euclaise/mathqa_programs huggingface dataset:
Problem: if x = 3 y , where y is a prime number greater than 2 , how many different positive even divisors does x have , including x ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it can not be determined from the information given
Rationale: for x to have even divisors , xx has to be an even number . we know that x = 3 y , where yy is a prime number greater than 2 . as 2 is the only even prime number , y has to be an odd prime number . this means that x must also be an odd number , since odd x odd = odd . as x is odd , it can not have any even divisors . therefore , a is the correct answer .
Answer: a
Python program:
a = 3 * 3
b = a / 3
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a sixth of a circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 360 , d ) 6000 , e ) 36000
Rationale: 1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 60 degrees = 6000 anglets answer - d
Answer: d
Python program:
a = 2 + 4 
b = 1 / a
c = 3600 / 10
d = c * 100
e = b * d
Problem: ratio of girl and boys in class is 5 : 6 . if 20 girl leave the class and ratio become 2 : 3 . calculate the no . of boys ?
Options: a ) 100 , b ) 120 , c ) 80 , d ) 90 , e ) none of the above
Rationale: girl 5 x and boys 6 x 5 x - 20 / 6 x = 2 / 3,15 x - 60 = 12 x , 3 x = 60 , x = 20 boys = 6 x = 120 answer b
Answer: b
Python program:
a = 20 * 3
b = 5 * 3
c = 6 * 2
d = b - c
e = a / d
f = e * 6
Problem: if 30 % of a number exceeds 20 % of it by 18 , then find the number ?
Options: a ) 120 , b ) 200 , c ) 180 , d ) 150 , e ) none of these
Rationale: "let the number be x . 30 % of x = 30 / 100 * x = 3 x / 10 20 % of x = 20 / 100 * x = x / 5 = 2 x / 10 . given that 3 x / 10 - 2 x / 10 = 18 = > x = 180 . required number is 180 . answer : c"
Answer: c
Python program:
a = 30 - 20
b = a / 100
c = 18 / b
d = c + 20
Problem: what is the sum of the numbers between 1 and 20 , inclusive ?
Options: a ) 310 , b ) 200 , c ) 215 , d ) 285 , e ) 210
Rationale: "sol . 1 + 2 + 3 . . . 17 + 18 + 19 + 20 answer . e"
Answer: e
Python program:
a = 1 * 20
b = a / 4
Problem: a company recently conducted a survey and found that 30,000 of its customers live in rural areas . if the number of customers who live in urban areas is 130 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 65,000 , b ) 67,000 , c ) 69,000 , d ) 71,000 , e ) 73,000
Rationale: "the number of customers in urban areas is 30,000 + 1.3 * 30,000 = 69,000 . the answer is c ."
Answer: c
Python program:
a = 4 * 2
b = 100 - a
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 3 / 4 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 6 / 22 , b ) 5 / 22 , c ) 7 / 22 , d ) 4 / 22 , e ) 3 / 22
Rationale: "# of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 c"
Answer: c
Python program:
a = 4 + 3 
b = a / 10
Problem: what is ( 24 ^ 7 + 24 ) / 24 ?
Options: a ) 159202573 , b ) 160902641 , c ) 172502765 , d ) 182302834 , e ) 191102977
Rationale: "( 24 ^ 7 + 24 ) / 24 = 24 * ( 24 ^ 6 + 1 ) / 24 = 24 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is e ."
Answer: e
Python program:
a = 24 ** 7
b = a + 24 
c = b / 24
Problem: 3 consecutive even numbers are such that thrice the first number exceeds double the third number by 7 . what is the third number ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: let the three numbers be x , x + 2 , and x + 4 . 3 x = 2 ( x + 4 ) + 7 x = 15 and then the third number is x + 4 = 19 . the answer is a .
Answer: a
Python program:
a = 7 * 3
b = a - 2
Problem: what is the units digit of ( 22 ^ 4 ) ( 16 ^ 3 ) ( 41 ^ 8 ) ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the units digit of 22 ^ 4 is the units digit of 2 ^ 4 which is 6 . the units digit of 16 ^ 3 is the units digit of 6 ^ 3 which is 6 . the units digit of 41 ^ 8 is the units digit of 1 ^ 8 which is 1 . the units digit of 6 * 6 * 1 is 6 . the answer is e ."
