euclaise/mathqa_programs huggingface dataset:
Problem: a searchlight on top of the watch - tower makes 1 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 20 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "1 revolutions per minute = 1 revolution every 60 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 60 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 20 seconds ) = 1 - p ( man in dark for max of 20 seconds ) = 1 - 20 / 60 = 1 - 1 / 3 = 2 / 3 or the other way would be : p ( man in dark for at least 20 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 60 seconds because that is the max . in this approach it would be 20 / 60 seconds = 1 / 3 . answer is b"
Answer: b
Python program:
a = const_60 * 1
b = a / 1
c = 20 / b
d = 1 - c
Problem: exactly 10 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 85 % , e ) 84 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 10 % of all reporters reporters covering politics / all reporters = 10 / 70 = 1 / 7 reporters not covering politics / all reporters = 6 / 7 = 85 % = d"
Answer: d
Python program:
a = 100 - 30
b = 10 / a
c = 1 - b
d = c * 100
Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 5 : 12 , find the age of sachin
Options: a ) 9 , b ) 24.8 , c ) 2 , d ) 3 , e ) 5
Rationale: explanation : if rahul age is x , then sachin age is x - 7 , so , 12 x - 84 = 5 x 7 x = 84 x = 12 so sachin age is 12 - 7 = 5 answer : e ) 5
Answer: e
Python program:
a = 12 - 5
b = 7 / a
c = b * 5
Problem: in a 6 - sided polygon xqrstv ∠ x measures 48 ° less than the average ( arithmetic mean ) of the remaining 5 angles . what does ∠ x equal to , in degrees ?
Options: a ) 72 , b ) 80 , c ) 88 , d ) 96 , e ) 104
Rationale: the sum of interior angle in a polygon is ( n - 2 ) * 180 so for a six sided figure , ( 6 - 2 ) * 180 = 720 let the a . m of the other 5 angles be ' m ' - - > m * 5 + ∠ x = 720 , we know ∠ x = m - 48 - - > m * 5 + m - 48 = 720 , solving we get m = 128 hence ∠ x = 128 - 48 = 80 ans b .
Answer: b
Python program:
a = 6 * 5
b = a + 48
Problem: a train crosses a platform of 150 m in 15 sec , same train crosses another platform of length 220 m in 18 sec . then find the length of the train ?
Options: a ) 200 m , b ) 180 m , c ) 272 m , d ) 210 m , e ) 267 m
Rationale: "length of the train be ‘ x ’ ( x + 150 ) / 15 = ( x + 220 ) / 18 5 x + 1100 = 6 x + 900 x = 200 m answer : a"
Answer: a
Python program:
a = 15 / 3
b = 15 / a
c = 220 * b
d = 15 / 3
e = 18 / d
f = 150 * e
g = c - f
Problem: if ( - 4 ) ^ ( 6 x ) = 4 ^ ( 30 + x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 6
Rationale: "since x is an integer , ( - 4 ) ^ ( 6 x ) is always positive . so , 4 ^ 6 x = 4 ^ ( 30 + x ) 6 x = 30 + x 5 x = 30 x = 6 answer : e"
Answer: e
Python program:
a = 30 / 4
Problem: working alone , a can complete a certain kind of job in 10 hours . a and d , working together at their respective rates , can complete one of these jobs in 5 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let total time taken by d to complete the job = d total time taken by a to complete the job = 10 work done by a in an hour 1 / a = 1 / 10 working together a and d can complete the job in 5 hours 1 / a + 1 / d = 1 / 5 = > 1 / d = 1 / 5 - 1 / a = 1 / 5 - 1 / 10 = 1 / 10 = > d = 10 hours answer b"
Answer: b
Python program:
a = 1/(5)
b = 1/(10)
c = a - b
d = 1/(c)
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 160 m long ?
