euclaise/mathqa_programs huggingface dataset:
Problem: simplify : 500 x 500 - 200 x 200
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 210000 , e ) none of them
Rationale: "( 500 ) ^ 2 - ( 200 ) ^ 2 = ( 500 + 200 ) ( 500 - 200 ) = 700 x 300 = 210000 . answer is d ."
Answer: d
Python program:
a = 500 * 500
b = 200 * 200
c = a + b
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 4320 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 12000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 4320 â ˆ — 100 / 12 â ˆ — 3 = rs 12000 option c"
Answer: c
Python program:
a = 4320 * 100
b = 12 * 3
c = a / b
Problem: a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 10 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 27 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 10 % are male i . e 10 / 100 * 20 = 2 geese ( males ) and now we know out of the total 20 geese , 2 are male , then 18 have to be female . now the ratio part , male geese ratios = 2 / 30 = 1 / 15 . - a female geese ratios = 18 / 70 = 9 / 35 - b cross multiply equations a and b and you get = 7 / 27 . ans d"
Answer: d
Python program:
a = 10 / 100
b = 30 / 100
c = a / b
d = 2 * 4
e = d * 10
f = e / 100
g = 30 / 100
h = f / g
i = c / h
Problem: of 64 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 64 thrower = 37 rest = 64 - 37 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 37 + 18 = 55 so b . 55 is the right answer"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 64 - 37
d = b * c
e = 37 + d
Problem: pipe a can fill a tank in 30 minutes . pipe b can fill the same tank 6 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 15 / 4 minutes , c ) 192 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 30 minutes - - > the rate of a = 1 / 30 tank / minute ; pipe b can fill the same tank 6 times fasterthan pipe a - - > the rate of b = 1 / 30 + 6 / 30 = 7 / 30 tank / minute . their combined rate = 1 / 30 + 7 / 30 = 4 / 15 tank / minute ; therefore , a and b can fill the tank in 15 / 4 minutes . answer : b"
Answer: b
Python program:
a = 1 / 30
b = 1 / 30
c = 6 / 30
d = b + c 
e = a + d 
f = 1/(e)
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 9 days , then c alone can do it in ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 19 , e ) 16
Rationale: "c = 1 / 4 - 1 / 12 – 1 / 9 = 1 / 18 = > 18 days ' answer : c"
Answer: c
Python program:
a = 1 / 12
b = const_0_25 - a
c = 1 / 9
d = b - c
e = 1 / d
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6.4 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: since michelle earns 6.4 % interest compounded semiannually , then she earns 3.2 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3.2 % * 5 = 16 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 16 % , only answer choice a fits . answer : a
Answer: a
Python program:
a = 6 / 4
b = a / 2
c = 1 + b 
d = 2 + 3 
e = c ** d
f = e * 100
Problem: a certain maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight . a certain green paint contains 30 percent blue pigment and 70 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 3 , b ) 3.5 , c ) 2.5 , d ) 4 , e ) 4.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 5 = 2.5 grams of red pigment
Answer: c
Python program:
a = 100 + 100 
b = 50 / a
c = b * 10
Problem: chris age after 15 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) 20 , b ) 25 , c ) 15 , d ) 22 , e ) 10
Rationale: "chris present age = x after 15 years = x + 15 5 years back = x - 5 x + 15 = 5 ( x - 5 ) x = 10 answer is e"
Answer: e
Python program:
a = 5 * 5
b = a + 15 
c = 5 - 1
d = b / c
e = 5 * 5
f = e + 15 
g = 5 - 1
h = f / g
i = h - 5
j = d - i
Problem: a can do a work in 14 days and working together a and b can do the same work in 10 days . in what time can b alone do the work ?
Options: a ) 25 days , b ) 30 days , c ) 23 days , d ) 35 days , e ) 45 days
Rationale: work done by b in 1 day = 1 / 10 - 1 / 14 = ( 7 - 5 ) / 70 = 1 / 35 so , b alone can do the work in 35 days . answer : d
Answer: d
Python program:
a = 1 / 10
b = 1 / 14
c = a - b
d = 1 / c
Problem: if the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 53 , c ) 49 , d ) 48 , e ) 44
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b"
Answer: b
Python program:
a = 45 * 5
b = a - 10
c = b / 5
d = c + 10
Problem: find the lowest common multiple of 24 , 30 and 40 .