Answer: e
Python program:
a = math.factorial(22)
b = math.factorial(4)
c = a * b
d = math.factorial(22)
e = math.factorial(3)
f = d * e
g = c + f 
h = g / 22
Problem: in a factory , each day the expected number of accidents is related to the number of overtime hour by linear equation . suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents . what is the expected number of accidents when no overtime hours are logged ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : let , the number of over time hours be x and expected number of accidents be y . we will use the equation y = mx + c , where m and c are constant . now , according to the question , if x = 1000 , then y = 8 i . e 8 = 1000 x + c - - - - ( i ) and , if x = 400 , then y = 5 i . e 5 = 400 x + c . - - - - ( ii ) on solving these equations , we get m = 1 / 200 and c = 3 . hence , in case , no overtime is there i . e x = 0 , then the number of expected accident will be 3 . answer : b
Answer: b
Python program:
a = 8 - 5
b = 1000 - 400
c = a / b
d = c * 1000
e = 8 - d
Problem: last week vartan spent 20 percent of his wages on recreation . this week , his wages are 20 percent less than last week ʼ s wages and he spent 40 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?
Options: a ) 150 % , b ) 170 % , c ) 175 % , d ) 160 % , e ) 180 %
Rationale: "say vartan ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.8 * 100 = $ 80 , so he spends 0.4 * 80 = $ 32 on recreation ; 32 / 20 = 1.6 , hence the amount he spends on recreation this week is 160 % of the amount he spent on recreation last week : 20 * 1.6 = 32 answer : d"
Answer: d
Python program:
a = 100 - 20
b = 40 * a
c = b / 20
Problem: 4 , 12 , 48 , 240 , ( . . . )
Options: a ) 1440 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , answer : option a"
Answer: a
Python program:
a = negate - (
Problem: rs 3200 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 400 , b ) s 200 , c ) s 800 , d ) s 500 , e ) s 100
Rationale: "explanation : average rate = ( 144 / 3200 ) * 100 = 4.5 ratio = 5 : 15 so , first part = ( 5 / 20 ) * 3200 = rs 800 . answer : c"
Answer: c
Python program:
a = 5 / 100
b = 3200 * a
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: if you add all the numbers on your mobile phone except 8 and 2 , what is the answer ?
Options: a ) 55 , b ) 25 , c ) 85 , d ) 45 , e ) 35
Rationale: "we have to add 0 , 1,3 , 4,5 , 6,7 & 9 to find the answer . therefore 0 + 1 + 3 + 4 + 5 + 6 + 7 + 9 = 35 answer is e"
Answer: e
Python program:
a = 10 - 1
b = 1 + a 
c = b / 2
d = 10 - 1
e = c * d
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 6 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 72 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 360 x = 72 min answer : c"
Answer: c
Python program:
a = 1 * 6
b = 10 * a
Problem: evaluate : 40 - 10 ÷ 2 × 2 =
Options: a ) 20 , b ) 25 , c ) 10 , d ) 16 , e ) 30
Rationale: "according to order of operations , 10 ÷ 2 × 2 ( division and multiplication ) is done first from left to right 10 ÷ 2 × 2 = 5 × 2 = 10 hence 40 - 10 ÷ 2 × 2 = 40 - 10 = 30 correct answer e ) 30"
Answer: e
Python program:
a = 10 * 2
b = a * 2
c = 40 - b
Problem: the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 10 of her stamps , the ration of the number of kaye had to the number of alberto had was 6 : 4 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 80 , b ) 85 , c ) 65 , d ) 55 , e ) 50
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 10 a 2 = 3 x + 10 k 2 / a 2 = 6 / 4 ( 5 x - 10 ) / ( 3 x + 10 ) = 6 / 4 4 * ( 5 x - 10 ) = 6 * ( 3 x + 10 ) 20 x - 40 = 18 x + 60 2 x = 100 x = 50 k 2 = 5 * 50 - 10 = 240 a 2 = 3 * 50 + 10 = 160 k 2 - a 2 = 80 answer : a"
Answer: a
Python program:
a = 5 + 3 
b = 6 + 4 
c = math.lcm(a, b)
d = 6 + 4 
e = c / d
f = 6 * e
Problem: the speed at which a man can row a boat in still water is 18 kmph . if he rows downstream , where the speed of current is 6 kmph , what time will he take to cover 100 metres ?
