euclaise/mathqa_programs huggingface dataset:
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 49 more . what was his original selling price ?
Options: a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840
Rationale: let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 49 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 49 = > 0.07 x = 49 = > x = $ 700 original purchase price = $ 700 hence , original selling price ( at 10 % of profit ) = 1.1 ( 700 ) = $ 770 option a
Answer: a
Python program:
a = 10 / 100
b = 1 - a
c = 30 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 + f 
h = e - g
i = 49 / h
j = 10 / 100
k = 1 + j 
l = i * k
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 612 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: difference in c . i . and s . i for 2 years = $ 612 - $ 600 = $ 12 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 12 rate = ( 100 * 12 ) / ( 300 ) = 4 % the answer is b .
Answer: b
Python program:
a = 612 - 600
b = 100 * a
c = 600 / 2
d = b / c
Problem: 3 numbers which are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073 . the sum of the 3 numbers is :
Options: a ) 81 , b ) 82 , c ) 85 , d ) 90 , e ) 95
Rationale: since the numbers are co - prime , they contain only 1 as the common factor . also , the given two products have the middle number in common . so , middle number = h . c . f of 551 and 1073 = 29 ; first number = 551 / 29 = 19 third number = 1073 / 29 = 37 . required sum = 19 + 29 + 37 = 85 . answer : c
Answer: c
Python program:
a = math.gcd(551, 1073)
b = 551 / a
c = math.gcd(551, 1073)
d = b + c 
e = math.gcd(551, 1073)
f = 1073 / e
g = d + f
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 17 km / hr , c ) 60 km / hr , d ) 77 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c"
Answer: c
Python program:
a = 100 + 100 
b = 1 + 2 
c = 8 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 110 mph + 88 mph ) / 2 = 99 mph correct answer is : e"
Answer: e
Python program:
a = 110 + 88 
b = a / 2
Problem: a person is traveling at 65 km / hr and reached his destiny in 3 hr then find the distance ?
Options: a ) 205 km , b ) 195 km , c ) 295 km , d ) 115 km , e ) 215 km
Rationale: "t = 3 hrs d = t * s = 65 * 3 = 195 km answer is b"
Answer: b
Python program:
a = 65 * 3
Problem: find the area of a parallelogram with base 12 cm and height 8 cm ?
Options: a ) 96 cm 2 , b ) 104 cm 2 , c ) 78 cm 2 , d ) 86 cm 2 , e ) 76 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 8 = 96 cm 2 answer : a"
Answer: a
Python program:
a = 12 * 8
Problem: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1260 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8235 , e ) 9255
Rationale: "you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1260 , we get the answer of 8235 . ( ans d )"
Answer: d
Python program:
a = 30 + 1 
b = 30 * a
c = 2 * 30
d = c + 1 
e = b * d
f = 3 + 3 
g = e / f
h = g - 1260
Problem: if the annual increase in the population of a town is 4 % and the present number of people is 15625 , what will the population be in 3 years ?
Options: a ) 15265 , b ) 16458 , c ) 25600 , d ) 17576 , e ) 14785
Rationale: "the required population is = 15625 ( 1 + 4 / 100 ) ^ 3 = 15625 * 26 / 25 * 26 / 25 * 26 / 25 = 17576 answer is d"
Answer: d
Python program:
a = 4 + 100 
b = a / 100
c = b * 15625
d = 4 + 100 
e = d / 100
f = c * e
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 224
Rationale: "white : yellow = x : ( x + 70 ) = 8 : 13 - - > 13 x = 8 x + 560 - - > x = 112 . the total # of balls originally x + x = 112 + 112 = 224 . answer : e ."
Answer: e
Python program:
a = 8 * 70
b = 13 - 8
c = a / b
d = c * 2
Problem: 80 x 100 + 80 x 11 = ?
