euclaise/mathqa_programs huggingface dataset:
Problem: if 20 men can build a wall 66 metres long in 4 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 278.4 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 567.6 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 4 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 4 * 20 ) = 567.6 mtrs answer : e"
Answer: e
Python program:
a = 86 * 8
b = 20 * 4
c = a / b
d = 66 * c
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 250 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 50 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 250 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 250 ) * 100 / 500 = 50 % answer : option c"
Answer: c
Python program:
a = 250 / 500
b = a * 100
Problem: a train , 800 meter long is running with a speed of 78 km / hr . it crosses a tunnel in 1 minute . what is the length of the tunnel ( in meters ) ?
Options: a ) 440 m , b ) 500 m , c ) 260 m , d ) 430 m , e ) 450 m
Rationale: "explanation : distance = 800 + x meter where x is the length of the tunnel time = 1 minute = 60 seconds speed = 78 km / hr = 78 × 10 / 36 m / s = 130 / 6 = 65 / 3 m / s distance / time = speed ( 800 + x ) / 60 = 65 / 3 = > 800 + x = 20 × 65 = 1300 = > x = 1300 - 800 = 500 meter answer : option b"
Answer: b
Python program:
a = 78 * 1000
b = a / 3600
c = b * const_60
d = c - 800
Problem: a library has an average of 150 visitors on sundays and 120 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 50 , b ) 75 , c ) 150 , d ) 125 , e ) 100
Rationale: "since the month begin with sunday , so there will be five sundays in the month required average = ( 150 * 5 + 120 * 25 ) / 30 = 3750 / 30 = 125 answer is d"
Answer: d
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 150
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 120
l = e + k 
m = l / 30
Problem: find the smallest number which should be multiplied with 520 to make it a perfect square .
Options: a ) 30 , b ) 120 , c ) 55 , d ) 35 , e ) none of these
Rationale: "520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square . answer : e"
Answer: e
Python program:
a = 520 / 3
b = a / 3
c = b / 4
d = c / 4
e = d / 4
Problem: in a company of 200 employees , 120 are females . a total of 100 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with a college degree only , how many employees are females with advanced degrees ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "the number of males is 200 - 120 = 80 . the number of males with advanced degrees is 80 - 40 = 40 . the number of females with advanced degrees is 100 - 40 = 60 . the answer is a ."
Answer: a
Python program:
a = 200 - 120
b = a - 40
c = 100 - b
Problem: in what ratio should a variety of rice costing rs . 4.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 12
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 4.5 ) = 5 / 12 answer : e"
Answer: e
Python program:
a = 8 - 75
b = 8 - 75
c = a / b
d = 8 - 75
e = 8 - 75
f = d / e
g = 1 - f
h = c / g
Problem: in a certain pond , 60 fish were caught , tagged , and returned to the pond . a few days later , 60 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1818 , d ) 2500 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 60 * 100 = 3.33 % . we are told that 3.33 % approximates the percent of tagged fish in the pond . since there are 60 tagged fish , then we have 0.033 x = 60 - - > x = 1,818 . answer : c ."
Answer: c
Python program:
a = 2 / 60
b = 60 / a
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 10 minutes . the length of the bridge is ?
Options: a ) 500 m , b ) 1110 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 10 minutes = 15 / 18 * 10 * 60 = 500 m answer is a"
Answer: a
Python program:
a = 15 * 1000
b = a / const_60
c = b * 10
Problem: 12 + 13 + 14 + . . . 61 + 62 + 63 = ?
Options: a ) 1361 , b ) 1362 , c ) 1950 , d ) 1364 , e ) 1365
Rationale: "sum = 12 + 13 + 14 + . . . 61 + 62 + 63 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 63 positive integers = 63 * 64 / 2 sum of first 11 positive integers = 11 * 12 / 2 sum = 12 + 13 + 14 + . . . 61 + 62 + 63 = 63 * 64 / 2 - 11 * 12 / 2 = 1950 answer : c"
Answer: c
Python program:
a = 61 + 12 
b = 61 * a
c = b / 13
Problem: tickets numbered from 1 to 21 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 21 = 1 / 3 the answer is a ."
