euclaise/mathqa_programs huggingface dataset:
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 560 at the end of 3 years and to $ 660 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 560 - $ 60 = 500 . the interest rate is $ 20 / $ 500 = 4 % the answer is b ."
Answer: b
Python program:
a = 660 - 560
b = a / 5
c = 660 - 560
d = c / 5
e = d * 3
f = 560 - e
g = b / f
h = g * 100
Problem: the average marks of a class of 25 students is 40 and that of another class of 30 students is 60 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 50.9 , e ) 52.9
Rationale: "sum of the marks for the class of 25 students = 25 * 40 = 1000 sum of the marks for the class of 30 students = 30 * 60 = 1800 sum of the marks for the class of 55 students = 1000 + 1800 = 2800 average marks of all the students = 2800 / 55 = 50.9 . answer : d"
Answer: d
Python program:
a = 25 * 40
b = 30 * 60
c = a + b 
d = 25 + 30 
e = c / d
Problem: a lady grows cabbage in her garden that is in the shape of a square . each cabbage takes 1 square foot of area in her garden . this year , she has increased her output by 211 cabbages when compared to last year . the shape of the area used for growing the cabbage has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 11236
b ) 11025
c ) 14400
d ) 12696
e ) can not be determined
Rationale: explanatory answer the shape of the area used for growing cabbages has remained a square in both the years . let the side of the square area used for growing cabbages this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cabbages last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cabbages grown has increased by 211 , the area would have increased by 211 sq ft because each cabbage takes 1 sq ft space . hence , x 2 - y 2 = 211 ( x + y ) ( x - y ) = 211 . 211 is a prime number and hence it will have only two factors . i . e . , 211 and 1 . therefore , 211 can be expressed as product of 2 numbers in only way = 211 * 1 i . e . , ( x + y ) ( x - y ) = 211 * 1 so , ( x + y ) should be 211 and ( x - y ) should be 1 . solving the two equations we get x = 106 and y = 105 . therefore , number of cabbages produced this year = x 2 = 1062 = 11236 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice d . 12696 is not the square of any number . check choice a : if this year ' s produce is 11236 , last year ' s produce would have been 11236 - 211 = 11025 11025 is the square of 105 . so , 11236 is the answer . choice a is the correct answer .
Answer: a
Python program:
a = 211 - 1
b = a / 2
c = b + 1 
d = c ** 2
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 3 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 6 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 3 ) = l cx = 3 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 3 l = 1 / 6 answer will be d"
Answer: d
Python program:
a = 1 / 3
b = 2 / 3
c = 1 - b
d = 2 / 3
e = c / d
f = a * e
Problem: find the number of factors of 9321 ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 16 , e ) 32
Rationale: "9321 = 3 x 13 x 239 = 31 x 13 1 x 239 1 ; add one to all the powers i . e . , ( 1 + 1 ) x ( 1 + 1 ) x ( 1 + 1 ) = 8 ; we get eight factors 1 , 3 , 13 , 39 , 239 , 717 , 3107 , 9321 answer : c"
Answer: c
Python program:
a = 2 + 2
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 60 , and what number ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 70 = 35 b"
Answer: b
Python program:
a = 20 + 40 
b = a + 60 
c = 5 * 3
d = c + 10 
e = d + 60 
f = b - e
Problem: on dividing a number by 357 , we get 39 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 39 = ( 17 * 21 * y ) + ( 17 * 2 ) + 5 = 17 * ( 21 y + 2 ) + 5 . required number = 5 . answer is b"
Answer: b
Python program:
a = 39 ** 2
b = a / 357
c = 39 ** 2
d = c / 357
e = math.floor(d)
f = b - e
g = f * 357
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 12 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 60 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 12 ] = ( 1 / 2 ) ( a + 12 ) 2 ( 2 a + 60 ) = 5 ( a + 12 ) a = 60 a"
Answer: a
Python program:
a = 1 / 2
b = 12 * a
c = 12 - b
d = 1 / 2
e = 2 / 5
f = d - e
g = c / f
Problem: potato chips are on sale , buy 2 get 1 free . there are only 9 bags of chips left ( 4 plain and 5 bbq ) . a shopper randomly grabs 3 bags . what is the probability the shopper will grab exactly 3 bags of bbq chips ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 42 , e ) 7 / 42
Rationale: combination probability formula : ncr = n ! / [ r ! ( n - r ) ! ] total possible , select 3 bags from 9 bags = 9 c 3 = 9 ! / [ 3 ! ( 9 - 3 ) ! ] = 84 . to have 3 bbq there must be 0 plain , select 0 plain from 4 = 4 c 0 = 1 . and , select 3 bbq from 5 = 5 c 3 = 10 . 3 bbq and 0 plain = ( 1 ) ( 10 ) = 10 probability = ( number outcomes favorable ) / ( total number outcomes ) = 10 / 84 = 5 / 42 answer : d
Answer: d
Python program:
a = 5 - 1
b = a - 1
c = 9 - 1
d = c - 1
e = b / d
f = 5 / 9
g = 5 - 1
h = 9 - 1
i = g / h
j = f * i
k = e * j
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 10 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 2 / 10 = ( r - 12 ) / r 2 r = 10 r - 120 r = 15 the answer is b ."