Options: a ) 6.67 seconds , b ) 18 seconds , c ) 26 seconds , d ) 14.99 seconds , e ) 6 seconds
Rationale: "speed of the boat downstream = 18 + 6 = 24 kmph = 24 * 5 / 18 = 6.67 m / s hence time taken to cover 100 m = 100 / 6.67 = 14.99 seconds . answer : d"
Answer: d
Python program:
a = 18 + 6 
b = a * const_0_2778
c = 100 / b
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 25 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.42 hr , b ) 2.22 hrs , c ) 3.24 hrs , d ) 5 hrs , e ) 6.02 hrs
Rationale: "to be ( 10 + 25 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 35 * 50 = 1.42 hrs answer is a"
Answer: a
Python program:
a = 10 + 25 
b = 50 / a
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 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 5000 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 ) 15,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 5000 ) solving for x , we get the shares as 15000 . ans : ( option d )"
Answer: d
Python program:
a = 5 + 6
Problem: the ratio of pens to pencils is 5 to 6 . there are 8 more pencils than pens . how many pencils are there ?
Options: a ) 30 , b ) 32 , c ) 48 , d ) 55 , e ) 64
Rationale: "let x equal the number of pens , and y the number of pencils . then , x = 5 / 6 y . we also know that x = y - 8 . and so , we can substitute : y - 8 = 5 / 6 y so to isolate y , we get : 1 / 6 y = 8 and therefore : y = 48 answer : c"
Answer: c
Python program:
a = 8 * 5
b = a + 8
Problem: if 0.4 of a number is equal to 0.06 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.4 a = 0.06 b ⇔ a / b = 0.06 / 0.40 = 6 / 40 = 3 / 20 . ∴ a : b = 3 : 20 . answer c"
Answer: c
Python program:
a = 0 * 6
b = 0 * 4
c = a / b
Problem: a 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 260 ) / 9 = 500 / 9 x + 260 = 500 x = 240 . b"
Answer: b
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 260
Problem: a boatman can row 96 km downstream in 8 hr . if the speed of the current is 4 km / hr , then find in what time he will be able to cover 8 km upstream ?
Options: a ) 3 hrs , b ) 7 hrs , c ) 9 hrs , d ) 2 hrs , e ) 6 hrs
Rationale: explanation : speed in downstream = 96 / 8 = 12 kmph speed of current = 4 km / hr speed of the boatman in still water = 12 â € “ 4 = 8 kmph speed in upstream = 8 â € “ 4 = 4 kmph time taken to cover 8 km upstream = 8 / 4 = 2 hours . answer : d
Answer: d
Python program:
a = 96 / 8
b = a - 4
c = b - 4
d = 8 / c
Problem: choose the number pair / group which is different from others ?
Options: a ) 8 : 39 , b ) 8 : 38 , c ) 8 : 33 , d ) 8 : 32 , e ) 8 : 31
Rationale: explanation : in all other pairs , 2 nd number = ( 1 st number × 3 ) + 1 . answer : c ) 8 : 33
Answer: c
Python program:
a = 4 + 4 
b = 10 * 3
c = 3 + b 
d = a / c
Problem: the ratio of two numbers is 2 : 3 and the sum of their cubes is 945 . the difference of number is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 2 x 3 x 8 x cube + 27 x cube = 945 35 x cube = 945 x cube = 27 = > x = 3 . answer : a
Answer: a
Python program:
a = 3 ** 3
b = 2 ** 3
c = a + b 
d = 945 / c
e = 3 * 3
f = d / e
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 21,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,300 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 21000 x 3 / 10 = rs . 6,300 . d"
Answer: d
Python program:
a = 4 + 1 
b = a * 4
c = 3 * 4
d = 2 * c
e = b * d
Problem: the mean of 1 ^ 22 ^ 23 ^ 24 ^ 25 ^ 26 ^ 27 ^ 2 is ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 25 , e ) 30
Rationale: 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + n ^ 2 = n ( n + 1 ) ( 2 n + 1 ) / 6 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + 7 ^ 2 = 7 * 8 * 156 = 140 required average is = 140 / 7 = 20 answer is c
Answer: c
Python program:
a = 2 ** 2
b = 3 ** 2
c = a + b 
d = 4 ** 2
e = 2 + 3 
f = e ** 2
g = d + f 
h = c + g 
i = 2 + 4 
j = i ** 2
k = 3 + 4 
l = k ** 2
m = j + l 
n = h + m 
o = 1 + n 
p = 3 + 4 
q = o / p
Problem: if 25 % of x is 20 less than 15 % of 1500 , then x is ?