Answer: a
Python program:
a = 21 / 3
b = a / 21
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 63 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 63 1 percent for 1 year = 21 = > 100 percent = 2100 answer : b"
Answer: b
Python program:
a = 63 / 3
b = a * 100
Problem: ( 128.5 x 64 ) + ( 13.8 x 465 ) = ? x 25
Options: a ) 524.48 , b ) 556.02 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 64 ) + ( 13.8 x 465 ) / 25 = 8224 + 6417 / 25 = 585.64 answer : option d"
Answer: d
Python program:
a = 4 + 1 
b = a ** 4
c = 128 * 5
Problem: 128 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 160 , b ) 190 , c ) 225 , d ) 250 , e ) 500
Rationale: let b be the number of boys in the school . 128 = xb / 100 b = 0.5 x 12800 = 0.5 x ^ 2 x ^ 2 = 25600 x = 160 the answer is a .
Answer: a
Python program:
a = 128 * 100
b = 50 / 100
c = a / b
d = math.sqrt(c)
Problem: a basket contains 5 apples , of which 1 is spoiled and the rest are good . if henry is to select 2 apples from the basket simultaneously and at random , what is the possibility that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 5 , b ) 3 / 10 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: "p ( both apples are not spoiled ) = 4 c 2 / 5 c 2 = 4 * 3 / 5 * 4 = 3 / 5 p ( one of the apple spoiled ) = 1 - 3 / 5 = 2 / 5 answer is c ."
Answer: c
Python program:
a = 5 - 1
b = math.comb(a, 1)
c = math.comb(5, 2)
d = b / c
Problem: the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference w would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference w = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Python program:
a = 40 * 3
b = a * 3
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 7500 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 87.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 7500 ⇔ 12 x 2 = 7500 ⇔ x 2 = 625 ⇔ x = 25 . so , length = 75 m and breadth = 100 m . perimeter = [ 2 ( 75 + 100 ) ] m = 350 m . ∴ cost of fencing = rs . ( 0.25 × 350 ) = rs . 87.50 . answer d"
Answer: d
Python program:
a = 3 * 4
b = 7500 / a
c = math.sqrt(b)
d = 3 * c
e = 3 * 4
f = 7500 / e
g = math.sqrt(f)
h = 4 * g
i = rectangle_perimeter * (
j = i / 25
Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is
Options: a ) 38 % , b ) 40 % , c ) 44 % , d ) 48 % , e ) 50 %
Rationale: let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy c )
Answer: c
Python program:
a = 100 + 20 
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 5 ?
Options: a ) 4 / 3 , b ) 3 / 2 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 5 + 1 ) / ( 5 - 1 ) = 6 / 4 = 3 / 2 answer : b"
Answer: b
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 5
d = c / 100
Problem: find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm ?
Options: a ) 140 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 182 cm 2 , e ) 200 cm 2
Rationale: "1 / 2 * 28 ( 8 + 2 ) = 140 cm 2 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 2 + 8 
c = a * b
d = c * 28
Problem: 3 machines operating independently , simultaneously , and at the same constant rate can fill a certain production order in 44 hours . if one additional machine were used under the same operating conditions , in how manyfewerhours of simultaneous operation could the production order be fulfilled ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 11 , e ) 48
Rationale: if 3 machines can do the work in 44 hr then 4 machines can do the work in 3 / 4 * 44 = 33 hrs . hence time saved will be 11 hr option d is the correct answer
Answer: d
Python program:
a = 3 * 44
b = 3 + 1 
c = a / b
d = 44 - c
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are accounting majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are accounting majors is p = 3 . the answer is a .
