euclaise/mathqa_programs huggingface dataset:
Problem: - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 170 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 230 , c ) 300 , d ) 400 , e ) 500
Rationale: since 170 students answered yes only for subject m , then the remaining 330 students who answered yes for subject m , also answered yes for subject r . so , 330 students answered yes for both subjects . if 320 students answered yes for both subjects , then 400 - 330 = 70 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 70 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 70 + 300 ) = 230 students did not answer yes for either subject . answer : b .
Answer: b
Python program:
a = 500 - 170
b = 170 + a 
c = 500 - 170
d = 400 - c
e = b + d 
f = 800 - e
Problem: a man can do a piece of work in 10 days , but with the help of his son , he can finish it in 5 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 15
Rationale: "son ' s 1 day work = 1 / 5 - 1 / 10 = 1 / 10 son alone can do the work in 10 days answer is d"
Answer: d
Python program:
a = 10 * 5
b = 10 - 5
c = a / b
Problem: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 4,400 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,700 , d ) 2,200 , e ) 3,400
Rationale: "assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 4400 therefore x = 3200 / 4 = 800 price of 28 inch + 30 inch = 1000 + 1200 = 2200 option d"
Answer: d
Python program:
a = 200 + 3600 
b = 1 + 2 
c = b + 3 
d = c * 200
e = a - d
f = e / 4
g = f + 200 
h = 200 + 3600 
i = 1 + 2 
j = i + 3 
k = j * 200
l = h - k
m = l / 4
n = m + 200 
o = n + 200 
p = g + o 
q = 2 * 10
r = q - 1
s = p / r
Problem: find large number from below question the difference of two numbers is 750 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1345 , b ) 1250 , c ) 897 , d ) 900 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 750 = 6 x + 15 5 x = 735 x = 147 large number = 147 + 1365 = 897 c"
Answer: c
Python program:
a = 750 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: a man , a woman and a boy can together complete a piece of work in 4 days . if a man alone can do it in 6 days and a boy alone in 18 days , how long will a woman take to complete the work ?
Options: a ) 36 days , b ) 32 days , c ) 34 days , d ) 42 days , e ) 49 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 4 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 4 – 2 / 9 = 1 / 36 therefore , the woman alone can finish the work in 36 days . answer : option a"
Answer: a
Python program:
a = 1/(4)
b = 1/(6)
c = 1/(18)
d = b + c 
e = a - d
f = 1/(e)
Problem: the price of lunch for 15 people was $ 210.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.72 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 210 is for 115 then we have to calculate for 100 for 115 210 for 100 x so by cross multiplication we get 115 x = 100 * 210 = > x = 100 * 210 / 110 by simplifying we get x as 190.90 which is the price of lunch before gratuity so the gratuity is 19.10 so as the question ask the average price person excluding gratuity is 190.90 / 15 = 12.72 so our answer is b )"
Answer: b
Python program:
a = 100 + 15 
b = 210 / 0
c = b * 100
d = 1 / 15
e = c * d
Problem: 82 a 7 + 6 b ____ 190 if a and b represent positive single digits in the correctly worked computation above , what is the value of a + 2 b ?
Options: a ) 2 , b ) 6 , c ) 9 , d ) 11 , e ) 12
Rationale: adding the digits in unit ' s place , 2 + 7 + b = 10 ( since a and b are positive single digits ) = > b = 1 now adding the digits in ten ' s place , 8 + a + 6 + 1 = 19 ( 1 has been carried over from unit ' s place addition ) = > a = 4 a + 2 b = 4 + 2 * 1 = 6 answer b
Answer: b
Python program:
a = 6 * 10
b = 190 - a
c = b - 82
d = c - 7
e = 6 * 10
f = 190 - e
g = f - 82
h = g - 7
i = h / 10
j = math.floor(i)
k = j * 10
l = d - k
m = l * 2
n = 6 * 10
o = 190 - n
p = o - 82
q = p - 7
r = q / 10
s = math.floor(r)
t = m + s
Problem: the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80
Rationale: "income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d"
Answer: d
Python program:
a = 85 * 6
b = 60 * 4
c = a + b 
d = c + 30 
e = 6 + 4 
f = d / e
Problem: in a certain alphabet , 13 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 3 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 13 + 24 = 37 ; next , we find the total # of letters without line : 40 - 37 = 3 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 3 - 0 = 3 . a"
Answer: a
Python program:
a = 13 + 24 
b = 40 - a
Problem: the tax on a commodity is diminished by 10 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 4 % , c ) 32 % , d ) 12 % , e ) 52 %
Rationale: "100 * 100 = 10000 80 * 120 = 9600 10000 - - - - - - - 400 100 - - - - - - - ? = 4 % answer : b"
Answer: b
Python program:
a = 100 + 20 
b = 100 - 10
c = a * b
d = c / 100
e = 100 - d
Problem: what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 4 . imo c ."
