euclaise/mathqa_programs huggingface dataset:
Problem: when a train travels at a speed of 90 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 18.75 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 90 km / h 50 km / h - - - - > x + 15 distance is equal so 90 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 90 x = 50 x + 750 so the would be in km and x = 18.75 answer : a"
Answer: a
Python program:
a = 15 / const_60
b = a * 50
c = b / 50
d = const_60 * c
Problem: a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 40 marks , find the maximum marks set for the test .
Options: a ) 180 , b ) 200 , c ) 220 , d ) 240 , e ) 260
Rationale: "60 % = 120 marks 1 % = 2 marks 100 % = 200 marks the answer is b ."
Answer: b
Python program:
a = 80 + 40 
b = 60 / 100
c = a / b
Problem: what is the sum of all even numbers from 1 to 401 ?
Options: a ) 122821 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 40200
Rationale: "explanation : 400 / 2 = 200 200 * 201 = 40200 answer : e"
Answer: e
Python program:
a = 1 * 401
b = a / 4
Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 21 - inch flat - screen television than a square 19 - inch flat - screen television ?
Options: a ) 42 , b ) 40 , c ) 38 , d ) 36 , e ) 48
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 21 - inch flat - screen television the diagonal ( hypotenuse ) = 21 so , we can apply the pythagorean theorem to get x ² + x ² = 21 ² simplify : 2 x ² = 21 ² divide both sides by 2 to get : x ² = 21 ² / 2 since the area of the square = x ² , we can see that the area of this square is 21 ² / 2 square 19 - inch flat - screen television the diagonal ( hypotenuse ) = 19 so , we can apply the pythagorean theorem to get x ² + x ² = 19 ² simplify : 2 x ² = 19 ² divide both sides by 2 to get : x ² = 19 ² / 2 since the area of the square = x ² , we can see that the area of this square is 19 ² / 2 difference in areas = 21 ² / 2 - 19 ² / 2 = ( 21 + 19 ) ( 21 - 19 ) / 2 = 40 b"
Answer: b
Python program:
a = 21 ** 2
b = a / 2
c = 19 ** 2
d = c / 2
e = b - d
Problem: the proportion of copper and zinc in the brass is 13 : 7 . how much zinc will there be in 100 kg of brass ?
Options: a ) 37 kg , b ) 35 kg , c ) 85 kg , d ) 45 kg , e ) 25 kg
Rationale: 7 / 20 * 100 = 35 answer : b
Answer: b
Python program:
a = 7 + 13 
b = 7 / a
c = b * 100
Problem: if a man lost 8 % by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 45 % ?
Options: a ) 33.56 , b ) 23.68 , c ) 11.42 , d ) 9.56 , e ) 23.55
Rationale: "92 % - - - - 18 145 % - - - - ? 92 / 145 * 18 = 11.42 answer : c"
Answer: c
Python program:
a = 100 - 8
b = a * 18
c = 100 + 45 
d = b / c
Problem: the time it took car p to travel 150 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 23 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 150 / x ) - ( 150 / ( x + 10 ) ) = 2 solving for x = 23 miles \ hr . a"
Answer: a
Python program:
a = negate + ( 
b = negate ** (
c = b - 2
d = 150 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
Problem: subtracting 2 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.98 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: answer let a - 2 % of a = ab . ⇒ ( 98 x a ) / 100 = ab ∴ b = 0.98 correct option : a
Answer: a
Python program:
a = 100 - 2
b = a / 100
Problem: a cistern 5 m long and 2 m wide contains water up to a breadth of 1 m 10 cm . find the total area of the wet surface .
Options: a ) 42 m sqaure , b ) 49 m sqaure , c ) 25 m sqaure , d ) 28 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 2 * 1.1 + 5 * 1.1 ) ] + 5 * 2 = 25 m square option c"
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = b * 2
d = 10 / 100
e = d + 1 
f = e * 5
g = c + f 
h = 2 * g
i = 2 * 5
j = h + i
Problem: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 42 years . what is molly ' s age right now ?
Options: a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36
Rationale: "now , sandy is 42 - 6 = 36 molly ' s age is ( 3 / 4 ) * 36 = 27 the answer is b ."