Options: a ) 360 , b ) 420 , c ) 120 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 5 = 120 . answer is c"
Answer: c
Python program:
a = math.lcm(24, 30)
b = math.lcm(a, 40)
Problem: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 13.3 hrs , c ) 1.9 hrs , d ) 7.2 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 5 - 1 / 8 ) = 3 / 40 the cistern will be filled in 40 / 3 hrs i . e . , 13.3 hrs . answer : b"
Answer: b
Python program:
a = 1 / 5
b = 1 / 8
c = a - b
d = 1 / c
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 4 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 2 / 5 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 4 / 8 * c : ( b + c ) / 2 = ( 4 / 8 ) * c b = 0 for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 0 ) / 2 = 0 median = ( a + c ) / 2 = ( 0 + c ) / 2 = c / 2 = ( 1 / 2 ) * c ( answer b )"
Answer: b
Python program:
a = 4 / 8
b = a * 2
c = b - 1
d = 3 / 4
e = d * 2
f = e - 1
g = 1 / f
h = c / g
i = 1 + h 
j = i / 2
Problem: a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 360 less than the sum lent . what was the sum lent ?
Options: a ) 540 , b ) 560 , c ) 580 , d ) 600 , e ) 680
Rationale: "p - 360 = ( p * 5 * 8 ) / 100 p = 600 the answer is d ."
Answer: d
Python program:
a = 5 * 8
b = a / 100
c = 1 - b
d = 360 / c
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 19 days more ?
Options: a ) 11 , b ) 40 , c ) 66 , d ) 55 , e ) 44
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 19 x * 19 = 760 * 20 x = 800 760 - - - - - - - 40 answer : b"
Answer: b
Python program:
a = 22 - 2
b = 760 * a
c = b / 19
d = c - 760
Problem: if p represents the product of the first 14 positive integers , then p is not a multiple of
Options: a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 85
Rationale: "answer is e . since prime factor of 85 is 5 x 17 . 17 is a prime number and not part of the first 14 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 5 x 17"
Answer: e
Python program:
a = 14 + 3 
b = a * 3
Problem: how many pieces of 0.36 meteres can be cut from a rod 26.5 meteres long
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 73
Rationale: "explanation : we need so simple divide 26.5 / 0.36 , = ( 2650 / 36 ) = 73 option d"
Answer: d
Python program:
a = 26 / 5
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 25 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 36 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.0 x = 1.4 x 1.4 x / 5 x = 0.28 the answer is a ."
Answer: a
Python program:
a = 40 / 100
b = 25 / 100
c = 4 * b
d = a + c 
e = 1 + 4 
f = d / e
g = 100 * f
Problem: the temperature of a certain cup of coffee 5 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 61.875 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 5 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 5 a ) + 60 60 = 120 * ( 2 ^ - 5 a ) 60 / 120 = 2 ^ - 5 a 1 / 2 = 2 ^ - 5 a 2 ^ - 1 = 2 ^ - 5 a - 1 = - 5 a 1 / 5 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 5 * 30 ) + 60 f = 120 * ( 2 ^ - 6 ) + 60 f = 120 * ( 1 / 2 ^ 6 ) + 60 f = 120 * 1 / 64 + 60 f = 1.875 + 60 = 61.875 answer b !"
Answer: b
Python program:
a = 60 / 5
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: 5 n + 2 > 12 and 7 n - 12 < 44 ; n must be between which numbers ?
Options: a ) 2 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: "5 n + 2 > 12 5 n > 10 n > 2 7 n - 12 < 44 7 n < 56 n < 8 so n must be between 2 and 8 2 < n < 8 correct answer a"
Answer: a
Python program:
a = 2 * 10
b = 44 + 12 
c = b / 7
d = a + c
Problem: a pupil ' s marks were wrongly entered as 73 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 56 , b ) 80 , c ) 20 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 73 - 45 ) = > x / 2 = 28 = > x = 56 . answer : a"
Answer: a
Python program:
a = 73 - 45
b = a * 2
Problem: a cube of edge 8 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 22 , c ) 1 : 52 , d ) 1 : 64 , e ) none
Rationale: "sol . required ratio = 6 * 1 * 1 / 6 * 8 * 8 = 1 / 64 = 1 : 64 . answer d"
Answer: d
Python program:
a = 4 / 100
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 6 ] ] ?
