euclaise/mathqa_programs huggingface dataset:
Problem: in a can , there is a mixture of milk and water in the ratio 8 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 12 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 18.4 , c ) 48 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 8 / 13 ( t - 8 ) after adding milk , quantity of milk in the mixture = 12 / 17 t . 12 t / 17 - 8 = 8 / 13 ( t - 8 ) 20 t = 1456 - 1088 = > t = 18.4 . answer : b"
Answer: b
Python program:
a = 12 / 5
b = a * 5
c = b - 8
d = 8 / c
e = 5 * d
f = 12 / 5
g = f * 5
h = g - 8
i = 8 / h
j = e + i 
k = j + 8
Problem: matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 8 days . in how many days peter complete the work separately .
Options: a ) 21 , b ) 24 , c ) 20 , d ) 25 , e ) 30
Rationale: "together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 8 days which means that the whole job ( 1 ) can be completed in x days . x = 8 / ( 8 / 20 ) = 20 c"
Answer: c
Python program:
a = 1 / 20
b = 12 * a
c = 1 - b
d = 8 / c
Problem: if 40 % of a number exceeds 25 % of it by 18 , then find the number ?
Options: a ) 120 , b ) 150 , c ) 200 , d ) 64 , e ) 100
Rationale: "use the elimination method to find the correct option . of all the options only 120 fits 40 % of 120 = 48 25 % of 120 = 30 48 - 30 = 18 required number is 180 . answer : a"
Answer: a
Python program:
a = 40 - 25
b = a / 100
c = 18 / b
d = c + 25
Problem: jack rode his bicycle at an average speed of 5 mph for some time and then at an average speed of 15 mph for the rest of the journey . if he made no stops during the trip , and his average speed for the entire journey was 10 miles per hour , for what fraction of the total time did he ride at 15 mph ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 3 , d ) 2 / 5 , e ) 1 / 2
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . the average speed for the entire journey is 10 mph ; so , he rode at 5 mph and 15 mph for an equal duration of time . difference is 5 and 5 , respectively . 5 - - - - 10 - - - - 15 this shows that you can divide the entire journey into 2 equal parts . thus , 1 / 2 of the journey he rode at 10 mph , and 1 / 2 of the journey he rode at 15 mph . answer : e
Answer: e
Python program:
a = 15 / 15
b = a / 2
Problem: of the female students at barkely university , 1 / 6 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ?
Options: a ) 8 / 5 , b ) 3 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 100 given 3 / 5 of the students are females = 60 then males = 2 / 5 = 40 1 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 5 = 16 ratio of m : f students on honor roll = 16 / 10 = 8 / 5 a"
Answer: a
Python program:
a = 1 * 2
b = a * 2
c = b + 2 
d = 5 * 1
e = 2 * d
f = c / e
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 7
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 7 = e"
Answer: e
Python program:
a = 3 * 0
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 105 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 85 + 20 ) kg = 105 kg the answer is e ."
Answer: e
Python program:
a = 2 * 5
b = a + 85
Problem: if it takes a tub 6 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 24 seconds , e ) 4 minutes , 12 seconds
Rationale: if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 6 minutes to drain 5 / 7 th of tub it takes 6 * ( 7 / 5 ) minutes to drain the entire tub and 6 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 2.4 minutes or 12 / 5 minutes or 2 minute 24 seconds so answer is d
Answer: d
Python program:
a = 5 / 7
b = 1 - a
c = 5 / 7
d = b + c
Problem: the compound ratio of 5 : 6 , 5 : 2 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 5 : 3 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 6 * 5 / 2 * 4 / 5 = 5 / 3 5 : 3 answer : b"
Answer: b
Python program:
a = 5 * 5
b = 6 * 2
c = a / b
d = 5 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: the average of 10 numbers is 60 . out of 10 numbers the average of first 6 no . is 68 , and last 6 numbers is 75 then find 7 th number ?
