euclaise/mathqa_programs huggingface dataset:
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 666 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1 = 666 answer : c"
Answer: c
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
Problem: how many 0 ' s are there in the binary form of 6 * 1024 + 4 * 64 + 2
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 9
Rationale: 6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e
Answer: e
Python program:
a = 6 + 4 
b = a - 1
Problem: what is 7 1 / 4 - 4 2 / 3 divided by 7 / 8 - 3 / 4 ?
Options: a ) 87 / 36 , b ) 36 / 17 , c ) 7 / 6 , d ) 62 / 3 , e ) 5 / 4
Rationale: "7 1 / 4 - 4 2 / 3 = 29 / 4 - 14 / 3 = ( 87 - 56 ) / 12 = 31 / 12 7 / 8 - 3 / 4 = ( 7 - 6 ) / 8 = 1 / 8 so 31 / 12 / 1 / 8 = 31 / 12 * 8 = 62 / 3 answer - d"
Answer: d
Python program:
a = 10 * 7
b = a + 7 
c = b / 4
d = 10 + 4 
e = d / 3
f = c - e
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 475 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c"
Answer: c
Python program:
a = 30 * 350
b = 15 * 225
c = a - b
d = c / 15
Problem: find out the c . i on rs . 8000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 489.66 , b ) 406.07 , c ) 406.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a"
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 8000 * d
f = e - 8000
Problem: jayes can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ?
Options: a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes .
Rationale: rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min
Answer: c
Python program:
a = 20 / 20
Problem: how many even number in the range between 10 to 120 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 37 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d"
Answer: d
Python program:
a = 120 - 10
b = a - 2
c = b / 2
d = 120 - 2
e = 3 * 4
f = d - e
g = f - 3
h = g - 3
i = h / 3
j = i / 2
k = c - j
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 74000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: 0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e
Answer: e
Python program:
a = 1000 * 100
b = a * 0
c = 74000 / 1000
d = b / c
Problem: if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c"
Answer: c
Python program:
a = 62 - 2
b = a * 2
c = 2 + 1 
d = b / c
Problem: a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 days , e ) 3 days
Rationale: "work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e"
Answer: e
Python program:
a = 1/(15)
b = 1/(10)
c = a + b 
d = 1/(c)
e = d + 10 
f = e - 3
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 4 ” 2 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "4 ” 2 = 4 - 4 = 0 answer : e"
Answer: e
Python program:
a = 2 ** 2
b = a - 4
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ?
Options: a ) 462 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer literate = 682 - 220 = 462 . answer : option a"
Answer: a
Python program:
a = 62 / 100
b = 60 / 100
c = 1 - b
d = 50 / 100
e = c * d
f = a - e
g = f * 1100
Problem: total 48 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 48 , b ) 47 , c ) 40 , d ) 42 , e ) 47
Rationale: "47 players answer : e"
Answer: e
Python program:
a = 48 + 1
Problem: in 130 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 26 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d"
Answer: d
Python program:
a = 130 / 45
b = 45 - 36
c = a * b
Problem: at a certain university , 69 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 50 , d ) 52.5 , e ) 75
Rationale: "answer is 75 % total women = 69 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 21 % but question wants to know the percent of men that are tenured 21 % / 40 % = 52.5 % d"
Answer: d
Python program:
a = 100 - 69
b = 90 - 69
c = a + b
Problem: in a dairy farm , 26 cows eat 26 bags of husk in 26 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 26 cows per day ⇒ 26 × 1 × 26 = 1 × 26 × x for one cow = 26 days answer : d"
Answer: d
Python program:
a = 26 / 26
b = a * 26
Problem: the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c ."
Answer: c
Python program:
a = 34 - 16
b = 16 - 14
c = a / b
Problem: the number 0.650 is how much greater than 1 / 8 ?
Options: a ) ½ , b ) 21 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b"
Answer: b
Python program:
a = 1 / 8
b = 0 - 650
Problem: if $ 1092 are divided between worker a and worker b in the ratio 5 : 8 , what is the share that worker b will get ?
Options: a ) 60.32 % , b ) 61.54 % , c ) 62.21 % , d ) 62.76 % , e ) 63.87 %
Rationale: "worker b will get 8 / 13 = 61.54 % the answer is b ."
Answer: b
Python program:
a = 5 + 8 
b = 1092 / a
Problem: a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ?
Options: a ) 8 / 58 , b ) 9 / 25 , c ) 1 / 26 , d ) 6 / 25 , e ) 8 / 45
Rationale: "here n ( s ) = 52 let e be the event of getting queen of the club or king of kings n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer ( c )"
Answer: c
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: 1000 men have provisions for 17 days . if 500 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.5 , c ) 11.3 , d ) 12.2 , e ) 12.1
Rationale: "1000 * 17 = 1500 * x x = 11.3 answer : c"
Answer: c
Python program:
a = 17 * 1000
b = 1000 + 500 
c = a / b
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 = > x = 1 . total distance = 3 * 1 = 3 km ."