Answer: b
Python program:
a = 42 - 6
b = a / 4
c = b * 3
Problem: how many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles ?
Options: a ) 40 , b ) 35 , c ) 20 , d ) 25 , e ) 30
Rationale: "c 20 240 pairs of bangles = 480 bangles = 40 dozens . 40 ÷ 2 = 20 boxes ."
Answer: c
Python program:
a = 240 / 12
Problem: in an election , candidate a got 85 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 404600 , d ) 356800 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 85 % therefore , the number of valid votes polled in favour of candidate a = 85 % of 476000 = 85 / 100 × 476000 = 40460000 / 100 = 404600 c )"
Answer: c
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 85 / 100
e = c * d
Problem: jerry bought a bottle of perfume for a gift for his wife . the perfume cost $ 92 before tax . if the total price including tax was $ 98.90 , find the tax rate
Options: a ) 7.5 % , b ) 5 % , c ) 12 % , d ) 8 % , e ) 10 %
Rationale: total price including tax is $ 98.90 perfume cost before tax is = 92 ie 92 * 7.5 % + 98.90 answer is 7.5 %
Answer: a
Python program:
a = 98 / 9
b = a - 1
c = b * 100
Problem: tea worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , what is the price of the third variety per kg ?
Options: a ) 175.5 , b ) 182.5 , c ) 170.0 , d ) 180.0 , e ) 190.0
Rationale: "tea worth rs . 126 ratio 1 : 1 average price = ( 126 + 135 ) / 2 = 130.5 mean price = ( x - 153 ) : 22.50 = > x - 153 = 22.50 x = 175.5 answer a"
Answer: a
Python program:
a = 153 + 10 
b = a + 10 
c = b + 2 
d = const_0_25 + const_0_25 
e = c + d
Problem: the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 3.6 miles in the seventh 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45
Rationale: "( 3.6 miles / 8 minutes ) * 60 minutes / hour = 27 mph let x be the original speed . x - 6 ( 3 ) = 27 x = 45 mph the answer is e ."
Answer: e
Python program:
a = 8 / const_60
b = 3 / 6
c = b + 3 
d = c + 3 
e = d + 3 
f = e + 3
Problem: a 7 - digit number comprises of only 2 ' s and 3 ' s . how many of these are multiples of 12 ?
Options: a ) 11 , b ) 12 , c ) 10 , d ) 22 , e ) 44
Rationale: detailed solution number should be a multiple of 3 and 4 . so , the sum of the digits should be a multiple of 3 . we can either have all seven digits as 3 , or have three 2 ' s and four 3 ' s , or six 2 ' s and a 3 . ( the number of 2 ' s should be a multiple of 3 ) . for the number to be a multiple of 4 , the last 2 digits should be 32 . now , let us combine these two . all seven 3 ' s - no possibility . three 2 ' s and four 3 ' s - the first 5 digits should have two 2 ' s and three 3 ' s in some order . no of possibilities = 5 ! 3 ! 2 ! = 10 six 2 ' s and one 3 - the first 5 digits should all be 2 ' s . so , there is only one number 2222232 . so , there are a total of 10 + 1 = 11 solutions . correct answer : a .
Answer: a
Python program:
a = 3 + 2 
b = math.factorial(a)
c = math.factorial(3)
d = math.factorial(2)
e = c * d
f = b / e
g = f + 1
Problem: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8110 / - . find out the amount that he borrowed .
