euclaise/mathqa_programs huggingface dataset:
Problem: simplify 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ( 7 â ˆ ’ 8 â ˆ ’ 5 â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ ) ) ]
Options: a ) 23 , b ) 25 , c ) 89 , d ) 30 , e ) 32
Rationale: explanation : = 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ( 7 â ˆ ’ 8 + 5 ) ) ] ( please check due to overline , sign has been changed ) = 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ã — 4 ) ) ] = 80 â ˆ ’ [ â ˆ ’ 9 ] = 80 + 9 = 89 option c
Answer: c
Python program:
a = 8 - 5
b = 6 - 5
c = 7 - 2
d = b + c 
e = a + d 
f = 80 + e
Problem: solve the equation for x : 19 ( x + y ) + 17 = 19 ( - x + y ) - 21 ?
Options: a ) - 1 , b ) 77 , c ) 8 , d ) 3 , e ) 2
Rationale: "19 x + 19 y + 17 = - 19 x + 19 y - 21 38 x = - 38 = > x = - 1 answer : a"
Answer: a
Python program:
a = 17 + 21 
b = 19 + 19 
c = a / b
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 5 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 9125 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 5 = 9125 answer : d"
Answer: d
Python program:
a = 100 + 4 
b = a / 100
c = 100 + 4 
d = c / 100
e = b * d
f = 7500 * e
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 204 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 36 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 204 = > . 1 x + 3 / 4 x = 204 = > x = 240 240 - 204 = pure gala = 36 . answer b"
Answer: b
Python program:
a = 10 / 100
b = 3 / 4
c = a + b 
d = 204 / c
e = d - 204
Problem: ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = ?
Options: a ) 54210 , b ) 54250 , c ) 52150 , d ) none of these , e ) 521500
Rationale: "its speed and accuracy which decides the winner . you can use various methods including vedic mathematics to do complex calculations quickly . ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = 80997 - 28847 = 52150 answer is c"
Answer: c
Python program:
a = 32323 + 7344 
b = a / 41330
Problem: an amount of rs . 1560 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) rs . 390 , b ) rs . 368 , c ) rs . 380 , d ) rs . 360 , e ) rs . 311
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 c = 3 / 13 * 1560 = rs . 360 . answer : d"
Answer: d
Python program:
a = 2 + 3 
b = a + 4 
c = 1560 / b
d = c * 4
Problem: 42 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 28 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 42 : : 18 : x [ please pay attention , we have written 27 : 42 rather than 42 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 42 \ times 18 } { 27 } } x = 28 so 28 days will be required to get work done by 27 men . answer : a"
Answer: a
Python program:
a = 18 * 42
b = a / 27
Problem: how many three - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 , 121,151 , 181,211 , 241,271 . . . . . 991 answer : none : a"
Answer: a
Python program:
a = 1 + 1 
b = a + 1
Problem: find the area of a parallelogram with base 32 cm and height 18 cm ?
Options: a ) 576 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 32 * 18 = 576 cm 2 answer : a"
Answer: a
Python program:
a = 32 * 18
Problem: the number 91 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 12 , c ) 21 , d ) 27 , e ) 39
Rationale: "3 ^ 3 + 4 ^ 3 = 91 therefore number is 3 * 4 = 12 b"
Answer: b
Python program:
a = 91 / 2
b = 1 / 3
c = a ** b
d = math.floor(c)
e = 91 / 2
f = 1 / 3
g = e ** f
h = math.floor(g)
i = h ** 3
j = 91 - i
k = 1 / 3
l = j ** k
m = d * l
Problem: a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error in the calculation ?
Options: a ) 54 , b ) 48 , c ) 65 , d ) 25 , e ) 64
Rationale: let the number be x . then , error = 5 / 3 x - 3 / 5 x = 16 / 15 x . error % = ( 16 x / 15 * 3 / 5 x * 100 ) % = 64 % answer e ) 64 %
Answer: e
Python program:
a = 5 / 3
b = 3 / 5
c = a - b
d = 5 / 3
e = c / d
f = e * 100
Problem: angelina walked 250 meters from her home to the grocery at a constant speed . she then walked 360 meters to the gym at double the speed . she spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 250 / x . . the speed to gym = 2 x . . so time taken = 360 / 2 x = 180 / x . . its given 250 / x - 180 / x = 70 . . 70 / x = 70 . . x = 1 m / secs . . so grocery to gym = 2 * 1 = 2 m / s . . . answer : a"
Answer: a
Python program:
a = 360 / 2
b = 250 - a
c = b / 70
d = c * 2
Problem: 2 + 2 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4 + 2 ^ 5 + 2 ^ 6 + 2 ^ 7 + 2 ^ 8 =
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 12 , d ) 2 ^ 16 , e ) 2 ^ 20
Rationale: let ' s see that : 2 + 2 is 2 ^ 2 , then : 2 ^ 2 + 2 ^ 2 becomes 2 x 2 ^ 2 that is 2 ^ 3 . you follow with the next : 2 ^ 3 + 2 ^ 3 is equal to 2 x 2 ^ 3 that is 2 ^ 4 . then is assumed right before 2 ^ 8 : 2 ^ 8 x 2 ^ 8 becomes 2 x 2 ^ 8 that is 2 ^ 9 . option a , 2 ^ 9 .