Answer: c
Python program:
a = 47 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > – 1 , 3 > x > 0 , and x + 2 < 4 , then x is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "0 < x < 7 , 0 < x < 15 , 5 > x > – 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ."
Answer: a
Python program:
a = 5 - 2
b = a - 2
Problem: 1 + 1
Options: a ) 9 , b ) 8 , c ) 3 , d ) 0 , e ) 2
Rationale: e
Answer: e
Python program:
a = 1 / 1
b = a * 100
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 150 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 150 * 2 / 5 = $ 60 answer is c"
Answer: c
Python program:
a = 3 + 2 
b = 2 / a
c = b * 150
Problem: a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b
Options: a ) 1000 yards , b ) 1200 yards , c ) 1400 yards , d ) 1600 yards , e ) 1800 yards
Rationale: if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b
Answer: b
Python program:
a = 300 * 4
Problem: a pineapple costs rs 7 each and a watermelon costs rs . 5 each . if i spend rs 38 on total what is the number of pineapple i purchased ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 2 , e ) 3
Rationale: explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d
Answer: d
Python program:
a = 4 * 7
b = 38 - a
c = b / 5
Problem: the sub - duplicate ratio of 25 : 16 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 5 : 4 , e ) 2 : 3
Rationale: "root ( 25 ) : root ( 16 ) = 5 : 4 answer : d"
Answer: d
Python program:
a = math.sqrt(25)
b = math.sqrt(16)
c = a / b
Problem: in δ pqs above , if pq = 7 and ps = 8 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 56 / 9 , d ) 15 / 4 , e ) 20 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 7 * 8 / 2 = pr * 9 / 2 pr = 56 / 9 c"
Answer: c
Python program:
a = 8 / 7
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 1250 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 1250 km in = 1250 / 50 * 1 = 25 hours answer is d"
Answer: d
Python program:
a = 1250 / 50
Problem: a boat covers a certain distance downstream in 1 hour , while it comes back in 11 â  „ 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 31 kmph , b ) 16 kmph , c ) 19 kmph , d ) 15 kmph , e ) 14 kmph
Rationale: "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x â ˆ ’ 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 â  „ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 11 â  „ 2 hour since distance = speed ã — time , we have ( x + 3 ) ã — 1 = ( x - 3 ) 3 / 2 2 ( x + 3 ) = 3 ( x - 3 ) 2 x + 6 = 3 x - 9 x = 6 + 9 = 15 kmph answer : d"
Answer: d
Python program:
a = 3 / 2
b = a * 3
c = b + 2 
d = 3 / 2
e = d - 1
f = c / e
Problem: in a division , a student took 87 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 58
Rationale: x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e
Answer: e
Python program:
a = 87 * 24
b = a / 36
Problem: what is the sum of all digits for the number 10 ^ 26 - 51 ?
Options: a ) 199 , b ) 209 , c ) 219 , d ) 229 , e ) 239
Rationale: "10 ^ 26 is a 27 - digit number : 1 followed by 26 zeros . 10 ^ 26 - 51 is a 26 - digit number : 24 9 ' s and 49 at the end . the sum of the digits is 24 * 9 + 4 + 9 = 229 . the answer is d ."
Answer: d
Python program:
a = 26 - 10
b = a - 2
c = b / 2
d = c + 10 
e = 26 - 10
f = e + 2 
g = f / 2
h = d * g
Problem: what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"
Answer: c
Python program:
a = const_180 / 3
Problem: what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum .
Options: a ) 1260 , b ) 1320 , c ) 1200 , d ) 1250 , e ) none of these
Rationale: solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 6000 * c
e = d - 6000
Problem: a fair 2 sided coin is flipped 8 times . what is the probability that tails will be the result at least twice , but not more than 8 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 7 / 8 , d ) 157 / 64 , e ) 143 / 128
Rationale: "at least twice , but not more than 8 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times , 8 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 8 c 2 / 2 ^ 8 + 8 c 3 / 2 ^ 8 + 8 c 4 / 2 ^ 8 + 8 c 5 / 2 ^ 8 + 8 c 6 / 2 ^ 8 + 8 c 7 / 2 ^ 8 = 143 / 128 option : e"
Answer: e
Python program:
a = 2 ** 8
b = 1/(a)
c = b * 8
d = 2 ** 8
e = 1/(d)
f = 2 ** 8
g = 1/(f)
h = e + g 
i = c + h 
j = 1 - i
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 54 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 54 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 54 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 54 r 2 = ( 54 * 2 ) / 3 = 36 = > r = 6 rate = 6 % answer : option e"
Answer: e
Python program:
a = math.sqrt(54)
Problem: find the compound ratio of ( 1 : 2 ) , ( 2 : 3 ) and ( 3 : 4 ) is
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 5 : 7 , d ) 1 : 4 , e ) 2 : 1
Rationale: "required ratio = 1 / 2 * 2 / 3 * 3 / 4 = 1 / 4 = 1 : 4 answer is d"
Answer: d
Python program:
a = 1 / 2
b = 1 / 2
c = 2 / 2
d = b * c
e = a * d
Problem: if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 2 / 3 , d ) 10 / 11 , e ) none of these
Rationale: explanation : let the required fraction be a / b . then ⇒ a / b + 1 = 1 / 2 ⇒ 2 a – b = 1 - - - - ( 1 ) ⇒ a + 1 / b = 1 ⇒ a – b = – 1 ⇒ a – b = – 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c
Answer: c
Python program:
a = 1 + 1 
b = 2 + 1 
c = a / b
Problem: if the ratio of two number is 2 : 3 and lcm of the number is 120 then what is the number .