Options: a ) 41.6 sec , b ) 11 sec , c ) 88 sec , d ) 19 sec , e ) 10 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 160 = 520 m required time = 520 * 2 / 25 = 41.6 sec answer : a"
Answer: a
Python program:
a = 45 - 160
b = a * const_0_2778
c = 360 / b
Problem: man can row upstream at 10 kmph and downstream at 20 kmph , and then find the speed of the man in still water ?
Options: a ) 5 , b ) 20 , c ) 30 , d ) 25 , e ) 15
Rationale: us = 10 ds = 20 m = ( 10 + 20 ) / 2 = 15 answer : e
Answer: e
Python program:
a = 10 + 20 
b = a / 2
Problem: at what rate percent of simple interest will a sum of money double itself in 44 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 2.27 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 44 ) = 100 / 44 = 2.27 % answer : e"
Answer: e
Python program:
a = 100 / 44
Problem: which is greatest in 16 ( 2 / 3 ) % , 2 / 5 and 0.17 ?
Options: a ) 2 / 3 , b ) 0.17 , c ) 3 / 2 , d ) 0.71 , e ) none of them
Rationale: 16 ( 2 / 3 ) % = [ ( 50 / 3 ) * ) 1 / 100 ) ] = 1 / 6 = 0.166 , 2 / 15 = 0.133 . clearly , 0.17 is the greatest . answer is b .
Answer: b
Python program:
a = 0 * 17
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 11 and 41 inclusive .
Options: a ) 351 , b ) 364 , c ) 416 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 11 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 11 + 41 = 52 2 ) now look at the ' next smallest ' and the ' next biggest ' : 13 + 39 = 52 now we have proof that there is no middle term . we have 8 bunches of 52 . 8 ( 52 ) = 416 c"
Answer: c
Python program:
a = 41 + 1 
b = a / 2
c = b ** 2
d = 11 - 2
e = d + 1 
f = e / 2
g = f ** 2
h = c - g
Problem: if 25 / 999 = 0.002 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "0 . [ u ] 25 [ / u = 0.002002002002 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 2 . since 81 is multiple of 3 , the 81 st digit is 2 . answer e"
Answer: e
Python program:
a = 2 + 3
Problem: if x is an integer and 6.1 × 10 ^ x is less than 620 what is the greatest possible value for x ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: if x = 2 6.1 × 10 ^ 2 = 610 < 620 so , x = 2 answer : a
Answer: a
Python program:
a = 620 / 6
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
Problem: in the game of dubblefud , red balls , blue balls and green balls are each worth 2 , 4 and 5 points respectively . in a certain selection of balls , the product of the point values of the balls is 16000 . if the number of blue balls in this selection equals the number of green balls , how many red balls are in the selection ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of red balls = 4 hence d
Answer: d
Python program:
a = 2 / 2
b = a * 2
c = 2 / 2
d = b + c 
e = 2 / 2
f = d + e
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability q that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days q = 15 / 64 ans a it is ."
Answer: a
Python program:
a = math.comb(6, 4)
b = 1 / 2
c = b ** 4
d = 1 / 2
e = d ** 2
f = c * e
g = 1/(f)
h = a / g
Problem: a man can row 4.5 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 4.5 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.5 km / hr . answer : d"
Answer: d
Python program:
a = 4 * 5
b = a - 4
c = b / 3
Problem: what is the smallest no . which must be added to 8261955 so as to obtain a sum which is divisible by 11 ?
Options: a ) 8 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 8261955 , difference = ( 8 + 6 + 9 + 5 ) - ( 2 + 1 + 5 ) = 28 - 8 = 20 . the units digit is at odd place . so we add 2 to the number = > 8261955 + 2 = 8261957 now , ( 8 + 6 + 9 + 7 ) - ( 2 + 1 + 5 ) = 30 - 8 = 22 = > 22 is a multiple of 11 and hence 8261957 is also divisible by 11 b
Answer: b
Python program:
a = 8261955 * 11
b = a / 8261955
Problem: if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 2 y ^ 2 = ?
