of the train in meter and v is its speed in kmph x / 9 = ( v - 2 ) ( 10 / 36 ) - - - ( 1 ) x / 10 = ( v - 4 ) ( 10 / 36 ) - - - ( 2 ) dividing equation 1 with equation 2 10 / 9 = ( v - 2 ) / ( v - 4 ) = > 10 v - 40 = 9 v - 18 = > v = 22 substituting in equation 1 , x / 9 = 200 / 36 = > x = 9 × 200 / 36 = 50 m answer : option c
Answer: c
Python program:
a = 4 * 1000
b = a / 3600
c = b * 10
d = 2 * 1000
e = d / 3600
f = e * 9
g = c - f
h = 2 * 1000
i = h / 3600
j = g - i
k = 9 * j
Problem: what is 15 percent of 68 ?
Options: a ) 7.6 , b ) 8.7 , c ) 9.1 , d ) 10.2 , e ) 11.6
Rationale: "( 15 / 100 ) * 68 = 10.2 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 = 15 * n
p = o / 100
Problem: if a - b = 2 and a 2 + b 2 = 25 , find the value of ab .
Options: a ) a ) 10.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 25 - 4 = 21 ab = 10.5 answer : a"
Answer: a
Python program:
a = 2 ** 2
b = 25 - a
c = b / 2
Problem: the area of a parallelogram is 98 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "2 x * x = 98 = > x = 7 answer : c"
Answer: c
Python program:
a = 98 / 2
b = math.sqrt(a)
Problem: tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 2 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 40 , b ) 72 , c ) 84 , d ) 90 , e ) 108
Rationale: "a is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 2 t ) = 8 t = = > t = 1 / 3 = = > 20 minutes to travel double distance , 2 ( 2 + 2 t ) = 8 t = = > 1 = = > 60 minutes difference , 40 minutes a"
Answer: a
Python program:
a = 2 * 2
b = 2 * 2
c = 8 - b
d = a / c
e = 8 - 2
f = 2 / e
g = d - f
h = g * const_60
Problem: a and b began business with rs . 3000 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 . 840 find the share of a .
Options: a ) 240 , b ) 388 , c ) 379 , d ) 277 , e ) 320
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 840 = 320 answer : e"
Answer: e
Python program:
a = 3000 * 8
b = 3000 - 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 = 840 / k
m = 3000 * 8
n = 3000 - 1000
o = 12 - 8
p = n * o
q = m + p 
r = l * q
Problem: set # 1 = { a , b , o , d , e } set # 2 = { k , l , m , n , u , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 3 , e ) 2 / 3
Rationale: at least questions are best solved by taking the opposite scenario and subtracting it from 1 . probability of choosing no vowel from set 1 is 2 / 5 and set 2 is 5 / 6 . multiply these to get 1 / 3 . therefore , probability of picking at least one vowel = 1 - 1 / 3 = 2 / 3 . answer = e
Answer: e
Python program:
a = 2 + 3 
b = 2 / a
c = 2 + 3 
d = 2 + 3 
e = d + 1 
f = c / e
g = b * f
h = 1 - g
Problem: the value of x + ( xx ) when x = 3 is :
Options: a ) a ) 36 , b ) b ) 12 , c ) c ) 18 , d ) d ) 64 , e ) e ) 10
Rationale: x + ( xx ) put the value of x = 2 in the above expression we get , 3 + ( 33 ) = 3 + ( 3 × 3 ) = 3 + ( 9 ) = 3 + 9 = 12 b
Answer: b
Python program:
a = 3 * 3
b = a + 3
Problem: roy is now 6 years older than julia and half of that amount older than kelly . if in 2 years , roy will be twice as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 84 , b ) 96 , c ) 100 , d ) 108 , e ) 120
Rationale: "r = j + 6 = k + 3 r + 2 = 2 ( j + 2 ) ( j + 6 ) + 2 = 2 j + 4 j = 4 r = 10 k = 7 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 9 = 108 the answer is d ."
Answer: d
Python program:
a = 6 - 2
b = 6 + a 
c = b + 2 
d = 6 - 2
e = 6 + d 
f = 6 / 2
g = e - f
h = g + 2 
i = c * h
Problem: if x is equal to the sum of the integers from 30 to 40 , inclusive , and y is the number of even integers from 30 to 40 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 591 , e ) 601
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 30 + ( 11 - 1 ) * 1 } = 11 * 35 = 385 = x number of even number = ( 40 - 30 ) / 2 + 1 = 6 = y x + y = 385 + 6 = 391 c"
Answer: c
Python program:
a = 30 + 40 
b = a / 2
c = 40 - 30
d = c + 1 
e = b * d
f = 40 - 30
g = f / 2
h = g + 1 
i = e + h
Problem: a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 850.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.40 , b ) $ 11.30 , c ) $ 12.14 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 850 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 850 / 70 ~ 12.14 c"
Answer: c
Python program:
a = 40 / 100
b = 4 + 3 
c = 40 / 100
d = 20 / 4
e = d / 100
f = c + e 
g = b + f 
h = a + g
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 100 feet . what is its area , in square feet ?