Options: a ) rs . 4,900 , b ) rs . 5,000 , c ) rs . 5,100 , d ) rs . 5266 , e ) none of these
Rationale: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8110 = p + ( 54 p / 100 ) 8110 = ( 100 p + 54 p ) / 100 8110 = 154 p / 100 p = ( 8110 * 100 ) / 154 = rs . 5266.233 answer d"
Answer: d
Python program:
a = 6 * 9
b = a / 100
c = 1 + b 
d = 8110 / c
Problem: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 10 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 5 % , b ) 10 % , c ) 25 % , d ) 40 % , e ) 55 %
Rationale: "assuming that the technician makes a round - trip of 40 miles ( each way is 20 miles ) , then the technician would have completed 20 miles + 2 miles ( 10 % of the remaining 20 miles ) . therefore , the total is 22 miles . 22 miles / 40 miles is 55 % of the entire trip . answer : e"
Answer: e
Python program:
a = 100 / 2
b = 100 / 2
c = 10 * b
d = c / 100
e = a + d
Problem: the banker â € ™ s discount of a certain sum of money is rs . 60 and the true discount on the same sum for the same time is rs . 54 . the sum due is
Options: a ) 210 , b ) 280 , c ) 360 , d ) 720 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 60 * 54 / 60 - 54 ] = rs . [ 72 * 60 / 6 ] = rs . 720 answer d"
Answer: d
Python program:
a = 60 * 54
b = 60 - 54
c = a / b
Problem: a certain number of workers can do a work in 25 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 15 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: number of workers = 10 * ( 25 - 10 ) / 10 = 15 answer is a
Answer: a
Python program:
a = 25 - 10
b = a * 10
c = 25 - 10
d = 25 - c
e = b / d
Problem: a big container is 30 % full with water . if 9 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 20 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 9 liters of water is added , the container becomes 75 % full . hence these 9 liters account for 45 % of the container , which means that the capacity of it is 9 / 0.45 = 20 liters . or : if the capacity of the container is x liters then : 0.3 x + 9 = 0.75 x - - > x = 20 liters . answer : a ."
Answer: a
Python program:
a = 3 / 4
b = 30 / 100
c = a - b
d = 9 / c
Problem: a man cheats while buying as well as while selling . while buying he takes 11 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 9.09 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 42.86 %
Rationale: there is a one step calculation method too . it requires more thought but is faster . the man takes 11 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 111 pounds for which he will take from the customer $ 111 . hence , in effect , there is a 11 % mark up . while selling , he sells 30 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 70 pounds and should have got only $ 70 for it . so this is again a mark up of $ 30 on $ 70 . but he also sells at 9.09 % less i . e . gives a discount of 1 / 11 . ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 10 / 7 * 10 / 11 = ( 1 + p % ) profit % = 42.86 % e
Answer: e
Python program:
a = 100 + 11 
b = 100 - 20
c = 9 + 9 
d = a - c
e = d * 2
Problem: a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 90 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 90 , d ) 110 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 90 solving for d and y , 15 y = 11 y + 480 4 y = 440 y = 110 answer d"
Answer: d
Python program:
a = 4 * 2
b = a * 10
c = 100 * 4
d = b + c 
e = 4 * 2
f = e * 10
g = 100 * 4
h = f + g 
i = h * 3
j = i / 90
k = 4 * 2
l = k + 3 
m = j - l
n = d / m
Problem: a number is doubled and 15 is added . if resultant is trebled , it becomes 75 . what is that number
Options: a ) 8 , b ) 10 , c ) 5 , d ) 14 , e ) 7
Rationale: "explanation : = > 3 ( 2 x + 15 ) = 75 = > 2 x + 15 = 25 = > x = 5 option c"
Answer: c
Python program:
a = 3 * 15
b = 75 - a
c = 3 * 2
d = b / c
Problem: divide rs . 2800 among a , b and c so that a receives 3 / 4 as much as b and c together and b receives 1 / 4 as a and c together . a ' s share is ?
Options: a ) 1300 , b ) 1200 , c ) 1375 , d ) 1400 , e ) 8400
Rationale: "a + b + c = 2800 a = 3 / 4 ( b + c ) ; b = 1 / 4 ( a + c ) a / ( b + c ) = 3 / 4 a = 1 / 7 * 8400 = > 1200 answer : b"
Answer: b
Python program:
a = 2800 / 3
Problem: if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 69 ) = ?
