euclaise/mathqa_programs huggingface dataset:
Problem: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.1 x ) = 0.88 x . the difference is 12 % . the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = a + 1 
c = 80 / 100
d = b * c
e = 1 - d
f = e * 100
Problem: of 3 numbers , the third is twice the second and the second is 4 times the first . if their average is 78 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 8 x . so , x + 4 x + 8 x = 78 × 3 = 234 . 13 x = 234 x = 234 / 13 hence , smallest number x = 18 . answer : a
Answer: a
Python program:
a = 78 * 3
b = 4 * 2
c = b + 4 
d = c + 1 
e = a / d
Problem: the area of a square is 625 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square .
Options: a ) 5 : 12 , b ) 5 : 13 , c ) 2 : 9 , d ) 1 : 15 , e ) 1 : 5
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 = 625 a = 25 l = 3 a and b = a - 20 b : l = a - 20 : 3 a = 5 : 75 = 1 : 15 answer : d"
Answer: d
Python program:
a = math.sqrt(625)
b = a - 20
c = math.sqrt(625)
d = c * 2
e = b / d
Problem: two pipes a and b can separately fill a tank in 20 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 540 liters , c ) 820 liters , d ) 900 liters , e ) 580 liters
Rationale: "1 / 20 + 1 / 15 - 1 / x = 1 / 15 x = 12 20 * 45 = 900 answer : d"
Answer: d
Python program:
a = 1 / 20
b = 1 / 15
c = a + b 
d = 1 / 45
e = c + d 
f = 1 / 15
g = e - f
h = 1/(g)
i = h * 3
j = i * 15
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 50 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 2 hours ?
Options: a ) 32 % , b ) 36 % , c ) 40 % , d ) 44 % , e ) 48 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.5 ( 6 ) = 3 gallons at the start , the amount of water is 0.5 ( 6 ) = 3 gallons after 2 hours , the amount of water is 3 - 0.5 ( 2 ) = 2 gallons the concentration of water is 2 / ( 3 + 2 ) = 2 / 5 = 40 % the answer is c ."
Answer: c
Python program:
a = 100 - 50
b = 2 * a
c = b / 100
d = 0 * 5
e = c - d
f = 0 * 5
g = 2 - f
h = e / g
i = h * 100
Problem: in what time will a train 55 m long cross an electric pole , it its speed be 36 km / hr ?
Options: a ) 5.5 , b ) 4.5 , c ) 3.5 , d ) 2.5 , e ) 1.5
Rationale: "speed = 36 * 5 / 18 = 10 m / sec time taken = 55 / 10 = 5.5 sec . answer : a"
Answer: a
Python program:
a = 36 * const_0_2778
b = 55 / a
Problem: a leak in the bottom of a tank can empty the tank in 6 hrs . an pipe fills water at the rate of 4 ltrs / minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs . the capacity of the tank is ?
Options: a ) 2345 , b ) 2350 , c ) 2457 , d ) 4657 , e ) 5760
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 e"
Answer: e
Python program:
a = 6 * 4
b = a * const_60
c = b * 4
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 20 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 20 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 stop . the integers ca n ' t be greater than 4 or we will score above 20 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 the only pair that matches is 4 ^ 2 + 2 ^ 2 = 20 . so 4 ^ 3 + 2 ^ 3 = 72 . answer a . )"
Answer: a
Python program:
a = math.gcd(20, 4)
Problem: a train is moving at 6 / 7 of its usual speed . the train is 10 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 10 minutes represents 1 / 6 of the usual time . the usual time is 1 hour . the answer is b ."
Answer: b
Python program:
a = 6 / 7
b = 10 * a
c = 6 / 7
d = 1 - c
e = 1/(d)
f = b * e
g = f / const_60
Problem: a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) 15500 , b ) 16000 , c ) 15000 , d ) 17000 , e ) 20000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.90 = 19 x / 25 = 36 x / 50 total sp = 12 x / 50 + 36 x / 50 = 48 x / 50 overall loss = x - 48 x / 50 = 2 x / 50 2 x / 50 = 600 = > x = 15000 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 20 / 100
f = 20 / 100
g = e * f
h = d - g
i = 400 / h
Problem: a bag contains 6 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 5 / 14 , b ) 8 / 21 , c ) 12 / 21 , d ) 43 / 91 , e ) 47 / 91
Rationale: the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 43 / 91 the answer is d .