Options: a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 32
Rationale: "3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 2 y ^ 2 = 2 * 16 = 32 answer is e"
Answer: e
Python program:
a = 40 + 20 
b = 3 + 2 
c = a / b
d = c * 3
e = 40 - d
f = e ** 2
g = 3 * f
Problem: a ’ s speed is 20 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 14 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 6 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 6 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 14 meters ) to reach the finish line . so b should get a head start of 6 / 20 th of the race . answer ( d )"
Answer: d
Python program:
a = 20 - 14
b = a / 20
Problem: what is the product of all the possible values of x if x ^ 2 ( x + 2 ) + 7 x ( x + 2 ) + 6 ( x + 2 ) = 0 ?
Options: a ) – 29 , b ) – 12 , c ) 12 , d ) 29 , e ) 168
Rationale: x ^ 2 ( x + 2 ) + 7 x ( x + 2 ) + 6 ( x + 2 ) = 0 = > ( x + 2 ) ( x ^ 2 + 7 x + 6 ) = 0 = > ( x + 2 ) ( x + 1 ) ( x + 6 ) = 0 = > x = - 1 or - 2 or - 6 product = - 12 answer option - 12 answer : b
Answer: b
Python program:
a = negate * (
b = 7 - 6
c = a * b
Problem: jar x is 1 / 5 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 10 , d ) 7 / 20 , e ) 9 / 20
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 5 + p / 4 = 9 / 20 the answer is e ."
Answer: e
Python program:
a = 1 / 2
b = 1 / 5
c = 1 / 5
d = b * c
e = a + d
Problem: a babysitter is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 30 hours per week . for any overtime hours worked in excess of 30 hours per week , the babysitter is paid a rate that is 75 % higher than his regular rate . if last week the babysitter earned $ 760 , how many total hours did she work that week ?
Options: a ) 40 , b ) 30 , c ) 35 , d ) 25 , e ) 45
Rationale: for 30 hrs = 30 * 16 = 480 excess = 760 - 480 = 280 for extra hours = . 75 ( 16 ) = 12 in addition to $ 16 . thus , 12 + 16 = 28 number of extra hrs = 280 / 28 = 10 total hrs = 30 + 10 = 40 answer a 40
Answer: a
Python program:
a = 16 * 30
b = 760 - a
c = 75 + 100 
d = c / 100
e = 16 * d
f = b / e
g = 30 + f
Problem: by travelling at 80 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 25 kmph , b ) 40 kmph , c ) 35 kmph , d ) 46 kmph , e ) 50 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 80 * 3 x = 240 x km he covered 2 / 3 * 240 x = 160 x km in 1 / 3 * 3 x = x hours so , the remaining 80 x km , he has to cover in 2 x hours . required speed = 80 x / 2 x = 40 kmph . answer : b"
Answer: b
Python program:
a = 80 * 3
b = 80 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
Problem: two employees m and n are paid a total of $ 594 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 240 , b ) $ 250 , c ) $ 260 , d ) $ 270 , e ) $ 280
Rationale: 1.2 n + n = 594 2.2 n = 594 n = 270 the answer is d .