Options: a ) 3675 , b ) 3575 , c ) 3475 , d ) 3375 , e ) 3275
Rationale: explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 69 = 1 + ( n - 1 ) 2 = > n = 35 use value of n in ( 1 ) then , sn = ( 35 / 2 ) ( 1 + 69 ) = 1225 ans : - 3 ( sn ) = 3675 answer : a
Answer: a
Python program:
a = 69 + 1 
b = 69 * a
c = b / 2
d = 69 - 1
e = d / 2
f = 69 - 1
g = f / 2
h = g + 1 
i = e * h
j = c - i
k = j * 3
Problem: if the average ( arithmetic mean ) of 8 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 407 , b ) b ) 518 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525
Rationale: a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 8 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 4 th and 5 th numbers in the set ) . this means that numbers 4 and 5 in this set are 413 and 415 . because we know that number 4 is 413 , we know that the smallest number is 3 odd numbers below this , which means that it is 3 * 2 = 6 below this ( every odd number is every other number ) . therefore 413 - 6 = 407 , answer choice a
Answer: a
Python program:
a = 414 - 8
b = a + 1
Problem: a shipment of 250 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? a . b . c . d . e .
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = ( 84 / 250 ) probability of choosing one defective phone from a lot of 249 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 249 ) combined probability of series of events = product of the probabilities = ( 84 / 250 ) * ( 83 / 249 ) 84 / 250 is close to ( 1 / 3 ) and ( 83 / 249 ) = ( 1 / 3 ) so answer is ( 1 / 3 ) * ( 1 / 3 ) = ( 1 / 9 ) answer : d
Answer: d
Python program:
a = 84 / 250
b = 84 - 1
c = 250 + 1 
d = b / c
e = a * d
Problem: what is the positive difference between the sum of the squares of the first 7 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 52 , c ) 83 , d ) 94 , e ) 99
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 7 ^ 2 = 140 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 140 is 99 . so the answer is ( e ) ."
Answer: e
Python program:
a = 2 ** 2
b = 1 + a 
c = 3 ** 2
d = b + c 
e = 4 ** 2
f = d + e 
g = 4 + 1 
h = g ** 2
i = f + h 
j = 7 ** 2
k = i + j 
l = 4 + 3 
m = l + 7 
n = 2 + 3 
o = 4 + 1 
p = n + o 
q = 4 + 3 
r = p + q 
s = 2 + 3 
t = s + 7 
u = r + t 
v = m + u 
w = k - v
Problem: 517 x 517 + 483 x 483 = ?
Options: a ) 79698 , b ) 80578 , c ) 500578 , d ) 81268 , e ) none of them
Rationale: "= ( 517 ) ^ 2 + ( 483 ) ^ 2 = ( 500 + 17 ) ^ 2 + ( 500 - 17 ) ^ 2 = 2 [ ( 500 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 250000 + 289 ] = 2 x 250289 = 500578 answer is c"
Answer: c
Python program:
a = 517 ** 483
b = 517 * a
Problem: on dividing a number by 5 , we get 3 as remainder . what will be the remainder when the square of this number is divided by 5 ?
Options: a ) 0
b ) 1
c ) 3
d ) 4
e ) 2
Rationale: let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x ^ 2 by 5 , we get 4 as remainder . answer is d
Answer: d
Python program:
a = 3 ** 2
b = a / 5
c = 3 ** 2
d = c / 5
e = math.floor(d)
f = b - e
g = f * 5
Problem: a certain car uses one gallon of gasoline every 38 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 45 % , e ) 50 %
Rationale: "4 miles on the highway = 4 / 38 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 38 + 4 / 20 = 29 / 95 gallons . 8 miles on the highway = 8 / 38 gallons . the % change = ( 29 / 95 - 8 / 38 ) / ( 8 / 38 ) = 0.45 . answer : d ."
