euclaise/mathqa_programs huggingface dataset:
Problem: if you wish to live to be 100 years old ( hypothetically ) , you must consume 500 calories less than your average daily allowance for your age . if you are in your 60 ' s , and your average daily allowance is 2000 calories per day , how many calories are you allowed in a week ?
Options: a ) 7000 , b ) 10500 , c ) 14000 , d ) 12000 , e ) 3500
Rationale: to determine the amount of calories allowed per day , you need to subtract 500 from 2000 , for a total of 1500 to determine the amount of calories allowed per week , you need to multiply the daily amount allowed ( 1500 ) by the number of days in a week ( 7 ) for a total of 10500 the correct answer is b
Answer: b
Python program:
a = 2000 - 500
b = 4 + 3 
c = a * b
Problem: 250 metres long yard , 51 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 5
Rationale: "51 trees have 50 gaps between them , required distance ( 250 / 50 ) = 15 e"
Answer: e
Python program:
a = 51 - 2
b = a + 1 
c = 250 / b
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 2783 in 3 years . find the rate percent ?
Options: a ) 15 , b ) 10 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 363 100 - - - ? = > 15 % answer : option a"
Answer: a
Python program:
a = 2783 - 2420
b = a / 2420
c = b * 100
Problem: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 16 ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 1 * 1 / 8 = 1 / 8 answer : b"
Answer: b
Python program:
a = 2 / 16
Problem: how many zeros are there in 50 !
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "to find the number of trailing zeroes in 50 ! factorial we must find the number of integral values in : 50 / 5 + 50 / 5 ^ 2 + 50 / 5 ^ 3 + . . . . . . . . . = 10 + 2 + 0 + 0 . . . . = 12 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 50 / a
c = 4 + 1 
d = 50 - c
e = 4 + 1 
f = e ** 2
g = d / f
h = b + g 
i = 4 + 1 
j = 50 - i
k = 4 + 1 
l = k ** 3
m = j / l
n = h + m
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 450 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 2 / 1 , c ) 8 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 450 / 3 = 150 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 150 / 75 = 2 / 1 answer b"
Answer: b
Python program:
a = 450 / 3
b = 300 / 4
c = a / b
Problem: pipe x that can fill a tank in an hour and pipe y that can fill the tank in half an hour are opened simultaneously when the tank is empty . pipe y is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 35 mins , b ) 30 mins , c ) 40 mins , d ) 32 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe x was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : b
Answer: b
Python program:
a = const_60 * 1
b = 15 / a
c = 1 - b
d = 1 + 2 
e = c / d
f = const_60 * 1
g = 15 / f
h = e + g 
i = h * const_60
Problem: a and b can complete a work in 15 days and 10 day . they started doing the work together but after 2 days b had to leave and a alone completed the remaining work . the whole work was completed in ?
Options: a ) 10 days , b ) 12 days , c ) 15 days , d ) 8 days , e ) 16 days
Rationale: "a + b 1 day work = 1 / 15 + 1 / 10 = 1 / 6 work done by a and b in 2 days = 1 / 6 * 2 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 now 1 / 15 work is done by a in 1 day 2 / 3 work will be done by a in 15 * 2 / 3 = 10 days total time taken = 10 + 2 = 12 days answer is b"
Answer: b
Python program:
a = 1 / 15
b = 1 / 10
c = a + b 
d = c * 2
e = 1 - d
f = e * 15
g = f + 2
Problem: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 6000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 6000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 6000 ) * t = = = > 3 d = ts + 6000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 6000 t - 2 d = - 2 st + 6000 t 2 d = 2 st - 6000 t d = st - 3000 t x 13 : d = s * t st - 3000 t = s * t s - 3000 = s - 1500 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 6000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 6000 2 = 3000 d = s * t d = 3000 * ( 1 / 2 ) d = 1500 answer : d"
Answer: d
Python program:
a = 6000 / 2
b = 1 / 2
c = a * b
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 30 , and 40 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 120 / 7 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 30 + 1 / 40 = 7 / 120 therefore they take 120 / 7 ratio = 120 / 7 = d"