Answer: d
Python program:
a = 120 / 100
b = a + 1 
c = 594 / b
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 42 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 7 min , c ) 8.2 min , d ) 9.6 min , e ) 40 min
Rationale: "d 9.6 min due to stoppages , it covers 8 km less . time taken to cover 9 km = ( 8 / 50 x 60 ) min = 9.6 min"
Answer: d
Python program:
a = 50 - 42
b = a / 50
c = const_60 * b
Problem: tough and tricky questions : functions . let a be a positive integer . let n # a equal n ^ ( 2 a ) if a is odd and n ^ ( 3 a ) if a is even . then ( 2 # 3 ) + ( 2 # 3 ) – ( 3 # 3 ) is equal to
Options: a ) 64 , b ) 82 , c ) 128 , d ) 729 , e ) 1522
Rationale: "answer : 3 ^ 6 + 3 ^ 6 - 3 ^ 6 = 3 ^ 6 = 729 ans d"
Answer: d
Python program:
a = 2 * 0
b = 2 ** a
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 900 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units , b ) 120 sq . units , c ) 187 sq . units , d ) 607 sq . units , e ) 815 sq . units
Rationale: "given that the area of the square = 900 sq . units = > side of square = √ 900 = 30 units the radius of the circle = side of the square = 30 units length of the rectangle = 2 / 5 * 30 = 12 units given that breadth = 10 units area of the rectangle = lb = 12 * 10 = 120 sq . units answer : b"
Answer: b
Python program:
a = math.sqrt(900)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: a rectangular grass field is 60 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1200 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 60 + 55 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : b"
Answer: b
Python program:
a = 2 * 5
b = 60 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 5 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 40 min , e ) 55 min
Rationale: "there are 8 hours in between 9 a . m . to 5 p . m . 8 * 5 = 40 minutes . answer : d"
Answer: d
Python program:
a = 3 + 5 
b = a * 5
Problem: a plant manager must assign 6 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 24 , b ) 27 , c ) 33 , d ) 45 , e ) 54
Rationale: "whatever : my take selecting team of 2 out of 10 to assign to the shifts = 6 c 2 = 15 ways . now 2 out of 10 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 2 out of 6 ) * arranging those teams in shifts = 15 * 3 = 45 ans : d"
Answer: d
Python program:
a = 6 / 2
b = math.factorial(a)
c = b / 2
d = math.factorial(6)
e = 6 - 2
f = math.factorial(e)
g = math.factorial(2)
h = f * g
i = d / h
j = c * i
Problem: the average of first four multiples of 4 is :
Options: a ) 3 , b ) 9 , c ) 10 , d ) 15 , e ) 17
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 ) / 4 = 40 / 4 = 10 answer c"
Answer: c
Python program:
a = 4 + 1
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 15 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 28 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 60.00
Rationale: without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 43 % , thus he must pay slightly more than $ 57 . only answer choice e fits . answer : e .
Answer: e
Python program:
a = 15 * 28
b = a / 100
c = 10 - b
d = c * 10
Problem: what is the sum of the greatest common factor and the lowest common multiple of 45 and 125 ?
Options: a ) 1920 , b ) 2201 , c ) 3240 , d ) 1130 , e ) 3840
Rationale: "prime factorization of the given numbers 45 = 3 ^ 2 125 = 5 ^ 3 greatest common factor = 5 lowest common multiple = 3 ^ 2 * 5 ^ 2 * 5 = 1125 sum = 5 + 1125 = 1130 answer d"
Answer: d
Python program:
a = 45 * 125
b = a / 4
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability e that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days e = 15 / 64 ans a it is ."
Answer: a
Python program:
a = math.comb(6, 4)
b = 1 / 2
c = b ** 4
d = 1 / 2
e = d ** 2
f = c * e
g = 1/(f)
h = a / g
Problem: you collect pens . suppose you start out with 10 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 59
Rationale: "solution start with 10 pens . mike gives you 22 pens : 10 + 22 = 39 pens . cindy doubles the number of pens you have : 39 ã — 2 = 78 pens . sharon takes 19 pens from you : 78 - 19 = 59 pens . so you have 59 at the end . correct answer : e"
Answer: e
Python program:
a = 22 + 10 
b = a * 2
c = b - 19
Problem: how many integer values are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: the inequality given is 1 < 3 x + 5 < 17 it can further reduced to - 4 < 3 x < 12 finally - 4 / 3 < x < 4 so can only take 5 integer values i . e . - 1 , 0,1 , 2,3 correct answer - d
Answer: d
Python program:
a = 17 - 5
b = a / 3
c = 1 - 5
d = c / 3
e = b - d
f = math.floor(e)
Problem: a portion of the 85 % solution of chemicals was replaced with an equal amount of 30 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 11 , b ) 6 / 11 , c ) 7 / 11 , d ) 9 / 11 , e ) 13 / 6
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.85 ( 1 - x ) + 0.3 * x = 0.4 - - > x = 9 / 11 . answer : d ."