Options: a ) a ) 78 , b ) b ) 65 , c ) c ) 258 , d ) d ) 62 , e ) e ) 48
Rationale: "7 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 68 + 6 * 75 - 10 * 60 = 258 answer is c"
Answer: c
Python program:
a = 6 * 68
b = 6 * 75
c = a + b 
d = 10 * 60
e = c - d
Problem: for a certain exam , a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 58.67 , e ) 82.2
Rationale: "mean - 5 sd = 42 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 3.33 mean = 58.67 ans . d"
Answer: d
Python program:
a = 42 * 2
b = 67 * 5
c = a + b 
d = 5 + 2 
e = c / d
Problem: how many integers between 1 and 1,050 are divisible by 10 , 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e"
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 1 - 50
Problem: a cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 4 x 1.25 ) + 4 x 4 ] = 36 the answer is c ."
Answer: c
Python program:
a = 4 * 4
b = 25 / 100
c = 1 + b 
d = 4 * c
e = 2 * d
f = a + e 
g = 25 / 100
h = 1 + g 
i = 4 * h
j = 2 * i
k = f + j
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 32.5 meters . how many times did the ball bounce ?
Options: a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 2 division of total diatance travelled will be 16 + 16 + 0.5 a"
Answer: a
Python program:
a = 16 / 2
b = a / 2
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 146 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 146 / 25 = 5 . . . . so the max is 5 146 / 20 = 7 . . . so the max is 7 146 - 145 = 1 ( 6 small box + 1 big box ) answer : d"
Answer: d
Python program:
a = 25 - 20
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 111 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 6000 , d ) $ 6400 , e ) $ 3700
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 111 x = 3700 answer e"
Answer: e
Python program:
a = 3 + 2 
b = 100 * a
c = 30 + 20 
d = c + 35 
e = 100 - d
f = 111 / e
g = b * f
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 40 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 0.4 * 48 + 0.4 * 52 = 40 , so percent of people who are less than 25 years old is 100 - 40 = 60 . answer : b ."
Answer: b
Python program:
a = 40 / 100
b = 100 - 40
c = b / 100
d = a * c
e = 1 - d
Problem: two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: let x be the total time it takes for the cistern to fill . 4 / 12 + x / 15 = 1 x / 15 = 2 / 3 x = 10 after the first pipe is turned off , it takes 6 more minutes to fill the cistern . the answer is a .
Answer: a
Python program:
a = 1 / 12
b = 1 / 15
c = a + b 
d = c * 4
e = 1 - d
f = e * 15
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container q ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Python program:
a = 9 + 16 
b = 9 / a
c = math.sqrt(b)
d = 1 - c
e = 15 / d
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 28 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) 18.5 %
Rationale: "explanation : cost price = ( 225 + 28 ) = 253 sell price = 300 gain = ( 47 / 253 ) * 100 = 18.5 % . answer : e"
Answer: e
Python program:
a = 225 + 28 
b = 300 / a
c = b * 100
d = c - 100
Problem: mr . hernandez , who was a resident of state x for only 10 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 750 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 4 % = 900 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 10 / 12 ) = 750 answer b"
Answer: b
Python program:
a = 4 * 100
b = a * 100
c = 100 * const_0_25
d = c * 100
e = b + d 
f = e / 100
g = f * 4
h = g * 10
i = 3 * 4
j = h / i
Problem: the cost price of 12 articles is equal to the selling price of 8 articles . what is the profit percent ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "8 * sp = 12 * cp sp = 1.5 * cp the profit percent is 50 % . the answer is c ."
Answer: c
Python program:
a = 12 * 4
b = 4 + 1 
c = a / b
Problem: two parallel sides of a trapezium are 4 cm and 5 cm respectively . the perpendicular distance between the parallel sides is 6 cm . find the area of the trapezium .
Options: a ) 24 cm 2
b ) 25 cm 2
c ) 26 cm 2
d ) 27 cm 2
e ) 28 cm 2
Rationale: area of trapezium when height and two parallel sides are given = 1 / 2 × h × ( a + b ) = 1 / 2 x 6 x ( 4 + 5 ) = 27 cm 2 answer d
Answer: d
Python program:
a = 4 + 5 
b = a / 2
c = b * 6
Problem: in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 5 . if the probability that a number 12 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 8 / 15 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 5 = 1 p ( set 2 ) = 8 / 15 answer ( a )"
Answer: a
Python program:
a = 12 / 3
b = 12 + a 
c = 2 / 5
d = b - c
Problem: a ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches . how much fraction of the ring x surface is not covered by the ring y ?