Answer: d
Python program:
a = 1 / 20
b = a * 4
c = 1 / 38
d = 4 * c
e = b + d 
f = 1 / 38
g = 8 * f
h = e - g
i = 1 / 38
j = 8 * i
k = h / j
l = k * 100
Problem: divide $ 300 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 100
Rationale: "sum of ratio terms = 1 + 2 = 3 a = 300 * 1 / 3 = $ 100 answer is e"
Answer: e
Python program:
a = 300 / 1
Problem: a man can row upstream at 45 kmph and downstream at 55 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 34 kmph , c ) 30 kmph , d ) 50 kmph , e ) 65 kmph
Rationale: "us = 45 ds = 55 m = ( 45 + 55 ) / 2 = 50 answer : d"
Answer: d
Python program:
a = 45 + 55 
b = a / 2
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each . the radius of the sphere is
Options: a ) 3 cm
b ) 4 cm
c ) 6 cm
d ) 8 cm
e ) none
Rationale: solution 4 î r 2 = 2 î 4 x 8 â ‡ ’ r 2 = ( 4 x 8 / 2 ) â ‡ ’ 16 â ‡ ’ r = 4 cm . answer b
Answer: b
Python program:
a = 8 / 2
b = 8 * a
c = math.pi * b
d = c * 2
e = math.pi * 4
f = d / e
g = math.sqrt(f)
Problem: the sum of the non - prime numbers between 30 and 40 , non - inclusive , is
Options: a ) 202 , b ) 217 , c ) 232 , d ) 247 , e ) 262
Rationale: "sum of consecutive integers from 31 to 39 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 31 + 39 ) / 2 * 9 = 35 * 9 = 315 sum of non - prime numbers b / w 30 and 40 , non inclusive = = = > 315 - 68 ( i . e . , 31 + 37 , being the prime # s in the range ) = 247 answer : d"
Answer: d
Python program:
a = 30 + 1 
b = 30 + 1 
c = b + 1 
d = a + c 
e = 30 + 1 
f = e + 1 
g = f + 2 
h = d + g 
i = 30 + 1 
j = i + 1 
k = j + 2 
l = k + 1 
m = h + l 
n = 30 + 1 
o = n + 1 
p = o + 2 
q = p + 1 
r = q + 1 
s = m + r 
t = 30 + 1 
u = t + 1 
v = u + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = s + y 
A = 30 + 1 
B = A + 1 
C = B + 2 
D = C + 1 
E = D + 1 
F = E + 1 
G = F + 1 
H = z + G
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 9 x + 4 = 0 ?
Options: a ) 17 , b ) 88 , c ) 14 , d ) 65 , e ) 89
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 9 / 1 = - 9 ab = 4 / 1 = 4 hence a / b + b / a = [ ( - 9 ) 2 - 2 ( 4 ) ] / 4 = 73 / 4 = 18.25 . b )"
Answer: b
Python program:
a = negate ** (
b = a / 2
c = b - 4
Problem: 6 wires are by average 80 cm long each . if the average length of one third of the wires is 70 cm , what is the average of the other wires ?
Options: a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .
Rationale: edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third wires is 70 . that means out 6 / 3 = 2 wires . let the avg length of two wires be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining wires . imo correct option is b .
Answer: b
Python program:
a = 6 * 80
b = 2 * 70
c = a - b
d = c / 4
Problem: when 15 is divided by integer u , the remainder is 4 . for how many values of u is this be true ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: when 15 is divided by u , the remainder is 4 i . e . 4 mangoes left over after grouping , so u must be greater than 4 . it also means that 11 is completely divisible by u . factors of 11 are 1 and 11 . out of these , u could be 11 . answer ( a )
Answer: a
Python program:
a = 15 - 4
b = a + 4 
c = b / 15
Problem: a dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare . compare their speeds ?
Options: a ) 4 : 5 , b ) 16 : 15 , c ) 9 : 13 , d ) 5 : 15 , e ) 9 : 17
Rationale: "let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y then 3 x = 4 y x = 4 / 3 y 4 x = 16 / 3 y ratio of speeds of dog and hare = ratio of distances covered by them in the same time = 4 x : 5 y = 16 / 3 y : 5 = 16 : 15 answer is b"
Answer: b
Python program:
a = 4 * 3
b = a / 5
Problem: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds ?
Options: a ) 4 , b ) 9 , c ) 39 , d ) 48 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 4 ) = 4 ^ 2 + 2 * 4 = 24 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 24 = 39 km / hr option c"
Answer: c
Python program:
a = 7 ** 2
b = 7 * 2
c = a + b 
d = 4 ** 2
e = 4 * 2
f = d + e 
g = c - f