Answer: c
Python program:
a = 4 + 3 
b = a + 2
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 2 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 1 hours , d ) 10 hours , e ) 12 hours
Rationale: to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 2 = 1 hours answer is c
Answer: c
Python program:
a = 12 - 10
b = a / 2
Problem: of 30 applicants for a job , 10 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: c . 9 30 - 3 = 27 27 - 10 - 18 = - 9 then 9 are in the intersection between 4 years experience and degree . answer c
Answer: c
Python program:
a = 10 + 18 
b = 30 - 3
c = a - b
d = 18 - 10
e = c + d
Problem: a paper is in a square form whose one side is 20 cm . two semi circles are drawn on its opposites as diameters . if these semi circles are cut down what is the area of the remaining paper ?
Options: a ) 8.76
b ) 8.79
c ) 8.75
d ) 8.74
e ) 8.72
Rationale: ( 5 * 3.5 ) / 2 = 8.75 answer : c
Answer: c
Python program:
a = square_area - (
b = 20 / 2
c = a / circle_area
Problem: of 70 players on a football team , 34 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 58 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 34 rest = 70 - 34 = 36 left handed = 36 / 3 = 12 right handed = 24 if all thrower are right handed then total right handed is 34 + 24 = 58 so b . 58 is the right answer"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 34
d = b * c
e = d + 34
Problem: if the digits 31 in the decimal 0.00031 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00031 ) ?
Options: a ) 31 , b ) 0.31 , c ) 0.0031 , d ) 0.00031 , e ) 3.1 e - 05
Rationale: "99 * 0.31 = 30.69 approx . 31 answer : a"
Answer: a
Python program:
a = 10 * 10
b = 10 * 10
c = b - 1
d = a * c
e = 10 * 10
f = e - 1
g = 31 / f
h = d * g
i = h / 1000
j = i * 10
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 24 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 16 / 21
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.24 - - - > x = 160 / 21 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 160 / 21 ) / 10 = 16 / 21 . hence , e is the correct answer ."
Answer: e
Python program:
a = 40 - 24
b = 40 - 19
c = a / b
Problem: if the sum of two numbers is 30 and the sum of their squares is 840 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 30
Rationale: sol . let the numbers be x and y . then , ( x + y ) = 30 and x 2 + y 2 = 840 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 30 ) 2 - 840 = 900 - 840 = 60 xy = 30 . answer e
Answer: e
Python program:
a = 30 ** 2
b = a - 840
c = b / 2
Problem: pavan travelled for 11 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan .
Options: a ) 298 km , b ) 278 km , c ) 278 km , d ) 300 km , e ) 267 km
Rationale: "let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 11 = > x / 60 + x / 50 = 11 = > ( 5 x + 6 x ) / 300 = 11 = > x = 300 km answer : d"
Answer: d
Python program:
a = 2 * 30
b = 1/(a)
c = 25 * 2
d = 1/(c)
e = b + d 
f = 1/(e)
g = f * 11
Problem: if 6 x ^ 2 + x - 12 = ( ax + b ) ( cx + d ) , then | a | + | b | + | c | + | d |
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: this is the hard one , definitely a 700 + level question . we need numbers a , b , c , and d such that 6 x ^ 2 + x - 12 = ( ax + b ) ( cx + d ) this means that ac = 6 , bd = – 12 , and ad + bc = 1 . the a & c pair could be ( 1 , 6 ) or ( 2 , 3 ) , in some order . the absolute values of the b & d pair could be ( 1 , 12 ) or ( 2 , 6 ) or ( 3 , 4 ) , and of course , in each case , one of the two would have to be negative . after some trial and error , we find : 6 x ^ 2 + x - 12 = ( 2 x + 3 ) ( 3 x - 4 ) thus , we see : | a | + | b | + | c | + | d | = 2 + 3 + 3 + 4 = 12 answer = b
Answer: b
Python program:
a = 2 + 3 
b = 3 + 4 
c = a + b
Problem: the speed of a boat in still water in 20 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 9.2 , b ) 10.2 , c ) 9.8 , d ) 9.6 , e ) 10.0
Rationale: "speed downstream = ( 20 + 4 ) = 24 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 24 = 9.6 km answer is d ."