Options: a ) 7500 , b ) 8880 , c ) 6200 , d ) 5200 , e ) none of them
Rationale: "= 80 x ( 100 + 11 ) ( by distributive law ) = 80 x 111 = 8880 answer is b"
Answer: b
Python program:
a = 100 ** 80
b = 80 * a
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 3.2 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 397.2
Rationale: "explanation : cost of each share = ( 20 + 3.2 % of 20 ) = rs . 20.64 therefore , number of shares = 8200 / 20.64 = 397.2 answer : e"
Answer: e
Python program:
a = 3 / 2
b = 20 + a 
c = 8200 / b
d = math.floor(c)
Problem: in a school of 850 boys , 44 % of muslims , 14 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 153 , d ) d ) 721 , e ) e ) 272
Rationale: "44 + 14 + 10 = 68 % 100 – 68 = 32 % 850 * 32 / 100 = 272 answer : e"
Answer: e
Python program:
a = 44 + 14 
b = a + 10 
c = 100 - b
d = 850 * c
e = d / 100
Problem: a train 125 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 51 , d ) 79 , e ) 80
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 45 = > x = 51 km / hr . answer : option c"
Answer: c
Python program:
a = 6 * const_0_2778
b = a * 6
c = 125 - b
d = c / 6
e = d / const_0_2778
Problem: what could be the range of a set consisting of odd multiples of 11 ?
Options: a ) 21 , b ) 24 , c ) 44 , d ) 62 , e ) 70
Rationale: range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 11 * ( 2 n + 1 ) where n is any positive integer . range = 11 * ( 2 m + 1 ) - 11 * ( 2 n + 1 ) = 11 * 2 * ( m - n ) = 22 * ( m - n ) . m , n - any positive integers the answer must be divisible by 22 , which is only 44 . the correct answer is c
Answer: c
Python program:
a = 11 * 4
Problem: a train covers a distance of 18 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 , b ) 168 , c ) 120 , d ) 882 , e ) 180
Rationale: "speed = ( 18 / 10 * 60 ) km / hr = ( 108 * 5 / 18 ) m / sec = 30 m / sec . length of the train = 30 * 6 = 180 m . answer : e"
Answer: e
Python program:
a = 18 / 10
b = a - 6
c = 18 / b
Problem: what quantity of water should be added to reduce 5 litres of 45 % acidic liquid to 25 % acidic liquid ?
Options: a ) 3 litres , b ) 2 litres , c ) 4 litres , d ) 4.5 litres , e ) 5 litres
Rationale: "quantity of acid in 5 litres = 45 * 5 / 100 = 2.25 litres let x litres of water is added to the solution , then there is 2.25 litres of acid in ( 5 + x ) litres of liquid . 25 % of ( 5 + x ) = 2.25 , 25 / 100 * ( 5 + x ) = 2.25 x = 225 - 125 / 25 = 4 answer : d"
Answer: d
Python program:
a = 45 / 100
b = 5 * a
c = b * 100
d = c / 25
e = d - 5
Problem: a certain company had a total annual expenditure of 2.55 ∗ 10 ^ 7 on employee salaries last year . if the company employed 425 people , what was the average employee salary ?
Options: a ) $ 60,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 2.55 ∗ 10 ^ 7 on employee salaries total employees = 425 observe that 425 * 6 = 2550 therefore try to bring the numerator in terms of 2550 average salary = ( 2550 * 10 ^ 4 ) / 425 = 6 * 10 ^ 4 = 60,000 option a"
Answer: a
Python program:
a = 10 * 7
b = 2 * 55
c = b / 425
d = c * 100
Problem: a no . when divided by 242 gives a remainder 100 , what remainder will be obtainedby dividingthe same no . 18 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "242 + 100 = 342 / 18 = 19 ( remainder ) e"
Answer: e
Python program:
a = 242 + 100 
b = a / 18
Problem: if each year the population of the country grows by 40 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 140 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 196 . . . . . . . . . . . . . 2 year elapsed year 2003 : population > 200 . . . . . . . . . . . . . . . . . . 3 year elapsed answer : a"
Answer: a
Python program:
a = 4 + 4
Problem: two pipes can fill a tank in 18 minutes and 20 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 21 - 1 / 45 = 1 / 12 so , the tank becomes full in 12 minutes . answer : e"
Answer: e
Python program:
a = 1 / 18
b = 1 / 20
c = a + b 
d = 1 / 45
e = c - d
Problem: a certain sum is invested at simple interest at 14 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 14000 , d ) s . 17000 , e ) s . 42000
Rationale: "let the sum be rs . x . ( x * 14 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 28 x / 100 - 24 x / 100 = 840 = > 4 x / 100 = 840 = > x = 42000 . answer : e"
Answer: e
Python program:
a = 14 - 12
b = a * 2
c = b / 100
d = 840 / c
Problem: a box contains 23 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 37 , d ) 21 / 95 , e ) none
Rationale: solution p ( none is defective ) = 19 c 2 / 23 c 2 = 25 / 37 . p ( at least one is defective ) = ( 1 - 25 / 37 ) = 12 / 37 . answer c
Answer: c
Python program:
a = 23 - 4
b = math.comb(a, 2)
c = math.comb(23, 2)
d = b / c
e = 1 - d
Problem: aarti can do a piece of work in 5 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 3 days , e ) 15 days
Rationale: we have the important relation , more work , more time ( days ) a piece of work can be done in 5 days . three times of work of same type can be done in 5 x 3 = 15 days answer e
Answer: e
Python program:
a = 3 * 5
Problem: a rectangular lawn 70 m × 30 m has two roads each 5 metres wide , running in the middle of it , one parallel to the length and the other parallel to the breadth . find the cost of gravelling the road at the rate of 4 per square metre .
