euclaise/mathqa_programs huggingface dataset:
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 1 * / 4 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 4 / 5 a"
Answer: a
Python program:
a = 1 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 2 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 18 , e ) e . 24
Rationale: rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 18 hours d
Answer: d
Python program:
a = 3 + 2 
b = 1 + a 
c = b + 1 
d = c + 1 
e = d + 1 
f = e + 1 
g = f + 2 
h = g + 1 
i = h + 1 
j = i + 1 
k = j + 1 
l = k + 1 
m = l + 1
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 5 of the mixture is sand , 3 / 4 of the mixture is water , and the remaining 6 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "let the total weight be x . sand content = ( 1 / 5 ) x water content = ( 3 / 4 ) x gravel = x - ( 1 / 5 ) x - ( 3 / 4 ) x = ( 1 / 20 ) x = 6 x = 120 then answer will be b = 120"
Answer: b
Python program:
a = 1 / 5
b = 3 / 4
c = a + b 
d = 1 - c
e = 6 / d
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - nineth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 11 / 3 , e ) 22
Rationale: let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 9 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 9 ( 11 + n ) = > 11 + 2 n / 10 = 11 + n / 9 = > 66 + 12 n = 110 + 10 n = > 2 n = 44 n = 22 answer : e
Answer: e
Python program:
a = 12 - 1
b = 12 - 3
c = 1/(b)
d = 1/(10)
e = c - d
f = a * e
g = 1 + 4 
h = 1/(g)
i = 12 - 3
j = 1/(i)
k = h - j
l = f / k
Problem: ajay can walk 3 km in 1 hour . in how many hours he can walk 50 km ?
Options: a ) 5 hrs , b ) 16.6 hrs , c ) 15.6 hrs , d ) 20.4 hrs , e ) 30 hrs
Rationale: "1 hour he walk 3 km he walk 50 km in = 50 / 3 * 1 = 16.6 hours answer is b"
Answer: b
Python program:
a = 50 / 3
Problem: the income of a broker remains unchanged though the rate of commission is increased from 4 % to 5 % . the percentage of slump in business is ?
Options: a ) 8 % , b ) 1 % , c ) 20 % , d ) 80 % , e ) none
Rationale: answer let the business value change from a to b . then , 4 % of a = 5 % of b ⇒ 4 a / 100 = 5 b / 100 ⇒ b = 4 a / 5 ∴ change in business = ( a - 4 a / 5 ) = a / 5 percentage slump in business = { ( a / 5 ) / a } x 100 % = 20 % correct option : c
Answer: c
Python program:
a = 4 / 100
b = 5 / 100
c = a / b
d = 1 - c
e = d * 100
Problem: find 44 % of 240
Options: a ) 96 , b ) 105.6 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 44 % of 240 44 / 100 × 240 = 105.6 answer : b"
Answer: b
Python program:
a = 44 / 240
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 324 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 837 , c ) 912 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 324 62 % - - - - - - - - ? = > 837 answer : b"
Answer: b
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 324 / c
e = d * 62
f = e / 100
Problem: r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) three , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , and 36 are even integers ( less than 51 ) that are in both sets . solution : three answer : b"
Answer: b
Python program:
a = 4 - 1
Problem: a die is rolled twice . what is the probability of getting a sum equal to 9 ?
Options: a ) 2 / 9 , b ) 5 / 7 , c ) 1 / 7 , d ) 1 / 9 , e ) 3 / 7
Rationale: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible when a die is rolled twice , n ( s ) = 6 × 6 = 36 e = getting a sum of 9 when the two dice fall = { ( 3 , 6 ) , { 4 , 5 } , { 5 , 4 } , ( 6 , 3 ) } hence , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 answer : option d
Answer: d
Python program:
a = 1 / 9
Problem: if xy > 0 , 1 / x + 1 / y = 2 , and 1 / xy = 8 , then ( x + y ) / 4 = ?
Options: a ) 1 / 16 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 2 canbe solved as { ( x + y ) / xy } = 8 . substituting for 1 / xy = 8 , we get x + y = 2 / 8 = = > ( x + y ) / 4 = 2 / ( 8 * 4 ) = 1 / 16 . a"
Answer: a
Python program:
a = 2 / 8
b = a / 8
Problem: the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference a would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference a = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Python program:
a = 3 * 100
b = 40 + a 
c = 2 * 10
d = b + c
Problem: an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of a ?