Answer: d
Python program:
a = 6 + 8 
b = 8 / a
c = 8 - 1
d = 6 + 8 
e = d - 1
f = c / e
g = b * f
h = 6 - 1
i = 6 + 8 
j = i - 1
k = h / j
l = 6 + 8 
m = 6 / l
n = k * m
o = g + n
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 45 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2700 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 45 = 30 x = 2700 km answer is d"
Answer: d
Python program:
a = 30 * 45
Problem: a snooker tournament charges $ 40.00 for vip seats and $ 10.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 190
b ) 180
c ) 170
d ) 160
e ) 148
Rationale: let no of sits in vip enclosure is x then x * 40 + 10 ( 320 - x ) = 7500 or 25 x = 7500 - 3200 , x = 4300 / 25 = 172 vip = 172 general = 320 - 172 = 148 e
Answer: e
Python program:
a = 3 + 4 
b = a * 1000
c = 2 + 3 
d = c * 100
e = b + d 
f = 320 * 10
g = e - f
h = 2 + 3 
i = 2 + 3 
j = h * i
k = g / j
l = 320 - k
Problem: if a and b are positive integers , and a = 2 b + 6 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 12
Rationale: "since a = 2 b + 6 , so we can say b = ( a / 2 - 3 ) . so we need to find not possible gcd values for a , ( a / 2 - 3 ) . a . 1 , we can easily get this value by making a = 8 . b . 2 . we can again get this value as gcd by keeping a = 10 c . 3 we will get this as gcd by keeping a = 12 d . 6 we can get gcd 6 by keeping ( a / 2 - 3 ) = 6 and a as 18 . e . 12 this is not possible as for 12 ( 2 ^ 2 * 3 ) to be gcd = 2 ^ 2 * 3 both a and a / 2 - 3 should be divisible by 4 and 3 . so a has to be a multiple of 4 . this means a / 2 has to be even and even - odd will be odd and odd number wont be divisible by 4 . this 12 cant be the gcd . answer e ."
Answer: e
Python program:
a = 6 / 2
b = a + 2
Problem: naomi drives to the beauty parlor in 60 minutes . on the way back , her average speed is half the average speed as it was to the way to the parlor . how much time will it take naomi to travel two round trips to the beauty parlor ?
Options: a ) 3 hours . , b ) 4 hours . , c ) 4 hours and 20 minutes . , d ) 5 hours and 50 minutes , e ) 6 hours .
Rationale: s 1 = 2 s 2 since , speed is inversely proportional to time we have , s 1 / s 2 = 2 / 1 = t 2 / t 1 therefore , the time taken for one trip = 60 + 120 = 180 minutes total = 180 * 2 = 360 minutes = 6 hours answer : e
Answer: e
Python program:
a = 60 / 10
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 39 ° is ?
Options: a ) 40 m 2 , b ) 45 m 2 , c ) 49 m 2 , d ) 51 m 2 , e ) 55 m 2
Rationale: "39 / 360 * 22 / 7 * 12 * 12 = 49 m 2 answer : c"
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 39 / g
i = f * h
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 2000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c )
Answer: c
Python program:
a = 10000 / 2000
b = a + 6
Problem: the radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 100 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 175 cm . then , circumference of wheel = 2 ï € r = 350 ï € = 1100 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 1100 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 1100 = 100 answer a"
Answer: a
Python program:
a = 1000 * 66
b = 100 * a
c = const_60 * 1
d = b / c
e = 2 * 175
f = 3 * 4
g = 2 + f 
h = 4 * 2
i = 2 + h 
j = i ** 2
k = g / j
l = 3 + k 
m = e * l
n = d / m
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 60 % profit on the first article and 60 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 600
Rationale: "profit on first article = 60 % of 1000 = 600 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e"
Answer: e
Python program:
a = 100 - 60
b = 100 / a
c = b * 1000
d = 100 + 60 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 60
l = 100 / k
m = l * 1000
n = 100 + 60 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 15 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 500 / ( 25 / 6 ) = 120 seconds the answer is b ."