Answer: d
Python program:
a = 1 / 30
b = 1 / 40
c = a + b 
d = 1 / c
e = 12 / d
Problem: the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 768 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 32 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "answer is a : 42 let w be the width , so length is 3 w . therefore : w * 4 w = 768 , solving for , w = 16 , so 3 w - w = 2 w = 2 * 16 = 32"
Answer: a
Python program:
a = 768 / 3
b = math.sqrt(a)
c = b * 3
d = 768 / 3
e = math.sqrt(d)
f = c - e
Problem: the sum of two numbers is 528 and their h . c . f . is 33 . the number of pairs of numbers satisfying the above conditions is :
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 15
Rationale: "explanation : let the required numbers be 33 a and 33 b . then , 33 a + 33 b = 528 . = > a + b = 16 . now , co - primes with sum 16 are ( 1 , 15 ) , ( 3 , 13 ) , ( 5 , 11 ) and ( 7 , 9 ) . â ˆ ´ required numbers are ( 33 * 1 , 33 * 15 ) , ( 33 * 3 , 33 * 13 ) , ( 33 * 5 , 33 * 11 ) , ( 33 x 7 , 33 x 9 ) . the number of such pairs is 4 . answer is a"
Answer: a
Python program:
a = 528 + 33 
b = 1 + 1 
c = a / b
d = 528 + 33 
e = 1 + 1 
f = d / e
g = f - 33
h = c * g
Problem: a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 3 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the sum of the numerator and denominator of the original fraction ?
Options: a ) 21 / 4 , b ) 35 , c ) 28 , d ) 26 , e ) 21
Rationale: x / y = 2 / 5 - > 1 ( x + 3 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 3 ) = 6 / 5 = > 10 x = 6 x + 18 = > x = 3 / 2 = > y = 5 / 2 * 3 / 2 = 15 / 4 so x + y = 21 / 4 the answer is a
Answer: a
Python program:
a = 5 / 2
b = a * 3
c = b + 3 
d = c / 2
Problem: it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 64 of the dish ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . after 25 days , the dish was 1 / 32 full . after 24 days , the dish was 1 / 64 full . the answer is c .
Answer: c
Python program:
a = math.log(64)
b = 30 - a
Problem: in what time will a train 95 m long cross an electric pole , it its speed be 214 km / hr ?
Options: a ) 1.6 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 214 * 5 / 18 = 59 m / sec time taken = 95 / 59 = 1.6 sec . answer : a"
Answer: a
Python program:
a = 214 * const_0_2778
b = 95 / a
Problem: q - 2 : how many two digit numbers of distinct digits can be formed by using digits 1 , 2 , 3 , 4 , 5 , 6 and 7 such that the numbers are divisible by 3 ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: concept : a number will be divisible by 3 if sum of all the digits of the number is divisible by 3 here the possible sum of the two distinct digits can be 3 , 6 , 9 and 12 only in order to satisfy the given condition if sum of digits = 3 , no . = 12 , 21 - - - 2 cases if sum of digits = 6 , no . = 15 , 24 , 42 , 51 - - - 4 cases if sum of digits = 9 , no . = 27 , 36 , 45 , 54 , 63 , 72 - - - 6 cases if sum of digits = 12 , no . = 57 , 75 - - - 2 cases total cases = 2 + 4 + 6 + 2 = 14 cases answer : option e
Answer: e
Python program:
a = 2 + 1 
b = a + 2 
c = b + 3 
d = c + 4 
e = d + 2
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 65 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 47 , e ) 49
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 65 t t = 1.4 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 1.4 = 49 miles answer : - e"
Answer: e
Python program:
a = 72 / const_60
b = a * 35
c = 65 - 35
d = b / c
e = 35 * d
Problem: the l . c . m . of two numbers is 42 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 35 , d ) 53 , e ) 54
Rationale: let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 42 or x = 7 . the numbers are 14 and 21 . hence , required sum = ( 14 + 21 ) = 35 . answer : option c
Answer: c
Python program:
a = 2 * 3
b = 42 / a
c = b * 3
d = 2 * 3
e = 42 / d
f = e * 2
g = c + f
Problem: if 20 % of a = b , then b % of 20 is the same as :
Options: a ) 4 % of a , b ) 8 % of a , c ) 12 % of a , d ) 9 % of a , e ) 1 % of a
Rationale: "20 % of a = b b % of 20 = = = = 4 % of a . answer : a"
Answer: a
Python program:
a = 20 / 20
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 150 . find the unknown rate of two towels ?