Options: a ) 1320 , b ) 1196 , c ) 1210 , d ) 1440 , e ) 1050
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 3120 = rs . 1440 answer : d"
Answer: d
Python program:
a = 2 + 3 
b = a + 4 
c = 3120 / b
d = c * 4
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number k is
Options: a ) 74 , b ) k = 75 , c ) k = 175 , d ) k = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Python program:
a = 34 * 2
b = 34 * 2
c = 8 * 5
d = b - c
e = 5 - 1
f = d / e
g = a + f
Problem: a circular road runs round a circular ground . if the difference between the circumferences of the outer circle and inner circle is 66 metres , the width of the road is :
Options: a ) 5.25 m
b ) 7 m
c ) 10.5 m
d ) 21 m
e ) 22 m
Rationale: 2 π ( r - r ) = 60 = > 2 * 22 / 7 * ( r - r ) = 60 . therefore , ( r - r ) = ( 66 * 7 / 44 ) = 10.5 m answer : c
Answer: c
Python program:
a = 2 * math.pi
b = 66 / a
Problem: find 12 × × 19
Options: a ) 238 , b ) 228 , c ) 208 , d ) 277 , e ) 101
Rationale: "mentally imagine this number as ( 10 + 2 ) × × 19 = 190 + 38 = 228 . answer : b"
Answer: b
Python program:
a = 12 / 19
Problem: how many integers between 334,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,239
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 334,700 and 458,600 is 458,600 - 334,700 = 123,900 - one number per each hundred gives 123,900 / 100 = 1,239 numbers . answer : e ."
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 458 - 600
Problem: if number divisible by both 3 and 2 , then the same number divisible by which number ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 6 , e ) 9
Rationale: obviously , the answer is 6 option d
Answer: d
Python program:
a = 3 * 2
b = a * 1
Problem: the radii of two cones are in ratio 2 : 1 , their volumes are equal . find the ratio of their heights .
Options: a ) 1 : 4
b ) 1 : 3
c ) 1 : 2
d ) 1 : 5
e ) none of these
Rationale: explanation : let their radii be 2 x , x and their heights be h and h resp . then , volume of cone = 1 / 3 π r 2 h 1 / 3 ∗ π ∗ ( 2 x ) 2 ∗ h / 1 / 3 ∗ π ∗ x 2 ∗ h = > hh = 14 = > h : h = 1 : 4 option a
Answer: a
Python program:
a = 2 ** 2
b = 1 / a
Problem: the average of first 50 non - zero positive integers is
Options: a ) 11.5 , b ) 25.5 , c ) 22 , d ) 25 , e ) 27
Rationale: "explanation : sum of first n non - zero positive integers n ( n + 1 ) / 2 so , average of first n non - zero positive integers n ( n + 1 ) / 2 n = ( n + 1 ) / 2 = > ( 50 + 1 ) / 2 = 25.5 answer : b"
Answer: b
Python program:
a = 50 + 1
Problem: excluding stoppages , the speed of the bus is 54 kms / hr and with stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 20
Rationale: by including stoppages , bus will cover 9 km less . . ( 54 km - 45 km = 9 km ) excluding stoppages , x = 54 kmph including stoppages , y = 45 kmph difference , z = 9 km time taken to cover that 9 km ( bus stops per hour ( 60 minutes ) ) = z / x ( 60 minutes ) = 9 / 54 ( 60 ) = 1 / 6 ( 60 ) = 10 minutes . answer : b
Answer: b
Python program:
a = 45 / 54
b = const_60 * a
c = const_60 - b
Problem: sanoop bought 8 t - shirts at an average price ( arithmetic mean ) of rs . 526 . if sanoop returned 1 t - shirts to the retailer , and the average price of the remaining t - shirts was rs . 505 , then what is the average price , of the 3 returned t - shirts ?