Options: a ) 3 , b ) 52 , c ) 15 , d ) 19 , e ) 25
Rationale: "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 6 ] ] = 6 ^ 2 + 2 * 6 + 4 = 52 . option b"
Answer: b
Python program:
a = 2 ** 2
b = 2 * 2
c = a + b 
d = c + 4
Problem: 2015.98 + 1275.087 – 175.98 × 0.95 + 988.09 = ?
Options: a ) 4004 , b ) 4725 , c ) 4404 , d ) 4044 , e ) 4055
Rationale: "explanation : = 2016 + 1275 – 275.98 × 1 + 988 = 2016 + 1275 - 275 + 988 = 4004 answer : option a"
Answer: a
Python program:
a = 1275 * 87
b = 0 / 95
c = a / b
d = 2015 + 98
Problem: the sum of ages of 5 children born 3 years different each is 50 yrs . what is the age of the elder child ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 19 , e ) 20
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . x + 12 = 4 + 12 = 16 c"
Answer: c
Python program:
a = 3 + 4 
b = 3 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 50 
g = f / 5
Problem: the average of 6 no . ' s is 5.40 . the average of 2 of them is 5.2 , while the average of the other 2 is 5.80 . what is the average of the remaining 2 no ' s ?
Options: a ) 5.2 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 5.40 * 6 ) - [ ( 5.2 * 2 ) + ( 5.8 * 2 ) ] = 32.40 - ( 10.4 + 11.6 ) = 32.40 - 22.0 = 10.40 . required average = ( 10.4 / 2 ) = 5.2 answer : a"
Answer: a
Python program:
a = 6 * 5
b = 2 * 5
c = 2 * 5
d = b + c 
e = a - d
f = e / 2
Problem: a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ?
Options: a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 60
Rationale: the weight of one car and one truck is 5.75 tons . 70 / 5.75 = 12 plus a remainder the ferry could carry 12 cars and 12 trucks for a total of 24 vehicles . the answer is b .
Answer: b
Python program:
a = 0 + 75 
b = 70 / a
c = 0 + 75 
d = 70 / c
e = b + d
Problem: x , a , z , and b are single digit positive integers . x = 1 / 8 a . z = 1 / 8 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 28 , b ) 35 , c ) 49 , d ) 63 , e ) 55
Rationale: "a = 8 x , b = 8 z therefore ( 8 x . 10 + 8 z ) - ( 10 x + z ) = ( 8 - 1 ) ( 10 x + z ) = 7 . ( 10 x + z ) number should be divisible by 7 e"
Answer: e
Python program:
a = 8 * 8
b = 8 * 10
c = a + b 
d = 8 * 10
e = d + 8 
f = c - e
g = f + 10 
h = g + 3
Problem: two positive integers differ by 4 , and sum of their reciprocals is 4 . then one of the numbers is
Options: a ) a ) 3 , b ) b ) 1 , c ) 2 , d ) d ) 21 , e ) e ) 28
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 4 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 4 or ( n ^ 2 + 4 n ) * 4 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , c"
Answer: c
Python program:
a = 4 + 4
Problem: if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 110 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 71 , b ) 72 , c ) 73 , d ) 74 , e ) 75
Rationale: let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 110 3 x = 105 x = 35 kg then the student ' s weight is 75 kg . the answer is e .
Answer: e
Python program:
a = 110 - 5
b = a / 3
c = 110 - b
Problem: what annual installment will discharge a debt of rs . 1428 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 345 , c ) 425 , d ) 335 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1428 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1428 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1428 * 25 ) x = ( 1428 * 25 ) / 84 = rs . 425 . therefore , each installment = rs . 425 . answer is c ."