Answer: b
Python program:
a = 10 + 12 
b = a + 10
Problem: there are two bags a and b . a contains 6 red flowers and 3 pink flowers . where as bag b contains 2 red flowers and 7 pink flowers . one flower is chosen from a bag randomly . what is the probability that the flower chosen is pink ?
Options: a ) 5 / 8 , b ) 5 / 6 , c ) 5 / 1 , d ) 5 / 9 , e ) 5 / 2
Rationale: bag a 6 red + 3 pink bag b 2 red + 7 pink probability of picking 1 pink from bag a is 3 / 9 probability of picking 1 pink from bag b is 7 / 9 total = 3 / 9 + 7 / 9 = 10 / 9 and probability of selecting a bag is 1 / 2 so finally probability of choosing a pink flower = 1 / 2 ( 10 / 9 ) = 5 / 9 answer : d
Answer: d
Python program:
a = 6 + 3 
b = 3 / a
c = 7 + 2 
d = 7 / c
e = b + d 
f = 1 / 2
g = e * f
Problem: a mixture of 50 litres of milk and water contains 10 % water . how many litres of water should be added to the mixture so that the mixture contains 15 % water ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 10
Rationale: quantity of milk in the mixture = 90 / 100 ( 50 ) = 45 litres . after adding water , milk would form 60 % of the mixture . hence , if quantity of mixture after adding x liters of water , ( 60 ) / 100 x = 45 = > x = 75 hence 75 - 50 = 25 litres of water must be added . answer : c
Answer: c
Python program:
a = 50 * 15
b = a / 10
c = b - 50
Problem: a train 100 m long crosses a platform 125 m long in 30 sec ; find the speed of the train ?
Options: a ) 36 , b ) 77 , c ) 27 , d ) 33 , e ) 99
Rationale: "d = 100 + 125 = 225 t = 30 s = 225 / 30 * 18 / 5 = 27 kmph answer : c"
Answer: c
Python program:
a = const_60 * 0
b = 30 * a
c = b - 100
Problem: a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 650.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.28 , b ) $ 11.30 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 650 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 650 / 70 ~ 9.28 a"
Answer: a
Python program:
a = 40 / 100
b = 4 + 3 
c = 40 / 100
d = 20 / 4
e = d / 100
f = c + e 
g = b + f 
h = a + g
Problem: each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 6 . we need to remove 10 of the 20 - pound boxes . the answer is b ."
Answer: b
Python program:
a = 20 * 20
b = 20 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 20
h = 20 * 18
i = g - h
j = 20 - 10
k = i / j
l = 20 - k
m = 20 * l
n = f + m 
o = 20 * 16
p = n - o
q = 20 - 16
r = p / q
Problem: a television have side 6 * 5 . its screen size is 5 * 4 . calculate the percentage of unscreened part t . v .
Options: a ) 30 , b ) 25 , c ) 33.33 , d ) 44.44 , e ) 28
Rationale: unscreened part = 30 - 20 = 10 . % unscreened part = 10 / 30 * 100 = 33.33 % answer c
Answer: c
Python program:
a = 6 * 5
b = 5 * 4
c = a - b
d = 6 * 5
e = c / d
f = e * 100
Problem: how many 5 digit number contain number 3 ?
Options: a ) 31512 , b ) 32512 , c ) 33512 , d ) 34512 , e ) 37512
Rationale: "total 5 digit no . = 9 * 10 * 10 * 10 * 10 = 90000 not containing 3 = 8 * 9 * 9 * 9 * 9 = 52488 total 5 digit number contain 3 = 90000 - 52488 = 37512 answer : e"
Answer: e
Python program:
a = 1000 - 10
b = 5 * 5
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: a train crosses a post in 15 seconds and a platform 100 m long in 25 seconds . its length is
Options: a ) 150 m , b ) 300 m , c ) 400 m , d ) 180 m , e ) 160 m
Rationale: explanation : assume x is the length of the train and v is the speed x / v = 15 = > v = x / 15 ( x + 100 ) / v = 25 = > v = ( x + 100 ) / 25 ie , x / 15 = ( x + 100 ) / 25 = > 5 x = 3 x + 300 = > x = 300 / 2 = 150 answer : option a
Answer: a
Python program:
a = 15 * 100
b = 25 - 15
c = a / b
Problem: how many factors does 49 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 36
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 6 * 6 = 36 answer e ."