Options: a ) 560 , b ) 561 , c ) 562 , d ) 563 , e ) 673
Rationale: total price of 8 t - shirts = 8 * 526 = 4208 total price of 7 t - shirts = 7 * 505 = 3535 total price of 1 t - shirts = 4208 - 3535 = 673 average price of 3 t - shirts = 673 correct option answer : e
Answer: e
Python program:
a = 8 * 526
b = 8 - 1
c = b * 505
d = a - c
Problem: in how many q ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: q = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Python program:
a = math.factorial(6)
b = math.factorial(5)
c = a / b
d = 5 - 1
e = math.factorial(d)
f = c * e
Problem: a number is doubled and 6 is added . if resultant is trebled , it becomes 72 . what is that number
Options: a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 6 ) = 72 = > 2 x + 6 = 24 = > x = 9 option c"
Answer: c
Python program:
a = 3 * 6
b = 72 - a
c = 3 * 2
d = b / c
Problem: i gain 70 paise on rs . 70 . my gain percent is :
Options: a ) 0.1 % , b ) 1 % , c ) 7 % , d ) 10 % , e ) noneof these
Rationale: solution 11.1 gain % = ( 0.70 / 70 x 100 ) % = 1 % . answer b
Answer: b
Python program:
a = 70 / 100
b = a * 100
c = b / 70
Problem: a fruit seller had some oranges . he sells 20 % oranges and still has 400 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 500 , e ) none of these
Rationale: "explanation : he sells 20 % of oranges and still there are 400 oranges remaining = > 80 % of oranges = 400 ⇒ ( 80 × total oranges ) / 100 = 400 ⇒ total oranges / 100 = 5 ⇒ total oranges = 5 × 100 = 500 answer : option d"
Answer: d
Python program:
a = 20 / 100
b = 400 * a
c = 400 + b
Problem: in a group of 800 people , 3 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 12 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 3 / 5 - 3 / 25 = 12 / 25 . answer b .
Answer: b
Python program:
a = 800 * 3
b = a / 5
c = b - 96
d = c / 800
Problem: the ratio of the volumes of two cubes is 1728 : 2197 . what is the ratio of their total surface areas ?
Options: a ) 12 : 18 , b ) 144 : 169 , c ) 44 : 22 , d ) 28 : 144 , e ) 96 : 12
Rationale: "ratio of the sides = â ³ â ˆ š 1728 : â ³ â ˆ š 2197 = 12 : 13 ratio of surface areas = 144 : 169 answer : b"
Answer: b
Python program:
a = 1728 / 2197
b = 1 / 3
c = a ** b
Problem: in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 400 , b ) 600 , c ) 800 , d ) 1000 , e ) 1200
Rationale: let v be the total number of votes . 0.4 v = 240 v = 600 the answer is b .
Answer: b
Python program:
a = 240 * 100
b = 100 - 60
c = a / b
Problem: a man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in a opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed .
Options: a ) 58 , b ) 62 , c ) 74 , d ) 81 , e ) 65
Rationale: "relative speed = ( 280 / 9 ) m / s = ( 280 / 9 ) * ( 18 / 5 ) = 112 kmph speed of goods train = 112 - 50 = 62 kmph answer is b"
Answer: b
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 50
Problem: what is the smallest 6 digit number exactly divisible by 111 ?
Options: a ) 100010 , b ) 100012 , c ) 100011 , d ) 100013 , e ) 120012
Rationale: "smallest 6 digit number = 100000 100000 / 111 = 900 , remainder = 100 . hence 11 more should be added to 100000 to get the smallest 6 digit number exactly divisible by 111 = > smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011 answer is c"
Answer: c
Python program:
a = 2 ** 3
b = 6 / a
Problem: a bag contains 4 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 17 / 33
Rationale: "drawing two balls of same color from four green balls can be done in 4 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 4 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 17 / 33 answer : e"
Answer: e
Python program:
a = 4 + 8 
b = 8 / a
c = 8 - 1
d = 4 + 8 
e = d - 1
f = c / e
g = b * f
h = 4 + 8 
i = 4 / h
j = 4 - 1
k = 4 + 8 
l = k - 1
m = j / l
n = i * m
o = g + n
Problem: jar x is 1 / 2 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 ) 3 / 4 , b ) 5 / 6 , c ) 7 / 8 , d ) 5 / 8 , e ) 7 / 12
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 / 2 + p / 4 = 3 p / 4 the answer is a .
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 2
d = b * c
e = a + d
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 6 strokes ?