Answer: d
Python program:
a = 85 - 40
b = 85 - 30
c = a / b
Problem: if the price of a book is first decreased by 20 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 4 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 20 % on rs 80 = 80 + 16 = 96 net change in price = 100 - 96 = 4 answer : c"
Answer: c
Python program:
a = 100 * 20
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 20
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j
Problem: a basketball is dropped from a height of 30 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 3 full bounces .
Options: a ) 50 , b ) 82.5 , c ) 60 , d ) 75 , e ) 80
Rationale: "initial distance = 30 feet first bounce = 15 feet up + 15 feet down = 30 feet second bouche = 7.5 feet up + 7.5 feet down = 15 feet third bounce = 375 feet up and 3.75 feet down = 7.5 feet total distance covered = 30 + 30 + 15 + 7.5 = 82.5 answer is b"
Answer: b
Python program:
a = 30 / 3
b = a / 3
c = b / 3
d = c / 3
e = 30 / 3
f = 30 + e 
g = 30 / 3
h = f + g 
i = 30 / 3
j = i / 3
k = h + j 
l = 30 / 3
m = l / 3
n = k + m 
o = 30 / 3
p = o / 3
q = p / 3
r = n + q 
s = 30 / 3
t = s / 3
u = t / 3
v = r + u 
w = d + v 
x = w * 3
y = 30 / 3
z = y / 3
A = z / 3
B = x - A
C = 30 / 3
D = C / 3
E = D / 3
F = B - E
G = 30 / 3
H = G / 3
I = H / 3
J = F - I
K = 30 / 3
L = K / 3
M = L / 3
N = J - M
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 600 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 50 sec , e ) 40 min
Rationale: "they meet every 600 / 7 + 8 = 40 sec answer is e"
Answer: e
Python program:
a = 8 + 7 
b = 600 / a
Problem: praveen age after 10 years will be 3 times his age 3 years back . what is the present age of chris ?
Options: a ) 20 , b ) 25 , c ) 10 , d ) 30 , e ) 15
Rationale: chris present age = x after 10 years = x + 10 3 years back = x - 3 x + 10 = 3 ( x - 3 ) x = 20 answer is a
Answer: a
Python program:
a = 3 * 10
b = 10 + a 
c = 3 - 1
d = b / c
Problem: how many multiples of 2 are there between 10 and 52 , 10 and 52 inclusive ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 21 , e ) 22
Rationale: "2 multiples are . . . 10,12 , 14,16 , 18,20 , 22,24 , 26,28 , 30,32 , 34,36 , 38,40 , 42,44 , 46,48 , 50,52 , . . . , the answer is = 22 answer is e"
Answer: e
Python program:
a = 52 - 10
b = a / 2
c = b + 1
Problem: what is the next number 12 13 15 17 111 113 117 119 123 129 ?
Options: a ) 154 , b ) 220 , c ) 129 , d ) 131 , e ) 224
Rationale: 131 . these are the first 10 prime numbers ( 2 , 3 , 5 . . . ) prefixed with a 1 answer : d
Answer: d
Python program:
a = reminder + ( 
b = 100 + a
Problem: david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 6 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 4 , e ) 1 / 3
Rationale: "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 2 x total tips for all months = 6 * x + 2 x = 8 x tips for august / total tips for all months = 2 x / 8 x = 1 / 4 answer : d"
Answer: d
Python program:
a = 10 - 2
b = a + 2 
c = 4 / 0