Answer: e
Python program:
a = 10 * 2
b = 49 / a
Problem: a cube of side one meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ?
Options: a ) 56 , b ) 60 , c ) 62 , d ) 64 , e ) 65
Rationale: "along one edge , the number of small cubes that can be cut = 100 / 25 = 4 along each edge 25 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 4 * 4 * 4 = 64 answer : d"
Answer: d
Python program:
a = 25 ** 2
b = a ** 3
c = 25 ** 3
d = b / c
Problem: last week john spent 10 percent of his wages on recreation . this week , his wages are 10 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 ) 180 % , b ) 360 % , c ) 200 % , d ) 220 % , e ) 250 %
Rationale: "say john ' s wages last week were $ 100 , so he spent 0.10 * 100 = $ 10 on recreation ; this week ' s wages is 0.90 * 100 = $ 90 , so he spends 0.4 * 90 = $ 36 on recreation ; 36 / 10 = 3.60 , hence the amount he spends on recreation this week is 360 % of the amount he spent on recreation last week : 10 * 3.6 = 36 answer : b"
Answer: b
Python program:
a = 40 / 100
b = 100 - 10
c = b / 100
d = c * 100
e = a * d
f = 10 / 100
g = f * 100
h = e / g
i = h * 100
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 8 / 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 ) 7 / 17 , b ) 14 / 31 , c ) 4 / 9 , d ) 17 / 35 , e ) 1 / 2
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 8 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 8 / 5 = 8 - - > total time for both of them would be 10 + 8 = 18 - - > deluxe / total = 8 / 18 = 4 / 9 . answer : c ."
Answer: c
Python program:
a = 3 + 2 
b = a / 10
Problem: the age of mother one decade age was 3 times the age of her daughter . 10 years hence , mother ’ s age will be two times that of her daughter . the proposition of their current ages is :
Options: a ) 7 : 3 , b ) 6 : 3 , c ) 8 : 3 , d ) 2 : 3 , e ) 6 : 3
Rationale: a 7 : 3 let , ages of mother and daughter 1 decade ago was 3 a and a years correspondingly then , ( 3 a + 10 ) + 10 = 2 [ ( a + 10 ) + 10 ] 3 a + 20 = 2 a + 40 x = 20 needed ratio = ( 3 a + 10 ) : ( a + 10 ) = 70 : 30 = 7 : 3
Answer: a
Python program:
a = 10 + 10 
b = 2 * a
c = 10 + 10 
d = b - c
e = 3 - 2
f = d / e
g = 3 * f
h = g + 10 
i = 10 + 10 
j = 2 * i
k = 10 + 10 
l = j - k
m = 3 - 2
n = l / m
o = n + 10 
p = h / o
Problem: a line with slope 2 intersects a line with slope 6 at the point ( 40 , 30 ) . what is the distance between the x - intercepts of these lines ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: the line with slope 2 passing through ( 40 , 30 ) has x - intercept 40 − ( 30 / 2 ) . the line with slope 6 passing through ( 40 , 30 ) has x - intercept 40 − ( 30 / 6 ) . so the difference in the x - intercepts is ( 30 / 2 ) − ( 30 / 6 ) = 10 . correct answer d
Answer: d
Python program:
a = 30 * 40
b = 6 * 2
c = a / b
d = c / 10
Problem: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 18 , e ) 11
Rationale: let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 = > x = 9 hence , b ' s age = 2 x = 18 years . answer : d
Answer: d
Python program:
a = 47 - 2
b = 3 + 2 
c = a / b
d = c * 2
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 20 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 120 , c ) $ 180 , d ) $ 200 , e ) $ 260
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 20 + 1.2 e = = > 11 a = 200 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 200 + 12 e = = > e = 200 d"
Answer: d
Python program:
a = 20 * 100
b = 12 + 1 
c = b * 10
d = 100 + 20 
e = c - d
f = a / e
Problem: at an election 2 candidates are participated a candidate got 45 % of votes and defeated by 9000 votes . 83 votes are invalid . find the total polled votes ?