Options: a ) 13 / 15
b ) 12 / 4
c ) 16 / 17
d ) 22 / 16
e ) 17 / 81
Rationale: the questions asks us to find the surface which is not covered by the ring x i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the ring x = pi * r ^ 2 , where r = 8 = > pi * 64 area of the ring y = pi * 81 surface not covered by the ring x = pi * 81 - pi * 64 = pi * 17 fraction of ring y ' s surface is not covered by a ring x = pi * 17 / total area of the ring y = > pi * 17 / pi * 81 17 / 81 answer e
Answer: e
Python program:
a = 18 / 2
b = circle_area - (
c = 16 / 2
d = b / circle_area
Problem: 7 / 9 of 3 / 5 of a number is greater than 2 / 9 of 5 / 6 of the same number by 152 . what is half of that number ?
Options: a ) 165 , b ) 195 , c ) 240 , d ) 270 , e ) 315
Rationale: "let no . be x 7 / 9 * 3 / 5 * x - 2 / 9 * 5 / 6 * x = 152 by further solving 21 x / 45 - 10 x / 54 = 152 114 x / 405 = 152 x = 540 we have to find x / 2 = 540 / 2 = 270 answer : d"
Answer: d
Python program:
a = 4 / 0
b = 3 / 5
c = a * b
d = 2 / 0
e = 7 / 9
f = d * e
g = c - f
h = 152 / g
i = h / 5
Problem: the smallest number which when diminished by 3 is divisible by 21 , 2836 and 45 is . . .
Options: a ) 829 , b ) 869 , c ) 859 , d ) 4320 , e ) 427
Rationale: 427 answer : e
Answer: e
Python program:
a = 21 * 45
b = a / 2
c = 45 - 10
d = b - c
Problem: if 45 % of z is 96 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 96 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 96 / 100 ) * ( 3 / 4 ) x i . e . z = ( 96 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.6 ) x = ( 160 / 100 ) x i . e . z is 160 % of x answer : option b"
Answer: b
Python program:
a = 75 / 100
b = 45 / 100
c = 96 / 100
d = b / c
e = a / d
f = e * 100
Problem: if ( 5 ^ 15 ) ( 9 ^ 8 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 15 ) ( 9 ^ 8 ) = 3 ( 15 ^ x ) = > 5 ^ 15 * 3 ^ 16 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 15 * 3 ^ 16 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 15 answer e"
Answer: e
Python program:
a = 5 ** 15
b = 9 ** 8
c = a * b
d = c / 3
e = math.log(d)
f = math.log(15)
g = e / f
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 830 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 638 , c ) s . 650 , d ) s . 810 , e ) s . 735
Rationale: "s . i . for 1 year = ( 830 - 825 ) = rs . 5 s . i . for 3 years = 5 * 3 = rs . 15 principal = ( 825 - 15 ) = rs . 810 . answer : d"
Answer: d
Python program:
a = 830 - 825
b = a * 3
c = b / 4
d = 825 - c
Problem: at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 45 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 30 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 45 = 50 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 45 , 100 % = 45 * 100 / 60 = 75 . . ans 40 % of 75 = 30 b"
Answer: b
Python program:
a = 70 * 300
b = a / 100
c = 300 - b
d = c - 45
e = d * 100
f = 100 - 40
g = e / f
h = g * 40
i = h / 100
Problem: after playing 40 games , the lesley basketball team had won 50 % of the games . the additional games played gave the team a 20 % total winning average . how many additional games must the team have won to obtain this average ?