Answer: a
Python program:
a = 2 + 3 
b = 2 + 3 
c = b + 2 
d = a * c
e = 10 + 3 
f = d * e
g = 1365 / f
Problem: a train 250 m long is running at a speed of 58 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : d . speed of the train relative to man = ( 58 - 8 ) kmph = ( 50 * 5 / 18 ) m / sec = ( 125 / 9 ) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 125 / 9 m / sec = 250 * 9 / 125 sec = 18 sec"
Answer: d
Python program:
a = 58 - 8
b = a * const_0_2778
c = 250 / b
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 10 ) . what is the slope of line m ?
Options: a ) - 3 , b ) 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : b solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 10 ) . midpoint is ( 4 , - 3 ) as we can see that the y axis of intercept point is ( 0 , - 2 ) means line m is parallel to x axis slope m = 1 ans : b"
Answer: b
Python program:
a = 4 - 10
b = a / 2
c = b + 2 
d = 2 + 6 
e = d / 2
f = c / e
Problem: on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: "0.20 p = rt + c 0.5 ( rt ) = no c = > 0.50 ( rt ) had c 0.20 p = 0.50 ( rt ) rt / p = 40 % answer - b"
Answer: b
Python program:
a = 100 - 50
b = a / 100
c = 20 / b
Problem: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108
Rationale: total students = 420 boys = 312 , girls = 108 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 108 - 35 = 73 . correct option : b
Answer: b
Python program:
a = 420 - 312
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 60 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 180 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 60 percent 180 min . answer : d
Answer: d
Python program:
a = 60 / 20
b = a * const_60
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 14 . what is the value of f ( 6 ) ?
Options: a ) 3 , b ) 0 , c ) 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 14 then f ( 5 ) = 14 - 5 = 9 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 9 - 6 = 3 . answer : a . questions on funtions to practice :"
Answer: a
Python program:
a = 1 + 4 
b = 14 - a
c = b - 6
Problem: the banker â € ™ s discount of a certain sum of money is rs . 80 and the true discount on the same sum for the same time is rs . 70 . the sum due is
Options: a ) 210 , b ) 280 , c ) 560 , d ) 450 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 80 * 70 / 80 - 70 ] = rs . [ 80 * 70 / 10 ] = rs . 560 answer c"
Answer: c
Python program:
a = 80 * 70
b = 80 - 70
c = a / b
Problem: in what time will a train 150 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 3.8 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 150 / 40 = 3.8 sec . answer : c"
Answer: c
Python program:
a = 144 * const_0_2778
b = 150 / a
Problem: from a container having pure milk , 10 % is replaced by water and the process is repeated twice . at the end of the second operation , the milk is ?
Options: a ) 50 % , b ) 60 % , c ) 55 % , d ) 75 % , e ) 81 %
Rationale: "let the total quantity of original milk = 1000 gm milk after 1 st operation = 90 % of 1000 = 900 gm milk after second operation = 90 % of 900 = 810 gm strength of final mixture = 81 % answer is e"
Answer: e
Python program:
a = 100 - 10
b = a / 100
c = b ** 3
d = c * 100
Problem: what is the smallest number which , when increased by 9 , is divisible by 8 , 11 , and 24 ?
Options: a ) 237 , b ) 246 , c ) 255 , d ) 264 , e ) 273
Rationale: lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 9 = 255 . the answer is c .
Answer: c
Python program:
a = math.lcm(24, 11)
b = a - 9
Problem: on an order of 19 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 0.05 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %
Rationale: "clearly , the retailer gets 1 dozen out of 20 dozens free . equivalent discount = 1 / 20 * 100 = 5 % . answer d ) 5 %"
Answer: d
Python program:
a = 19 / 4
b = a * 100
c = 100 - b
Problem: a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.02 % , c ) 0.2 % , d ) 4 % , e ) 40 %
Rationale: we are given that 0.02 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.02 by 20 . this gives us : 0.02 x 20 = 0.4 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.4 / 10 ) x 100 % ( 4 / 100 ) x 100 % = 4 % answer d
Answer: d
Python program:
a = 0 * 2
b = a / 10
c = b * 100
Problem: i sold a book at a profit of 10 % . had i sold it for $ 140 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 2800 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 140 5 % of cost = $ 140 cost = 140 * 100 / 5 = $ 2800 answer is d"
Answer: d
Python program:
a = 140 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
Problem: a glass was filled with 15 ounces of water , and 0.05 ounce of the water evaporated each day during a 15 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.005 % , b ) 0.05 % , c ) 0.5 % , d ) 5 % , e ) 25 %
Rationale: "in 15 days 15 * 0.05 = 0.75 ounces of water evaporated , which is 0.75 / 15 â ˆ — 100 = 5 of the original amount of water . answer : d ."