Options: a ) 2,000
b ) 1,800
c ) 1,900
d ) 1,700
e ) none of these
Rationale: total area of road = area of road which parallel to length + area of road which parallel to breadth – overlapped road = 70 × 5 + 30 × 5 – 5 × 5 = 350 + 150 – 25 = 500 – 25 = 475 m 2 ∴ cost of gravelling the road = 475 × 4 = 1900 answer c
Answer: c
Python program:
a = 70 * 5
b = 30 * 5
c = a + b 
d = 5 * 5
e = c - d
f = e * 4
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 11 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 92 , c ) 95 , d ) 88 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 11 total people can seat = 81 + 11 = 92 answer : b"
Answer: b
Python program:
a = 15 - 3
b = 15 + a 
c = b * 3
d = c + 11
Problem: in a 300 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 79 , b ) 77 , c ) 85 , d ) 83 , e ) 61
Rationale: "solution simple out of 300 20 % are male i . e 60 and 25 % are female i . e 75 , so total homeowner is 135 . now min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option . so ans is 61 . answer : e"
Answer: e
Python program:
a = 25 / 100
b = a * 20
c = 25 / 100
d = c * 20
e = b * d
f = 300 - 20
g = f / 20
h = e + g
Problem: two cars , one from austin to dallas and the other from dallas to austin , start simultaneously . after they meet , the cars reach their destinations after 4 hours and 9 hours respectively the ratio of their speeds is
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 3 : 6 , d ) 4 : 5 , e ) none
Rationale: solution let us name the cars as a and b . = ( car a ' s speed ) : ( car b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 4 : â ˆ š 9 = 2 : 3 answer a
Answer: a
Python program:
a = math.sqrt(4)
b = math.sqrt(9)
c = a / b
Problem: chlorination is used in industry for the purification of water ; 1 gm solution of chlorine will remove half of the germs in 1 liter of water . if water containing less than 0.09 % of germs is considered clean , what is the minimum amount of chlorine required to purify 150 liter of water containing 0.3 liter of harmful substances ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assuming that it ' s supposed to state ` ` 0.3 ' ' liters of harmful substances , here ' s how you can answer this question . first , we have to figure out what . 09 % of 150 liters is . . . 1 % = . 01 . 1 % = . 001 . 09 % = . 0009 so , . 0009 ( 150 ) = . 135 liters we need enough doses of chlorine to get the 0.3 liters down to less than . 135 liters . each ` ` dose ' ' of chlorine will remove half of the harmful substances . . . start = 0.3 liters after 1 st dose = . 15 liters after 2 nd dose = . 075 liters we ' re now below the . 135 liters that we need to be less than . final answer : b
Answer: b
Python program:
a = 150 * 0
b = a * 0
c = b / 2
Problem: a train 175 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 49 , b ) 50 , c ) 12 , d ) 13 , e ) 68
Rationale: "speed of the train relative to man = ( 175 / 10 ) m / sec = ( 35 / 2 ) m / sec . [ ( 35 / 2 ) * ( 18 / 5 ) ] km / hr = 63 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 63 = = > x = 68 km / hr . answer : option e"
Answer: e
Python program:
a = 5 * const_0_2778
b = a * 5
c = 175 - b
d = c / 5
e = d / const_0_2778
Problem: on a purchase of $ 127 , a store offered a payment plan consisting of a $ 27 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 18.3 % , b ) 15.3 % , c ) 21.3 % , d ) 22.3 % , e ) 25.3 %
Rationale: "12 * 10 + 27 = 147 ( 27 / 127 ) * 100 = 21.3 answer : c"
Answer: c
Python program:
a = 10 * 12
b = a + 27 
c = 10 * 12
d = b - c
e = d / 127
f = e * 100
Problem: in how many r ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: r = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Python program:
a = 5 - 1
b = math.factorial(a)
c = b * 6
Problem: 50 men do a work in 100 days . how many men are needed to finish the work in 20 days ?