Options: a ) 400 , b ) 450 , c ) 500 , d ) 550 , e ) 600
Rationale: "10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 – 1050 = 450 b"
Answer: b
Python program:
a = 3 + 5 
b = a + 2 
c = b * 150
d = 5 * 150
e = c - d
f = 3 * 100
g = e - f
Problem: a present value of a machine is $ 400 . its value depletiation rate is 25 % per annum then find the machine value after 2 years ?
Options: a ) $ 125 , b ) $ 100 , c ) $ 200 , d ) $ 215 , e ) $ 225
Rationale: "p = $ 400 r = 25 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 400 * 3 / 4 * 3 / 4 = $ 225 approximately answer is e"
Answer: e
Python program:
a = 25 / 100
b = 1 - a
c = b ** 2
d = 400 * c
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 60.50 , his capital is ?
Options: a ) 24,200 , b ) 28,888 , c ) 24,600 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 60.50 32 x - 31 x = 6050 * 4 x = 24,200 . answer : a"
Answer: a
Python program:
a = 4 / 4
b = 60 / 50
Problem: a merchant purchased a jacket for $ 60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 20 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "actual cost = $ 60 sp = actual cost + mark up = actual cost + 20 % sp = 60 * 100 / 80 on sale sp = 80 / 100 ( 60 * 100 / 80 ) = 60 gross profit = $ 0 answer is a"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 60 / b
d = 20 / 100
e = 1 - d
f = c * e
g = f - 60
Problem: a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 50 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: "2240 = x * 1.4 = x * ( 7 / 5 ) . therefore , x = 2240 * 5 / 7 . 2240 is easily divided by 7 to be 320 , which is then easily multiplied by 5 to give x = 1600 . to get 50 % profit , you need 1600 * 1.5 = 2400 . answer : a"
Answer: a
Python program:
a = 100 + 50 
b = 100 + 40 
c = a / b
d = 2240 * c
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 80 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 8 : 5
b ) 9 : 25
c ) 5 : 8
d ) 25 : 9
e ) can not be determined from the information provided
Rationale: same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 40 / speed b since the times are same , 50 pi / speed a = 80 pi / speed b speeda / speed b = 50 pi / 80 pi = 5 / 8 correct option : c
Answer: c
Python program:
a = 50 / 2
b = circumface / (
Problem: what is the area inscribed by the lines y = 3 , x = 2 , y = x + 3 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 6 , e ) e ) 10
Rationale: "first , let ' s graph the lines y = 3 and x = 2 at this point , we need to find the points where the line y = x + 3 intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = x + 3 to get y = 2 + 3 = 5 perfect , when x = 2 , y = 5 , so one point of intersection is ( 2,5 ) for the horizontal line , we know that y = 3 , so we ' ll plug y = 3 into the equation y = x + 3 to get 3 = x + 3 . solve to get : x = 0 so , when y = 3 , x = 0 , so one point of intersection is ( 0,3 ) now add these points to our graph and sketch the line y = x + 3 at this point , we can see that we have the following triangle . the base has length 2 and the height is 2 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 2 ) = 2 answer : b"
Answer: b
Python program:
a = 3 - 2
b = a - 3
c = 3 * const_0_25
d = 3 - 3
e = d - 3
f = c * e
g = b * f
Problem: tough and tricky questions : distance / rate . on a reconnaissance mission , a state - of - the - art nuclear powered submarine traveled 300 miles to reposition itself in the proximity of an aircraft carrier . this journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster . what was the average speed , in miles per hour , for the actual journey ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 50
Rationale: say , if speed is 60 , 300 / 50 = 6 hrs and 300 / 60 = 5 hrs ( a reduction of 1 hr - > correct answer ) answer ( e )
Answer: e
Python program:
a = 300 * 10
b = a * 4
c = 10 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 10
g = f / 2
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 12000 . a ' s share is ?