Answer: d
Python program:
a = 0 * 5
b = a / 15
c = b * 100
Problem: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 10 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 15 days , c ) 12 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 10 x = 15 days answer : option b"
Answer: b
Python program:
a = 1/(10)
b = 1/(15)
c = 5 * b
d = 1 - c
e = a * d
f = 1/(e)
Problem: in a hostel there were 100 students . to accommodate 25 more students the average is decreased by rupees 10 . but total expenditure increased by rs . 500 . find the total expenditure of the hostel now ?
Options: a ) 7500 , b ) 5000 , c ) 5400 , d ) 7000 , e ) 8500
Rationale: let average is x 100 x + 500 = 125 ( x – 10 ) x = 70 100 * 70 + 500 = 7500 answer : a
Answer: a
Python program:
a = 100 + 25 
b = a * 10
c = b + 500 
d = c / 25
e = d - 10
f = 100 + 25 
g = e * f
Problem: the area of a square is 4356 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 7 : 12 , d ) 5 : 13 , e ) 7 : 22
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4356 a = 66 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 42 : 132 = 7 : 22 answer : e"
Answer: e
Python program:
a = math.sqrt(4356)
b = a - 24
c = math.sqrt(4356)
d = c * 2
e = b / d
Problem: pat , kate , and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 80 , c ) 72 , d ) 90 , e ) 108
Rationale: "80 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 144 = > x = 16 32 : 16 : 96 96 - 16 = 80 answer b"
Answer: b
Python program:
a = 1 / 3
b = 1 + a 
c = 3 * 2
d = 1 / c
e = b + d 
f = 144 / e
g = 1 / 3
h = 1 + g 
i = 3 * 2
j = 1 / i
k = h + j 
l = 144 / k
m = 3 * 2
n = l / m
o = f - n
Problem: at the end of the first quarter , the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 50 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 15.3 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 50 = 30 + b + 30 b / 100 b = 15.3 answer ( a )"
Answer: a
Python program:
a = 100 + 50 
b = 100 + 30 
c = a / b
d = c - 1
e = d * 100
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 50 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: percent of students who are 25 years old or older is 0.5 * 48 + 0.2 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 3 = 66 . answer : b .
Answer: b
Python program:
a = 50 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 1 - d
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6200 ?
Options: a ) rs . 7070 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6200 * 6 ) – 30,130 ] = rs . ( 37200 – 30,130 ) = rs . 7070 answer a"
Answer: a
Python program:
a = 5 + 1 
b = a * 6200
c = 5420 + 5660 
d = c + 6200 
e = d + 6350 
f = e + 6500 
g = b - f
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 1 , 000,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 1000 ( 1 , 000,000 / 1,000 = 1000 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 1000 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . i . e . the population has to double 10 times . since it takes the population 2 minutes to double once it takes 10 * 2 minutes = 20 minutes to double nine times . thus , solution e = 20 is correct ."
Answer: e
Python program:
a = 4 + 1 
b = a * 1
c = b * 100
d = c / 1
e = math.log(d)
f = e * 3
Problem: the present worth of rs . 1183 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 1093.75 , e ) none
Rationale: "solution present worth = rs . [ 1183 / ( 1 + 4 / 100 ) ² ] = rs . ( 1183 x 25 / 26 x 25 / 26 ) = rs . 1093.75 answer d"
Answer: d
Python program:
a = 4 / 100
b = a + 1 
c = b ** 2
d = 1183 / c