Options: a ) 872 , b ) 820 , c ) 837 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 20 = > x / 4 = 205 = > x = 820 . answer : b"
Answer: b
Python program:
a = 15 / 100
b = 1500 * a
c = b - 20
d = 25 / 100
e = c / d
Problem: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 15 more revolutions than gear p ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: gear q makes 30 more revolutions each 60 seconds . the time to make 15 = 30 / 2 more revolutions is 60 / 2 = 30 seconds . the answer is e .
Answer: e
Python program:
a = 40 / const_60
b = 10 / const_60
c = a - b
d = 15 / c
Problem: ( 8956231 x 465 ) = ?
Options: a ) 4584638125 , b ) 4164647415 , c ) 4584638135 , d ) 4584638140 , e ) 4584638145
Rationale: 8956231 x 465 = 4164647415 ans b
Answer: b
Python program:
a = 4 + 1 
b = a ** 4
c = 8956231 * b
Problem: population is 25000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 33275 , c ) 36625 , d ) 26625 , e ) 26825
Rationale: population after 1 st year = 25000 * 10 / 100 = 2500 = = = > 25000 + 2000 = 27500 population after 2 nd year = 27500 * 10 / 100 = 2750 = = = > 27500 + 2750 = 30250 population after 3 rd year = 30250 * 10 / 100 = 3025 = = = > 30250 + 3025 = 33275 answer : b
Answer: b
Python program:
a = 3 * 10
b = a / 100
c = 1 + b 
d = 25000 * c
Problem: a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 8 / x ) > x ?
Options: a ) 1 / 5 , b ) 2 / 8 , c ) 1 / 3 , d ) 2 / 3 , e ) 7 / 9
Rationale: number x has to be chosen from numbers 1 - 9 ( 8 / x ) > x = > 8 > x ^ 2 = > x ^ 2 - 8 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 8 answer b
Answer: b
Python program:
a = 10 - 8
b = a / 8
Problem: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 2 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 4
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 2 ^ 2 = 9 / 4 answer : e"
Answer: e
Python program:
a = 3 ** 2
b = 1 * a
c = 2 ** 2
d = b / c
Problem: it takes 1.5 hours for tim to mow the lawn . linda can mow the same lawn in 2 hours . how long will it take john and linda , work together , to mow the lawn ?
Options: a ) 51.1 minutes , b ) 51.3 minutes , c ) 51.5 minutes , d ) 51.7 minutes , e ) 51.9 minutes
Rationale: we first calculate the rate of work of john and linda john : 1 / 1.5 and linda 1 / 2 let t be the time for john and linda to mow the lawn . the work done by john alone is given by t * ( 1 / 1.5 ) the work done by linda alone is given by t * ( 1 / 2 ) when the two work together , their work will be added . hence t * ( 1 / 1.5 ) + t * ( 1 / 2 ) = 1 multiply all terms by 6 6 ( t * ( 1 / 1.5 ) + t * ( 1 / 2 ) ) = 6 and simplify 4 t + 3 t = 6 solve for t t = 6 / 7 hours = 51.5 minutes . answer c
Answer: c
Python program:
a = 1 * 5
b = 1 / a
c = 2 * const_60
d = 1 / c
e = b + d 
f = 1/(e)
Problem: you collect pens . suppose you start out with 5 . mike gives you another 20 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 ) 31 , d ) 42 , e ) 43
Rationale: "solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 ã — 2 = 50 pens . sharon takes 19 pens from you : 50 - 19 = 31 pens . so you have 31 at the end . correct answer : c"
Answer: c
Python program:
a = 20 + 5 
b = a * 2
c = b - 19
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 50,000 , how much profit did the business make ?
Options: a ) $ 80,000 , b ) $ 100,000 , c ) $ 120,000 , d ) $ 150,000 , e ) $ 200,000
Rationale: let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 50000 p = $ 80,000 the answer is a .