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b"
Answer: b
Python program:
a = 2 * 3
b = 120 / a
Problem: find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 244.83 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a"
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 4000 * d
f = e - 4000
Problem: bert and rebecca were looking at the price of a condominium . the price of the condominium was 40 % more than bert had in savings , and separately , the same price was also 75 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 4 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 5 : 4
Rationale: suppose bert had 100 so price becomes 140 , this 140 = 1.75 times r ' s saving . . so r ' s saving becomes 80 so required ratio is 100 : 80 = 5 : 4 answer : e
Answer: e
Python program:
a = 100 + 40 
b = 100 / a
c = 100 + 75 
d = 100 / c
e = b / d
Problem: walking at 5 / 6 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be her normal speed and let t be her normal time . d = ( 5 / 6 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 5 / 6 ) v * ( t + 12 ) t / 6 = 10 t = 60 the answer is e ."
Answer: e
Python program:
a = 5 * 12
Problem: if 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 12 minute , c ) 120 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 12 ( lions ) * 12 ( min ) / 12 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 12 answer : b"
Answer: b
Python program:
a = 12 / 12
b = a * 12
Problem: a man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) .
Answer: d
Python program:
a = 6 + 18 
b = 18 - 6
c = a / b
d = 18 / c
e = 18 - d
f = e / 1
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 27000 × 9 = 45 × 12 : 27 × 9 = 15 × 12 : 9 × 9 = 20 : 9 answer is a"
Answer: a
Python program:
a = 45000 * 12
b = 4 + 3 
c = 27000 * b
d = a / c
Problem: the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 20 , b ) 55 / 4 , c ) 25 , d ) 14 , e ) 13
Rationale: "after passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 4 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 11 / 12 miles to meet the waiting cyclist . the hiker will need 55 / 4 mins to cover the remaining 11 / 12 miles . so the answer is b ."
Answer: b
Python program:
a = 15 - 4
b = 5 / const_60
c = a * b
d = c / 4
e = d * const_60
Problem: if x + y = 10 , x - y = 18 , for integers of x and y , x = ?
Options: a ) 14 , b ) 15 , c ) 25 , d ) 13 , e ) 42
Rationale: x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a
Answer: a
Python program:
a = 10 + 18 
b = a / 2
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 2 / 3 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 4 / 15 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 2 / 3 * ( 1 - 3 / 5 ) = 4 / 15 . answer : a ."
Answer: a
Python program:
a = 2 / 3
b = 3 / 2
c = 1 - b
d = a * c
Problem: find the least number must be subtracted from 964807 so that remaining no . is divisible by 8 ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a"
Answer: a
Python program:
a = 964807 / 8
b = math.floor(a)
c = b * 8
d = 964807 - c
Problem: if 8 people take an hour to complete a piece of work , then how long should 16 people will take to complete the same piece of work ?
Options: a ) 15 min , b ) 30 min , c ) 26 min , d ) 28 min , e ) 18 min
Rationale: if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b
Answer: b
Python program:
a = 8 / 16
b = a * const_60
Problem: find the area of a parallelogram with base 25 cm and height 15 cm ?
Options: a ) 295 cm 2 , b ) 385 cm 2 , c ) 275 cm 2 , d ) 375 cm 2 , e ) 285 cm 2
Rationale: "area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d"
Answer: d
Python program:
a = 25 * 15
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 4 ] = ?
Options: a ) [ 12 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 6 ] * [ 4 ] = ( 6 / 2 + 1 ) ( 4 / 2 + 1 ) = [ 12 ] . ans - a"
Answer: a
Python program:
a = 6 / 2
b = a + 1 
c = 2 * 4
d = c + 1 
e = b * d
Problem: in a certain company , a third of the workers do not have a retirement plan . 60 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 180 , d ) 120 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c"
Answer: c
Python program:
a = 1 / 3
b = 1 / 3
c = 60 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i 
k = 120 / j
l = 1 / 3
m = 60 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v