Answer: d
Python program:
a = 20 + 4 
b = 24 / const_60
c = a * b
Problem: a bag contains 3 red , 5 yellow and 7 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 13 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 3 + 5 + 7 = 15 n ( s ) = 15 c 3 = 455 n ( e ) = 3 c 1 * 5 c 1 * 7 c 1 = 105 probability = 105 / 455 = 3 / 13 answer is c"
Answer: c
Python program:
a = math.comb(4, 0)
b = 3 + 0 
c = math.comb(b, 1)
d = a * c
e = 3 + 5 
f = e + 7 
g = math.comb(f, 3)
h = d / g
Problem: two cars are driving toward each other . the first car is traveling at a speed of 100 km / h , which is 25 % faster than the second car ' s speed . if the distance between the cars is 720 km , how many hours will it take until the two cars meet ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: the speed of the first car is 100 km / h . the speed of the second car is 100 / 1.25 = 80 km / h . the two cars complete a total of 180 km each hour . the time it takes the cars to meet is 720 / 180 = 4 hours . the answer is c .
Answer: c
Python program:
a = 100 * 4
b = 4 * 100
c = 1 + 4 
d = b / c
e = d * 4
f = a + e 
g = 4 * 100
h = 1 + 4 
i = g / h
j = 100 + i 
k = f / j
Problem: a tiger is chasing its prey at a constant speed . it entire body passes a blade of grass in 1 second . it then runs above a fallen tree trunk that is 20 meters long in 5 seconds . what is the length of the tiger ?
Options: a ) 6 m , b ) 5 m , c ) 4 m , d ) 3 m , e ) none of the above
Rationale: sol . let the length of the tiger be x metres and its speed be y m / sec . then , x / y = 1 ⇒ y = x ∴ ( x + 20 ) / 5 = x ⇔ x = 5 m . answer b
Answer: b
Python program:
a = 5 - 1
b = 20 / a
Problem: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 25 % . their gross income from sales for one month increases by what percent ?
Options: a ) 5 % , b ) 7.5 % , c ) 10 % , d ) 12.5 % , e ) 15 %
Rationale: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.25 x = 1.125 * ( p * x ) , an increase of 12.5 % . the answer is d ."
Answer: d
Python program:
a = 25 - 10
b = 25 / 10
c = a - b
Problem: 5 / 8 th of a job is completed in 10 days . if a person works at the same pace , how many days will he take to complete the job ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 2 , e ) 1
Rationale: explanation : solution : it is given that 5 / 8 th of the work is completed in 10 days . = > remaining work = 3 / 8 th of total applying unitary method : total work will be completed in 10 * 8 / 5 days = > it takes 16 days to complete total work = > hence , remaining work days = 16 - 10 = 6 days answer : c
Answer: c
Python program:
a = 5 / 8
b = 1 - a
c = b * 10
d = 8 / 5
e = c * d
Problem: find the number of different prime factors of 12800
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "explanation : l . c . m of 12800 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 2 , 5 number of different prime factors is 2 . answer : option b"
Answer: b
Python program:
a = 2 + 2
Problem: the sum of two numbers is 30 and their difference is 10 . find their product .
Options: a ) 104 , b ) 114 , c ) 315 , d ) 200 , e ) 335
Rationale: let the numbers be x and y . then x + y = 30 and x - y = 10 x = 20 ; y = 10 xy = 20 * 10 = 200 answer : d
Answer: d
Python program:
a = 30 + 10 
b = 1 + 1 
c = a / b
d = 30 + 10 
e = 1 + 1 
f = d / e
g = f - 10
h = c * g
Problem: difference of two numbers is 1660 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2490 and 4150 , b ) 249 and 415 , c ) 2400 and 4100 , d ) 2290 and 4350 , e ) 229 and 435
Rationale: let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1660 5 * y / 3 – y = 1660 2 * y / 3 = 1660 y = [ ( 1660 * 3 ) / 2 ] = 2490 . one number = 2490 , second number = 5 * y / 3 = 4150 answer is a .
Answer: a
Python program:
a = 7 / 5
b = 7 / 5
c = 1 - b
d = 1660 / c
e = a * d
Problem: a car is running at a speed of 120 kmph . what distance will it cover in 12 sec ?
Options: a ) 396 m , b ) 267 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 120 kmph = 120 * 5 / 18 = 33 m / s distance covered in 12 sec = 33 * 12 = 396 m answer is a"
Answer: a
Python program:
a = 120 / const_3_6
b = a * 12
Problem: jack and christina are standing 360 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 5 feet per second and christina walks in a straight line toward jack at a constant speed of 7 feet per second . lindy runs at a constant speed of 12 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 270 , b ) 300 , c ) 330 , d ) 360 , e ) 390
Rationale: "the relative speed of jack and christina is 5 + 7 = 12 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 360 / 12 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 12 * 30 = 360 feet . answer : d ."