Options: a ) 50 , b ) 100 , c ) 250 , d ) 300 , e ) 400
Rationale: men required to finish the work in 2 days = 50 * 100 / 20 = 250 answer is c
Answer: c
Python program:
a = 50 * 100
b = a / 20
Problem: what is the rate percent when the simple interest on rs . 900 amount to rs . 160 in 4 years ?
Options: a ) 4.44 , b ) 5.44 , c ) 6.44 , d ) 7.44 , e ) 8.44
Rationale: "160 = ( 900 * 4 * r ) / 100 r = 4.44 % answer : a"
Answer: a
Python program:
a = 100 * 160
b = 900 * 4
c = a / b
Problem: a car takes 6 hours to cover a distance of 432 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 ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: "time = 6 distence = 432 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 432 / 9 = 48 kmph a"
Answer: a
Python program:
a = 6 * 3
b = a / 2
c = 432 / b
Problem: in a recent election , james received 5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001
Rationale: "james = ( 5 / 100 ) * 2000 = 100 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 100 = 901 answer : option a"
Answer: a
Python program:
a = 1000 + 1000 
b = 1000 + 1000 
c = b * 0
d = a - c
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 14 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 40 points as end of season we need another 26 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 hence option a - 6"
Answer: a
Python program:
a = 40 - 14
b = 20 - 5
c = a - b
d = c / 2
e = math.floor(d)
f = e + 1
Problem: find large number from below question the difference of two numbers is 1390 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1665
Rationale: "let the smaller number be x . then larger number = ( x + 1390 ) . x + 1390 = 6 x + 15 5 x = 1375 x = 275 large number = 275 + 1390 = 1665 e"
Answer: e
Python program:
a = 1390 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 105 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 105 - 55 = 50 n = 10 the answer is b ."
Answer: b
Python program:
a = 105 - 50
b = 55 - 50
c = a / b
d = c - 1
Problem: a company sells pens and pencils . the revenue from pens in 2007 was up 5 % from 2006 . the revenue from pencils declined 13 % over the same period . overall revenue was down 1 % from 06 to 07 . what was the ratio of pencil revenue to pen revenue in 2006
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: let the revenue of pens be ' x ' let the revenue of pencils be ' y ' the revenue of pens up from 2006 by 5 % = > 105 % the revenue of pencils down from 2006 by 13 % = > 87 % overall revenue down by 1 % = > 99 % hence the ratio of pencils to pens = 6 / 12 = 1 / 2 answer : a
Answer: a
Python program:
a = 5 + 100 
b = 100 - 1
c = a - b
d = 100 - 1
e = 100 - 13
f = d - e
g = c / f
Problem: a family made a down payment of $ 300 and borrowed the balance on a set of encyclopedias that cost $ 750 . the balance with interest was paid in 9 monthly payments of $ 57 each and a final payment of $ 21 . the amount of interest paid was what percent of the amount borrowed ?
Options: a ) 6 % , b ) 12 % , c ) 14 % , d ) 18.66 % , e ) 20 %
Rationale: interest paid = 57 * 9 + 21 - 450 = 84 % off the balance = ( 84 / 450 ) * 100 = 18.66 % answer is d .
Answer: d
Python program:
a = 9 * 57
b = a + 21 
c = 750 - 300
d = b - c
e = 750 - 300
f = d / e
g = f * 100
Problem: there are 10 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 50
Rationale: "10 c 2 = 45 the answer is d ."
Answer: d
Python program:
a = 10 - 1
b = 10 * a
c = b / 2
Problem: consider a quarter of a circle of radius 20 . let r be the radius of the circle inscribed in this quarter of a circle . find r .
Options: a ) 20 * ( sqr 2 - 1 )
b ) 8 * ( sqr 3 - 1 )
c ) 4 * ( sqr 7 - 1 )
d ) 12 * ( sqr 7 - 1 )
e ) none of these
Rationale: i got 20 / ( sqr 2 + 1 ) and just forgot to multiply by ( sqr 2 - 1 ) . answer a
Answer: a
Python program:
a = math.sqrt(2)
b = a - 1
c = 20 * b
Problem: what two - digit number is less than the sum of the square of its digits by 12 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 12 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 12 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 99 thus the answer is b"
Answer: b
Python program:
a = 12 - 5
b = a + 1 
c = 10 * b
d = c + 5