Options: a ) 4,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 100 , you can deduce the following a = 60 b = 80 60 x 80 = 4,800 a is the answer ."
Answer: a
Python program:
a = 2 + 3 
b = 100 / a
c = b * 3
d = 2 + 3 
e = 100 / d
f = e * 4
g = c * f
Problem: 19 balls are numbered 1 to 19 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 2 / 9 , b ) 4 / 19 , c ) 6 / 29 , d ) 8 / 39 , e ) 10 / 49
Rationale: "p ( 1 st ball is even ) = 9 / 19 p ( 2 nd ball is also even ) = 8 / 18 p ( both balls are even ) = 9 / 19 * 8 / 18 = 4 / 19 the answer is b ."
Answer: b
Python program:
a = 4 + 4 
b = a / 19
c = 4 + 4 
d = c - 1
e = 19 - 1
f = d / e
g = b * f
Problem: in the first 12 overs of a cricket game , the run rate was only 4.5 . what should be the run rate in the remaining 38 overs to reach the target of 360 runs ?
Options: a ) 9.55 , b ) 6.25 , c ) 6.75 , d ) 8.05 , e ) 7.25
Rationale: required run rate = 360 - ( 4.5 x 12 ) / 38 = 306 / 38 = 8.05 option d
Answer: d
Python program:
a = 12 * 4
b = 360 - a
c = b / 38
Problem: a car during its journey travels 1 hour at a speed of 40 kmph , another 30 minutes at a speed of 60 kmph , and 2 hours at a speed of 60 kmph . the average speed of the car is
Options: a ) 63.07 kmph , b ) 54.28 kmph , c ) 62.02 kmph , d ) 64.02 kmph , e ) none of these
Rationale: first car travels 1 hrs at speed of 40 kmph distance = 40 x 1 = 40 m then car travels 30 min at a speed of 60 kmph distance = 30 min at speed of 60 kmph distance = 60 x 1 / 2 = 30 m at last it travels 2 hours at speed of 60 kmph distance = 60 x 2 = 120 m total distance = 40 + 30 + 120 = 190 total time = 1 + 1 / 2 + 2 = 3.50 average speed of the car = 190 / 3.25 = 54.28 answer : b
Answer: b
Python program:
a = 40 + 30 
b = 60 + 60 
c = a + b 
d = 30 / const_60
e = 1 + d 
f = e + 2 
g = c / f
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 26 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 9 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 26 s = ( 27 x + 17 y ) / ( x + y ) = 26 = ( 27 x + 17 y ) / = 26 ( x + y ) = x = 9 y = x / y = 9 / 1 answer : b"
Answer: b
Python program:
a = 27 - 26
b = 26 - 17
c = a / b
Problem: 5358 x 56 = ?
Options: a ) 272258 , b ) 272358 , c ) 300048 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 6 ) = 5358 x 50 + 5358 x 6 = 267900 + 32148 = 300048 . c )"
Answer: c
Python program:
a = 5358 / 56
b = a * 100
Problem: excluding stoppages , the speed of a bus is 80 kmph and including stoppages , it is 60 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 12 min , b ) 20 min , c ) 25 min , d ) 30 min , e ) 15 min
Rationale: "due to stoppages , it covers 20 km less . time taken to cover 20 km = ( 20 / 80 x 60 ) min = 15 min answer : e"
Answer: e
Python program:
a = 80 - 60
b = a / 80
c = const_60 * b
Problem: the average age of a , b and c is 27 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 23
Rationale: age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 27 ã — 3 â € “ 29 ã — 2 = 81 â € “ 58 = 23 years e
Answer: e
Python program:
a = 27 * 3
b = 29 * 2
c = a - b
Problem: a man buys a cycle for rs . 1400 and sells it at loss of 15 % . what is the selling price of the cycle ?
Options: a ) 1192 , b ) 1191 , c ) 1118 , d ) 1190 , e ) 1112
Rationale: "explanation : s . p = 85 % of rs . 1400 ⇒ rs . ( 8510085100 × 1400 ) = rs . 1190 . answer : d"
Answer: d
Python program:
a = 100 - 15
b = a * 1400
c = b / 100