Answer: a
Python program:
a = 1 + 4 
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i 
k = c / j
Problem: in a group of 28 junior high school students , 7 take french , 10 take spanish , and 2 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
Rationale: "c 9 add 7 + 10 + 2 to get 19 then subtract 21 from the total students ⇒ 28 – 19 = 9 . answer is c"
Answer: c
Python program:
a = 7 + 10 
b = 28 - a
Problem: a wheel rotates 10 times every minute and moves 20 cm during each rotation . how many ems does the wheel move in 1 hour ?
Options: a ) 20000 , b ) 14000 , c ) 23000 , d ) 120000 , e ) none of these
Rationale: explanation : number of wheel moves in 1 hour = 10 * 60 = 600 distance moved = 600 * 200 = 12000 answer : d
Answer: d
Python program:
a = const_60 * 10
b = 20 * 10
c = a * b
Problem: the average ( arithmetic mean ) of the integers from 200 to 400 , inclusive , is how much greater than the average of the integers from 100 to 200 , inclusive ?
Options: a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 300
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 200 to 400 , inclusive = ( 200 + 400 ) / 2 = 300 average of numbers between 100 to 200 , inclusive = ( 100 + 200 ) / 2 = 150 difference = 300 - 150 = 150 answer is a"
Answer: a
Python program:
a = 200 + 400 
b = a / 2
c = 100 + 200 
d = c / 2
e = b - d
Problem: the total circumference of two circles is 64 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 6.7 , d ) 10.2 , e ) 18.0
Rationale: let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 64 where 2 r = r thus : 2 π r + 4 π r = 64 6 π r = 64 r = approx 3.4 π r + 2 r π = 64 3 π r = 64 r = approx 6.8 r + r = approx 10.2 answer d
Answer: d
Python program:
a = 64 / 3
b = a / 3
c = 64 / 3
d = c * 2
e = d / 3
f = b + e 
g = f / 2
Problem: a car takes 6 hours to cover a distance of 469 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: "time = 6 distence = 469 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 469 / 9 = 52 kmph c"
Answer: c
Python program:
a = 6 * 3
b = a / 2
c = 469 / b
Problem: excluding stoppages , the speed of a bus is 62 kmph and including stoppages , it is 56 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 16 min , c ) 7 min , d ) 6 min , e ) 40 min
Rationale: "d 10 min due to stoppages , it covers 6 km less . time taken to cover 6 km = ( 6 / 62 x 60 ) min = 6 min"
Answer: d
Python program:
a = 62 - 56
b = a / 62
c = const_60 * b
Problem: the greatest number that divides 3560 and 3450 leaving remainder 4 and 6 respectively is :
Options: a ) 23 , b ) 25 , c ) 26 , d ) 28 , e ) 30
Rationale: "explanation : 3560 - 4 = 3556 , 3450 - 6 = 3444 highest number that can divide 3556 and 3444 is hcf of numbers hcf of 3556 and 3444 = 28 answer : d"
Answer: d
Python program:
a = 3450 - 6
b = math.gcd(3560, 3450)
c = a / b
Problem: if the cost price is 75 % of selling price then what is the profit percentage .
Options: a ) 30.33 , b ) 31.33 , c ) 32.33 , d ) 33.33 , e ) 34.33
Rationale: "selling price = rs 100 : then cost price = rs 75 : profit = rs 25 . profit = { ( 25 / 75 ) * 100 } % = 33.33 % answer is d ."
Answer: d
Python program:
a = 100 - 75
b = a / 75
c = b * 100
Problem: find the simple interest on $ 500 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 150 , e ) $ 100
Rationale: "si = ptr / 100 = 500 * 3 * 10 / 100 = $ 150 answer is d"
Answer: d
Python program:
a = 3 / 100
b = 500 * a
Problem: what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 12 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "denote | x - 4 | as y : y ^ 2 + y = 12 - - > y = - 4 or y = 3 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 3 - - > x = 7 or x = 0 . the sum = 7 . answer : e ."
Answer: e
Python program:
a = 4 + 4 
b = 4 - 4
c = a + b
Problem: a cistern is normally filled in 4 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 12 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 4 - 1 / x = 1 / 6 , solving 1 / x = 1 / 12 so in 12 hours full cistern will be empty . answer : e"
Answer: e
Python program:
a = 1 / 4
b = 4 + 2 
c = 1 / b
d = a - c
e = 1/(d)