Options: a ) 2 , b ) 15 , c ) 7 , d ) 10 , e ) 9
Rationale: explanation : identify the parts , set up equation , and solve . number of games initially won by the team : 50 % * 40 = 20 additional games won by the team leaving a 20 % average . ( let x represent the unknown number of additional games won . ) therefore , the total number of games played is 40 + x , and the total number of games won is 20 + x . this gives the equation as : 20 % * ( 40 + x ) = 20 + x solve : let ' s get rid of the percent sign 20 / 100 * ( 40 + x ) = 20 + x 1 / 5 * ( 40 + x ) = 20 + x get rid of the fraction : 5 [ 1 / 5 * ( 40 + x ) ] = 5 ( 20 + x ) 1 * ( 40 + x ) = 100 + 5 x 40 + x = 100 + 5 x ( 40 - 100 ) + x = ( 100 - 100 ) + 5 x - 60 + x = 5 x - 60 + ( x - x ) + 5 x - x - 60 = 4 x 15 = x answer : b
Answer: b
Python program:
a = 50 - 20
b = a / 2
Problem: ( x ) + 9088 + 1090 - 9156 = 19845 . calculate the value of x
Options: a ) 11123 , b ) 18153 , c ) 11282 , d ) 18825 , e ) 18823
Rationale: "( x ) + 9088 + 1090 - 9156 = 19845 = x + 9088 + 1090 = 19845 + 9156 = x + 10178 = 29001 = x = 29001 - 10178 = 18823 answer is e"
Answer: e
Python program:
a = 19845 + 9156 
b = a - 1090
c = b - 9088
d = const_60 / 2
e = c * d
Problem: a and b invests rs . 8000 and rs . 15000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 75 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 15000 * 6 ) + ( 10000 * 6 ) 64000 : 150000 32 : 75 answer : a"
Answer: a
Python program:
a = 8000 * 4
b = 15000 / 3
c = 2 * 4
d = b * c
e = a + d 
f = 2 * 3
g = 15000 * f
h = 15000 / 3
i = 15000 - h
j = 2 * 3
k = i * j
l = g + k 
m = e / l
Problem: the market value of a certain machine decreased by 15 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 4,400 , e ) $ 800
Rationale: "b . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 15 / 100 ) = 8000 - 1200 = $ 6800 market value in 1984 = market value in 1983 - ( 15 % of $ 8000 ) = 6800 - 1200 = $ 5600"
Answer: b
Python program:
a = 100 * 10
b = 2 * 4
c = a * b
d = 100 * 15
e = 2 * 4
f = d * e
g = 15 / 100
h = g * 2
i = f * h
j = c - i
Problem: a water tank is four - fifths full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only four - fifths full , the time is ( 4 / 5 ) * 15 = 12 minutes the answer is d .
Answer: d
Python program:
a = 2 + 3 
b = 4 / a
c = 1/(6)
d = 1/(10)
e = c - d
f = b / e
Problem: a doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ?
Options: a ) 8 % , b ) - 25 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 12 c . c % prescribed dosage greater than the typical dosage = ( 12 - 16 / 16 ) * 100 % = ( - 4 / 16 ) * 100 % = - 25 % answer b"
Answer: b
Python program:
a = 2 / 15
b = a * 120
c = b - 12
d = 2 / 15
e = d * 120
f = c / e
g = f * 100
Problem: mr . smith calculated the average of 10 3 digit numbers . but due to a mistake he reversed the digits of a number and thus his average increased by 19.8 the difference between the unit digit and hundreds digit of that number is :
Options: a ) 2 , b ) 6 , c ) 5 , d ) 3 , e ) 4
Rationale: since the average increased by 29.7 and there were a total of 10 numbers , it means the incorrect number was 198 greater than the correct number . say , the correct number was abc ( where a , b and c are the digits of the 3 digit number ) then the incorrect number was cba . 100 c + 10 b + a - ( 100 a + 10 b + c ) = 198 99 c - 99 a = 99 ( c - a ) = 198 198 = 99 * 2 = 99 ( c - a ) so c - a = 2 answer ( a )
Answer: a
Python program:
a = 10 * 19
b = 100 - 1
c = a / b
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 4 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 4 years ago ? i . e . d - 4 = 14 - 4 = 10 years answer : b"
Answer: b
Python program:
a = 6 + 8 
b = a - 4
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 24 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 101
Rationale: "use the options . the options which after getting added to 24 shows a cube of a number could be right . here 64 + 24 = 88 72 + 24 = 96 86 + 24 = 110 98 + 24 = 122 101 + 24 = 125 - - - ( 5 * 5 * 5 ) so we have 101 as the answer ! e"
Answer: e
Python program:
a = 1 + 3 
b = 1 + a 
c = b ** 3
d = c - 24