Answer: b
Python program:
a = 15 * const_0_2778
b = 500 / a
Problem: the compound ratio of 5 : 7 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 7 , b ) 6 : 5 , c ) 6 : 7 , d ) 4 : 7 , e ) 6 : 9
Rationale: "5 / 7 * 3 / 2 * 4 / 5 = 6 / 7 6 : 7 answer : c"
Answer: c
Python program:
a = 5 * 3
b = 7 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 = > 450 hence answer will be ( d ) 450"
Answer: d
Python program:
a = 0 * 65
b = a * 12
Problem: the ratio of the incomes of rajan and balan is 7 : 6 and the ratio of their expenditure is 6 : 5 . if at the end of the year , each saves $ 1000 then the income of rajan is ?
Options: a ) $ 7600 , b ) $ 7000 , c ) $ 8000 , d ) $ 9000 , e ) $ 5000
Rationale: let the income of rajan and balan be $ 7 x and $ 6 x let their expenditures be $ 6 y and $ 5 y 7 x - 6 y = 1000 - - - - - - - 1 ) 6 x - 5 y = 1000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 rajan ' s income = 7 x = 7 * 1000 = $ 7000 answer is b
Answer: b
Python program:
a = 7 / 6
b = a * 1000
c = 1000 - b
d = 7 / 6
e = 6 / 5
f = d - e
g = c / f
h = g + 1000 
i = h * 7
j = i / 6
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 12 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 36 , e ) 96
Rationale: d 36 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 12 mph = 36 miles
Answer: d
Python program:
a = 36 / 2
b = a / 6
c = 12 * b
Problem: a 300 meter long train crosses a platform in 51 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 550 , b ) 289 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 51 = 50 / 3 3 ( x + 300 ) = 2550 è x = 550 m . answer : a"
Answer: a
Python program:
a = 300 / 18
b = a * 51
c = b - 300
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 43 , b ) 26 , c ) 33 , d ) 21 , e ) 28
Rationale: "b 26 let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 26 ."
Answer: b
Python program:
a = 48 * 4
b = a - 140
c = b / 2
Problem: when 1 / 10 percent of 2,000 is subtracted from 1 / 10 of 2,000 , the difference is
Options: a ) 1980 , b ) 1998 , c ) 198 , d ) 200 , e ) 20
Rationale: "( 1 / 10 ) * 2000 - ( 1 / 10 ) % * 2000 = 200 - ( 1 / 1000 ) * 2000 = 200 - 2 = 198 the answer is c ."
Answer: c
Python program:
a = 3 + 4 
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4 
h = g * 1000
i = f * h
j = d - i
Problem: find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2875 , b ) 2654 , c ) 2645 , d ) 2456 , e ) 2522
Rationale: principal = rs . 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = rs . [ 16000 x ( 1 + ( 5 / 100 ) ) 3 ] = rs . 18522 . ci . = rs . ( 18522 - 16000 ) = rs . 2522 answer : e
Answer: e
Python program:
a = 20 / 4
b = a / 100
c = 1 + b 
d = c ** 3
e = 4 * 4
f = e * 100
g = math.sqrt(100)
h = f * g
i = d * h
j = 4 * 4
k = j * 100
l = math.sqrt(100)
m = k * l
n = i - m
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 51 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 51 2 x = 8 = > x = 4 answer : e"
Answer: e
Python program:
a = 3 * 9
b = 51 - a
c = 3 * 2
d = b / c
Problem: a certain quantity of 40 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "original quantity = a substituted quantity = b then : ( a * 0.4 + 0.25 * b т а у 0.4 * b ) / a = 0.35 0.4 + ( b / a ) * ( - 0.15 ) = 0.35 b / a = - 0.05 / - 0.15 = 1 / 3 answer : b"
Answer: b
Python program:
a = 35 - 25
b = 40 - 35
c = a / b
d = c + 1 
e = 1/(d)
Problem: on the first day of her vacation , louisa traveled 250 miles . on the second day , traveling at the same average speed , she traveled 350 miles . if the 250 - mile trip took 3 hours less than the 350 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 31 , b ) 33.33 , c ) 35 , d ) 37 , e ) 39.33
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 250 / t = 350 / ( t + 3 ) - - > 5 / t = 7 / ( t + 3 ) - - > 5 t + 15 = 7 t - - - - > 2 t = 15 . t = 7.5 - - - - > ( rate ) = 250 / 7.5 = 33.33 answer : b"
Answer: b
Python program:
a = 350 - 250
b = a / 3
Problem: a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e ."