Answer: d
Python program:
a = 5 + 7 
b = 360 / a
c = b * 12
Problem: rs . 6000 is lent out in two parts . one part is lent at 6 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 3
Rationale: "let the amount lent at 6 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 6 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 4 x / 100 = > 600 - 1 / 25 x = 450 = > x = 3750 amount lent at 10 % = 2250 required ratio = 3750 : 2250 = 75 : 45 = 15 : 9 = 5 : 3 answer : e"
Answer: e
Python program:
a = 450 * 100
b = 6000 * 6
c = a - b
d = 10 - 6
e = c / d
f = 450 * 100
g = 6000 * 6
h = f - g
i = 10 - 6
j = h / i
k = e / j
Problem: average age of students of an adult school is 52 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 150 , c ) 360 , d ) 240 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 52 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 30 so , required no . of students after joining the new students = x + 120 = 150 answer : b"
Answer: b
Python program:
a = 32 + 4 
b = a * 120
c = 120 * 32
d = b - c
e = 32 + 4 
f = 52 - e
g = d / f
h = g * 4
Problem: the h . c . f and l . c . m of two numbers are 11 and 385 respectively . if one number lies between 75 and 125 , then that number is
Options: a ) 77 , b ) 88 , c ) 99 , d ) 110 , e ) 120
Rationale: "explanation : product of numbers = 11 x 385 = 4235 let the numbers be 11 a and 11 b . then , 11 a x 11 b = 4235 inline fn _ jvn rightarrow ab = 35 now , co - primes with product 35 are ( 1,35 ) and ( 5,7 ) so , the numbers are ( 11 x 1 , 11 x 35 ) and ( 11 x 5 , 11 x 7 ) since one number lies 75 and 125 , the suitable pair is ( 55,77 ) hence , required number = 77 . answer : a"
Answer: a
Python program:
a = 11 * 385
b = a / 125
c = math.sqrt(b)
d = c * 125
Problem: a train running at the speed of 54 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 299 meter , c ) 135 meter , d ) 155 meter , e ) 144 meter
Rationale: "speed = 54 * ( 5 / 18 ) m / sec = 15 m / sec length of train ( distance ) = speed * time ( 15 ) * 9 = 135 meter answer : c"
Answer: c
Python program:
a = 54 * 1000
b = a / 3600
c = b * 9
Problem: simplify 3 / 4 of 6 0 – 8 / 5 of 60 + ? = 12
Options: a ) 48 , b ) 24 , c ) 56 , d ) 63 , e ) 14
Rationale: 60 × 3 / 4 = 45 , 60 × 8 / 5 = 96 45 – 96 + ? = 12 = > 96 + 12 = 108 – 45 = 63 [ 63 + 45 = 108 – 96 = 12 ] option d
Answer: d
Python program:
a = 3 / 4
b = a * 60
c = 8 / 5
d = c * 60
e = b - d
f = negate + (
Problem: a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "there are 60 siblings in junior class and 60 their pair siblings in the senior class . we want to determine probability of choosing one sibling from junior class and its pair from senior . what is the probability of choosing any sibling from junior class ? 60 / 1000 ( as there are 60 of them ) . what is the probability of choosing pair of chosen sibling in senior class ? as in senior class there is only one pair of chosen sibling it would be 1 / 800 ( as there is only one sibling pair of chosen one ) . so the probability of that the 2 students selected will be a sibling pair is : 60 / 1000 ∗ 1 / 800 = 3 / 40000 answer : a ."
Answer: a
Python program:
a = 1 / 3
Problem: what is the average ( arithmetic mean ) of all the multiples of 10 from 10 to 160 inclusive ?
Options: a ) 90 , b ) 95 , c ) 70 , d ) 105 , e ) 110
Rationale: 10 and 190 inclusive would mean there are 15 terms . no need to add up all the terms and further divide by 15 since the terms are evenly spaced in ascending order from 10 , 20 , 30 . . . . . . . . 160 the middle term is the average which is the tenth term = 70 c is the answer .
Answer: c
Python program:
a = 10 * 2
b = 160 - a
c = b / 2
Problem: michael earns $ 7.00 per hour for the first 40 hours he works per week , and twice this rate for overtime . if michael earned $ 320 last week , how many hours did he work ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47
Rationale: $ 7 * 40 + $ 12 * x = $ 320 - - > x = 3 hours . total working hours = 40 + 3 = 43 . answer : a .
Answer: a
Python program:
a = 7 * 2
b = 40 / a
c = b + 40
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is ?
Options: a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) rs . 9000
Rationale: "explanation : a = 7500 ( 26 / 25 ) 2 = 8112 answer is d"
Answer: d
Python program:
a = 100 + 4 
b = a / 100
c = 100 + 4 
d = c / 100
e = b * d
f = 7500 * e
Problem: steve traveled the first 2 hours of his journey at 50 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 50 = 100 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 100 = 340 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 340 / 5 = 68 mph answer : a"
Answer: a
Python program:
a = 80 * 3
b = 50 * 2
c = a + b 
d = 3 + 2 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g