Options: a ) 63 / 64 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 left after 4 th stroke = 1 / 2 * 1 / 8 = 1 / 16 left after 5 th stroke = 1 / 2 * 1 / 16 = 1 / 32 left after 6 th stroke = 1 / 2 * 1 / 32 = 1 / 64 so removed = 1 - 1 / 64 = 63 / 64"
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = b / 2
d = a + c 
e = 1 / 2
f = e / 2
g = f / 2
h = d + g 
i = 1 / 2
j = i / 2
k = j / 2
l = k / 2
m = h + l 
n = 1 / 2
o = n / 2
p = o / 2
q = p / 2
r = q / 2
s = m + r
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were left - handed - - > 12 * 1 / 3 = 4 were left - handed and 8 right - handed . the number of right - handed players who were not at practice that day is 9 - 8 = 1 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 1 / 5 . answer : a .
Answer: a
Python program:
a = 1 / 2
b = 1 / 3
c = 1 - b
d = 1 / 3
e = 1 / 3
f = 1 - e
g = d * f
h = c - g
i = a - h
j = 1 / 2
k = 1 / 3
l = 1 / 3
m = 1 - l
n = k * m
o = j - n
p = i / o
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 4 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: "d = s * t given condition is for up the mountain hikers takes 4 miles per day and total 2 days . . . miles = 8 miles . . . for down speed they take = 3 / 2 ( 4 ) = 6 miles per day and for the same 2 days . . . miles = 12 miles . . answer : option d is correct answer"
Answer: d
Python program:
a = 4 * 2
b = 3 / 2
c = a * b
Problem: rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 200 pages , of which 80 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1360 , b ) $ 1620 , c ) $ 1650 , d ) $ 680 , e ) $ 770
Rationale: "for 200 - 80 - 20 = 100 pages only cost is 5 $ per page for the first time page is typed - 100 * 5 = 500 $ ; for 80 pages the cost is : first time 5 $ + 3 $ of the first revision - 80 * ( 5 + 3 ) = 640 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 500 + 640 + 220 = 1360 $ . answer : a ."
Answer: a
Python program:
a = 200 * 5
b = 80 * 3
c = a + b 
d = 20 * 3
e = d * 2
f = c + e
Problem: the line y = 5 x / 3 + b goes through the point ( 7 , – 1 ) . what is the value of b ?
Options: a ) 3 , b ) – 5 / 3 , c ) – 7 / 5 , d ) 16 / 3 , e ) – 38 / 3
Rationale: “ finding the equation ” procedure . plug ( x , y ) = ( 7 , – 1 ) into this equation : { - 1 } = { { 5 ( 7 ) } / 3 } + b = { 35 / 3 } + b b = { - 35 / 3 } - 1 = { - 35 / 3 } - { 3 / 3 } = - { 38 / 3 } answer = e
Answer: e
Python program:
a = negate - (
Problem: the average monthly salary of 20 employees in an organisation is rs . 1700 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 6003 , b ) rs . 3800 , c ) rs . 1288 , d ) rs . 6108 , e ) rs . 6011
Rationale: "explanation : manager ' s monthly salary rs . ( 1800 * 21 - 1700 * 20 ) = rs . 3800 . answer : b"
Answer: b
Python program:
a = 1700 + 100 
b = 20 + 1 
c = a * b
d = 1700 * 20
e = c - d
Problem: on dividing 17698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 199 , b ) 154 , c ) 852 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 17698 - 14 ) / 89 = 199 answer ( a )"
Answer: a
Python program:
a = 17698 - 14
b = a / 89
Problem: two trains start from same place at same time at right angles to each other . their speeds are 36 km / hr and 48 km / hr respectively . after 30 seconds the distance between them will be ?
Options: a ) 270 mts , b ) 190 mts , c ) 100 mts , d ) 500 mts , e ) 110 mts
Rationale: explanation : using pythagarous theorem , distance travelled by first train = 36 x 5 / 18 x 30 = 300 m distance travelled by second train = 48 x 5 / 18 x 30 = 400 m so distance between them = â ˆ š ( 90000 + 160000 ) = â ˆ š 250000 = 500 mts . answer : d
Answer: d
Python program:
a = 36 * 30
b = a * const_0_2778
c = b ** 2
d = 48 * 30
e = d * const_0_2778
f = e ** 2
g = c + f 
h = math.sqrt(g)