Answer: e
Python program:
a = 5 / 100
b = a * 90
c = 6 + 5
Problem: if an object travels at six feet per second , how many feet does it travel in one hour ?
Options: a ) 21600 , b ) 3778 , c ) 12788 , d ) 18000 , e ) 2881
Rationale: "explanation : if an object travels at 6 feet per second it covers 6 x 60 feet in one minute , and 6 x 60 x 60 feet in one hour . answer = 21600 answer : a ) 21600"
Answer: a
Python program:
a = 3 * const_60
b = a * const_60
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq . m . find the length of each stone slab ?
Options: a ) 150 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 67.5 / 30 m 2 = 2.25 m 2 length of each slab √ 2.25 = 1.5 m = 150 cm"
Answer: a
Python program:
a = 67 / 5
b = math.sqrt(a)
c = b * 100
Problem: machine r takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine r to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of r is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and r reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of r . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Python program:
a = 40 - 25
b = a - 3
Problem: i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) rs . 28 , b ) rs . 280 , c ) rs . 140 , d ) rs . 70 , e ) rs . 80
Rationale: x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 answer : b
Answer: b
Python program:
a = 100 + 19 
b = 480 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: a gardener changed the size of his rectangle shaped garden by increasing it ' s length by 40 % & decreasing is ' s width by 20 % . find area of new garden .
Options: a ) 1.04
b ) 1.12
c ) 1.24
d ) 1.4
e ) 1.5
Rationale: a 1 = l * b a 2 = ( l * 140 / 100 ) * ( b * 80 / 100 ) = 1.12 * lb so , area of garden is by 1.12 times of old area . answer : b
Answer: b
Python program:
a = 100 + 40 
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and dennison have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and dennison submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Python program:
a = 80 * 0
b = 2 * a
c = 100 - 25
d = c / 100
e = 160 * d
f = e * 0
g = b - f
h = g / 2
Problem: what is the sum of the integers from - 190 to 191 inclusive ?
Options: a ) 0 , b ) 191 , c ) 375 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 191 / 2 = 0.5 number of items ( n ) = b - a + 1 = 191 - ( - 190 ) + 1 = 195 + 191 = 382 . sum = average * n = 0.5 * 382 = 191 . answer is b"
Answer: b
Python program:
a = 190 * 191
b = a / 4
Problem: 9000 + 16 2 / 3 % of ? = 10500
Options: a ) 2387 , b ) 2888 , c ) 9000 , d ) 2837 , e ) 2271
Rationale: "explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c"
Answer: c
Python program:
a = 16 * 2
b = 3 / 3
c = a / b
d = 9000 + c
Problem: the ratio of the cost price and selling price is 2 : 3 . the profit percent is ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 100 %
Rationale: let the c . p . = $ 2 x then s . p . = $ 3 x then , gain = 3 x - 2 x = $ x gain % = x / 2 x * 100 = 50 % answer is c
Answer: c
Python program:
a = 3 / 2
b = a - 1
c = b * 100
Problem: 10 is 6 % of a , and 6 is 10 % of b . c equals b / a . what is the value of c ?
Options: a ) 3 / 10 , b ) 6 / 17 , c ) 9 / 25 , d ) 10 / 33 , e ) 12 / 35
Rationale: "6 a / 100 = 10 a = 500 / 3 b / 10 = 6 b = 60 c = b / a = 60 * 3 / 500 = 9 / 25 the answer is c ."
Answer: c
Python program:
a = 6 / 10
b = a * 100
c = 10 / 6
d = c * 100
e = b / d
Problem: the slant height of a cone is 12 cm and radius of the base is 4 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 28 , c ) 48 , d ) 26 , e ) 28
Rationale: "π * 12 * 4 = 48 answer : c"
Answer: c
Python program:
a = math.pi * 4
b = a * 12
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 5 cm , and bd = 6 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 5 ( ac = 5 ) d - 8 ( bd = 6 ) cd is 8 - 5 = 3 . ans c
Answer: c
Python program:
a = 5 - 2
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 8 and the other one , that is cheaper , costs $ 3 . the factory holds a $ 100 worth stock of 25 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "so the number of $ 3 modules must be 20 so that the leftover 5 modules are of $ 8 which will give a total value $ 100 . 20 * 3 + 5 * 8 = 60 + 40 = 100 . answer : b"
Answer: b
Python program:
a = 100 - 8
b = a / 3