Options: a ) 100000 , b ) 85236 , c ) 89562 , d ) 90083 , e ) 95842
Rationale: "winners votes = 100 - 45 = 55 % invalid votes = 83 polled votes = [ ( 100 * 9000 ) / ( 2 * 55 - 100 ) ] + 83 = 90083 answer is d"
Answer: d
Python program:
a = 100 - 0
b = a - 45
c = 9000 / b
d = c * 83
e = 100 + d
Problem: a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 6 seconds ?
Options: a ) 5 / 6 , b ) 4 / 5 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 2
Rationale: "the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 6 / 30 = 1 / 5 . the probability that he will stay in the dark is 1 - 1 / 5 = 4 / 5 the answer is b ."
Answer: b
Python program:
a = 6 * 3
b = 6 / a
c = 1 - b
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 40 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 112 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 112 - 80 ) / 80 * 100 = ~ 40 % answer : d ."
Answer: d
Python program:
a = 100 + 12 
b = 100 - 20
c = a - b
d = c * 100
e = 100 - 20
f = d / e
Problem: tough and tricky questions : number properties . if ( z + 3 ) / 9 is an integer , what is remainder when z is divided by 9 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: assume the answer choices as the value of z 9 / 9 = 1 ans e
Answer: e
Python program:
a = 9 - 3
Problem: if x dollars is invested at 9 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 9 percent investment will exceed the annual income from the 8 percent investment by $ 48 . if $ 2,000 is the total amount invested , how much is invested at 9 percent ?
Options: a ) 300 , b ) 250 , c ) 1223.53 , d ) 1133.24 , e ) 776.47
Rationale: "2 equations with 2 unknowns 9 x / 100 - 8 y / 100 = 48 and x + y = 2000 solving these 2 equations , x = 1223.53 and y = 776.47 answer - c"
Answer: c
Python program:
a = 100 * 9
b = a * 2
c = 9 * 8
d = c * 2
e = d + 48 
f = 9 / 100
g = 8 / 100
h = f + g 
i = e / h
j = b - i
Problem: if the wheel is 8 cm then the number of revolutions to cover a distance of 948 cm is ?
Options: a ) 11 , b ) 14 , c ) 14 , d ) 12 , e ) 19
Rationale: "2 * 22 / 7 * 8 * x = 948 = > x = 18.9 answer : e"
Answer: e
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 8
h = 948 / g
Problem: the cost price of 11 articles is equal to the selling price of 10 articles . what is the profit percent ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "10 * sp = 11 * cp sp = 1.1 * cp the profit percent is 10 % . the answer is b ."
Answer: b
Python program:
a = 11 * 4
b = 4 + 1 
c = a / b
Problem: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value d of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] d = z - x = x + 9 - x = 9 ans : d"
Answer: d
Python program:
a = 5 + 2 
b = a + 2
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 70 / r years . if pat ' s parents invested $ 5,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: since investment doubles in 70 / r years , then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a .
Answer: a
Python program:
a = 2 + 3 
b = a * 1000
c = b * 8
d = c / 2
Problem: how many multiples of 5 are there between 5 to 90 ?
Options: a ) 9 , b ) 16 , c ) 17 , d ) none of these , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 . answer : b"
Answer: b
Python program:
a = 90 - 5
b = a / 5
c = b + 1
Problem: instead of multiplying a number by 9 , the number is divided by 9 . what is the percentage of error obtained ?
Options: a ) 97.765 % , b ) 99.765 % , c ) 96.765 % , d ) 95.765 % , e ) 98.765 %
Rationale: "let the number be x the right number is 9 x the wrong number is x / 9 error is ( 9 x - x / 9 ) = 80 x / 9 percentage of error is ( ( 80 x / 9 ) / 9 x ) * 100 = 98.765 % answer : e"
Answer: e
Python program:
a = 9 / 9
b = 9 * 9
c = a / b
d = c * 100
e = 100 - d
Problem: 1500 men have provisions for 17 days . if 320 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 14 , d ) 15 , e ) 16
Rationale: "1500 * 17 = 1820 * x x = 14 answer : c"
Answer: c
Python program:
a = 17 * 1500
b = 1500 + 320 
c = a / b
Problem: the cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is rs . 36 . the breadth of the room is ?
Options: a ) 6 meters , b ) 8 meters , c ) 9 meters , d ) 10 meters , e ) 12 meters
Rationale: length of carpet = total cost / rate = 3600 / 30 = 120 m area of carpet = ( 120 x 75 ) / 100 m 2 = 90 m 2 ∴ area of the room = 90 m 2 breadth of the room = area / length = 90 / 15 m = 6 m answer : a
Answer: a
Python program:
a = 36 * 100
b = a / 30
c = 75 / 100
d = b * c
e = d / 15