Options: a ) 2500 , b ) 3500 , c ) 4500 , d ) 2800 , e ) 4000
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 12000 = 4000 answer : e"
Answer: e
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 12000 / h
j = a * i
Problem: one computer can upload 100 megabytes worth of data in 3 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 30 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 10 , c ) 9 , d ) 11 , e ) 13
Rationale: since the first computer can upload 100 megabytes worth of data in 3 seconds then in 3 * 10 = 30 seconds it can upload 10 * 100 = 1000 megabytes worth of data , hence the second computer in 30 seconds uploads 1300 - 1000 = 300 megabytes worth of data . the second computer can upload 100 megabytes of data in 10 seconds . answer : b .
Answer: b
Python program:
a = 1300 / 30
b = 100 / 3
c = a - b
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 40 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 40 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 140 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 140 - 90 ) / 90 * 100 = 40 % answer : d ."
Answer: d
Python program:
a = 100 + 40 
b = 100 - 10
c = a - b
d = c * 100
e = 100 - 10
f = d / e
Problem: two trains 130 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.44 , e ) 10.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 130 + 160 = 290 m . required time = 290 * 9 / 250 = 261 / 25 = 10.44 sec . ' answer : d"
Answer: d
Python program:
a = 130 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number w of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible w : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer
Answer: d
Python program:
a = 48 * 3
b = 3 * 4
c = a / b
d = 3 * 4
e = 48 - d
f = 48 * 3
g = 3 * 4
h = f / g
i = e / h
j = c + i
Problem: how many pieces of 75 cm can be cut from a rope 57 meters long ?
Options: a ) 30 , b ) 40 , c ) 76 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 57 meters long is = ( 57 meters ) / ( 75 cm ) = ( 57 meters ) / ( 0.75 meters ) = 76 answer : c"
Answer: c
Python program:
a = 57 / 75
Problem: if r is a positive integer and r ^ 2 is divisible by 12 , then the largest positive integer that must divide r ^ 3 is
Options: a ) 2 ^ 3 , b ) 2 ^ 6 , c ) 3 ^ 3 , d ) 6 ^ 3 , e ) 12 ^ 2
Rationale: since r is an integer so r can not have a 2 and sqrt 3 ( because squaring this will give us a 2 ^ 2 and 3 ( making the product as 12 , and making r ^ 2 as a multiple of 12 ) ) r ^ 2 is divisible by 12 ( 12 = 2 * 2 * 3 ) , so , r should have at least one 2 and one 3 so that r ^ 2 has a 2 ^ 2 and two 3 so , r will have a 2 and a 3 . or r will be a multiple of 6 so , largest possible integer than should divide r ^ 3 is 6 ^ 3 so , answer will be d
Answer: d
Python program:
a = 12 / 4
b = a ** 2
c = 4 * b
d = math.sqrt(c)
e = d ** 3
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "soln : - ( 406 / 116 ) 110 = 385 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 11 = 385 ( 350 + 35 ) answer : c"
Answer: c
Python program:
a = 16 / 100
b = 1 + a 
c = 406 / b
d = 10 / 100
e = 16 / 100
f = 1 + e 
g = 406 / f
h = d * g
i = c + h
Problem: what is the average of first 21 multiples of 6 ?
Options: a ) a ) 66 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82
Rationale: "required average = 6 ( 1 + 2 + . . . . + 21 ) / 21 ( 6 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 66 a"
Answer: a
Python program:
a = 21 + 1 
b = 21 * a
c = b / 2
d = c / 21
e = d * 6
Problem: a contractor undertook to do a piece of work in 8 days . he employed certain number of laboures but 3 of them were absent from the very first day and the rest could finish the work in only 14 days . find the number of men originally employed ?
Options: a ) 6 , b ) 7.5 , c ) 5 , d ) 6 , e ) 7
Rationale: "let the number of men originally employed be x . 8 x = 14 ( x â € “ 3 ) or x = 7 answer e"
Answer: e
Python program:
a = 14 * 3
b = 14 - 8
c = a / b
Problem: what is the sum of two consecutive even numbers , the difference of whose squares is 84 ?
Options: a ) 42 , b ) 84 , c ) 48 , d ) 24 , e ) 43
Rationale: let the numbers be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 4 x + 4 = 84 4 x = 80 x = 20 . the required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer a 42
Answer: a
Python program:
a = 2 * 2
b = 84 - a
c = 2 * 2
d = b / c
e = 2 * 2
f = 84 - e
g = 2 * 2
h = f / g
i = h + 2 
j = d + i