Answer: c
Python program:
a = 12 / 1428
b = 100 * 0
c = b * 3
Problem: in a group of ducks and cows , the total number of legs are 16 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 8 , d ) 12 , e ) 14
Rationale: let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 16 = > 2 x = 16 = > x = 8 c
Answer: c
Python program:
a = 16 / 2
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 4 . if x invested rs . 40,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 40000 / y = 2 / 4 â € ¹ = â € º y = ( 40000 ã — 4 / 2 ) . â € ¹ = â € º y = 80000 . answer d"
Answer: d
Python program:
a = 1 + 4 
b = a * 1000
c = b * 2
d = c / 4
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 110 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 55 , c ) 56 , d ) 16 , e ) 14
Rationale: 10 x = 110 = > x = 11 therefore the secretary who worked the longest spent 11 x 5 = 55 hours on the project option ( b )
Answer: b
Python program:
a = 2 + 3 
b = a + 5 
c = 110 / b
d = c * 5
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 155 kg then find the average weight of all the 7 rounds ?
Options: a ) 98.5 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 155 / 7 = 88.5 kgs answer : b"
Answer: b
Python program:
a = 1 + 3 
b = a * 155
c = b / 7
Problem: set j consists of 18 consecutive even numbers . if the smallest term in the set is - 12 , what is the range of the positive integers in set j ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "since there are only 18 integers , another approach is the just list all 18 . we get : - 12 , - 10 , - 8 , - 6 , - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 range of positive integers = 22 - 2 = 20 answer : c"
Answer: c
Python program:
a = negate + ( 
b = 18 - 1
c = b * 2
d = a - c
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many s hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in s = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 4
c = a - b
d = 1/(c)
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 56 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 640,000
Rationale: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 56 years , the investment will get doubled 56 / 14 = 4 times . so the amount invested will get doubled thrice . so , 40000 * 2 ^ 4 = 640000 hence , the answer is e .
Answer: e
Python program:
a = 3600 / 10
Problem: having received his weekly allowance , a student spent 2 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.20 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 2.00 , b ) $ 2.25 , c ) $ 2.50 , d ) $ 2.75 , e ) $ 3.00
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 3 / 5 ) x = 120 cents ( 2 / 5 ) x = 120 x = $ 3.00 the answer is e ."
Answer: e
Python program:
a = 2 * 5
b = a * 1
c = b / 4
Problem: ashley paid 5 dollars for 1 notebook and 1 pencil . if both prices were integers , how many pencils did ashley buy if she paid 93 dollars for the pencils and for 15 notebooks ?
Options: a ) 6 . , b ) 16 . , c ) 18 , d ) 21 , e ) 26
Rationale: 5 = 1 p + 1 n 93 = xp + 15 n , where x is the number of pencils possible prices for 1 p & 1 n ( integers ) : n = 1 p = 4 then 15 n = 15 , 4 x = 93 - 15 = 78 , x = 19.5 ( not an integer ) n = 2 p = 3 then 15 n = 30 , 3 x = 93 - 30 = 63 , x = 21 ( the answer we were looking for , no need to continue calculations ) n = 3 p = 2 n = 4 p = 1 answer : d
Answer: d
Python program:
a = 15 + 5 
b = a + 1
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 5 - 1 / 6 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 85 / 2 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 5 - 1 / 6 = ( 6 - 5 ) / 30 = 1 / 30 so 17 / 12 / 1 / 30 = 17 / 12 * 30 = 85 / 2 answer - d"
Answer: d
Python program:
a = 10 * 5
b = a + 2 
c = b / 3
d = 10 + 1 
e = d / 4
f = c - e
Problem: a train running at the speed of 142 km / hr crosses a pole in 12 seconds . find the length of the train .
Options: a ) 540 , b ) 288 , c ) 200 , d ) 340 , e ) 712
Rationale: "speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time 45 * 12 = 540 meter answer : a"
Answer: a
Python program:
a = 142 * 1000
b = a / 3600
c = b * 12
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 10 inches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 10 , b ) 20 , c ) 17.5 , d ) 43 , e ) 50
Rationale: "his height was = 5 feet 5 inch = 10 + 60 = 70 inch . required % correction = 70 * ( 1.25 - 1 ) = 17.5 c"
Answer: c
Python program:
a = const_0_25 + const_0_25 
b = 25 + a 
c = b - 5
d = const_0_25 + const_0_25 
e = 25 + d 
f = e - 5
g = 100 + f 
h = c / g
i = h * 100