Answer: a
Python program:
a = 2 ** 6
b = 2 ** 5
c = 2 ** 4
d = 2 ** 3
e = 2 ** 2
f = 2 + 2 
g = e + f 
h = d + g 
i = c + h 
j = b + i 
k = a + j 
l = 2 ** 7
m = k + l 
n = 2 ** 8
o = m + n
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 400 before any discount ?
Options: a ) $ 230.00 , b ) $ 224.00 , c ) $ 263.80 , d ) $ 282.00 , e ) $ 210.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 400 would be . . . . . ( $ 400 ) ( . 7 ) ( . 8 ) = ( $ 400 ) ( . 56 ) = 224 final answer : b"
Answer: b
Python program:
a = 30 + 20 
b = a / 100
c = 400 * b
Problem: logx 16 = 0.8 then what is the value of x ?
Options: a ) 32 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: x ^ 0.8 = 16 x = ( 2 ^ 4 ) ^ ( 10 / 8 ) x = 2 ^ 5 x = 32 answer : a
Answer: a
Python program:
a = 0 * 8
b = a + 0 
c = b * 16
d = c / 2
Problem: a 16 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 200
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 16 , money invested = 100 × 16 / 8 = rs . 175 ie , market value of the stock = rs . 200 answer is e ."
Answer: e
Python program:
a = 100 / 8
b = a * 16
Problem: at an elementary school , 70 % of the faculty members are women and 40 % of the faculty members are married . if 1 ⁄ 3 of the men are single , what fraction of the men are married ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 2 / 7
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 20 - - - - - 20 - - - - - - - - - 40 not married - - - - - 10 - - - - - 50 - - - - - - - - - 60 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married man / total man , so 20 / 30 = 2 / 3 c"
Answer: c
Python program:
a = 1 / 3
b = 1 - a
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 12 of money ?
Options: a ) 1200 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 12 ( 100 / 10 ) 2 = > p = 1200 answer : a"
Answer: a
Python program:
a = 10 * 2
b = 12 / a
c = b * 100
d = 10 * 2
e = c * d
Problem: a man whose bowling average is 12.4 , takes 3 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "12.4 * x + 26 = ( 3 + x ) 12 solve equation x = 25 answer : c"
Answer: c
Python program:
a = math.floor(12, 4)
b = a * 3
c = b - 26
d = math.floor(12, 4)
e = 12 - 4
f = c / e
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 3.5 liters of alcohol and 6.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 8 % , b ) 11 % , c ) 14 % , d ) 17 % , e ) 20 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 3.5 ) / 50 = 5.5 / 50 = 11 % the answer is b ."
Answer: b
Python program:
a = 5 / 100
b = 40 * a
c = b + 3 
d = 3 + 5 
e = 40 + d 
f = c / e
g = f * 100
Problem: how long does a train 110 m long traveling at 90 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 110 + 170 = 280 m s = 90 * 5 / 18 = 50 / 2 t = 280 * 2 / 50 = 11.2 sec answer : d"
Answer: d
Python program:
a = 110 + 170 
b = 90 * const_0_2778
c = a / b
Problem: if 12 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 300 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 12 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 12 * 30 / 24 * 80 x = 300 answer : c"
Answer: c
Python program:
a = 36 * 30
b = 12 * 24
c = b / 80
d = a / c
Problem: a martian bat flies at 60 yards per second from its nest to a dry lake . when it arrives there , it immediately continues at 45 yards per second to a nearby cave . if the distance between the lake and the cave is half the distance between the nest and the lake , what is the average speed , in yards per second , of the bat during the whole flight ?
Options: a ) 36 , b ) 40 , c ) 42 , d ) 54 , e ) 65
Rationale: distance from nest to lake = d , speed = 60 , time = d / 60 distance from lake to cave = d / 2 , speed = 45 , time = d / 90 average speed = ( d + d / 2 ) / ( d / 60 + d / 90 ) = ( 3 / 2 ) / ( 1 / 36 ) = 54 answer : d
Answer: d
Python program:
a = 60 + 60 
b = a + 45 
c = b / 3
Problem: the sum of all the integers k such that – 20 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 37
Rationale: "- 19 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 19 - 18 sum of which is - 37 . hence option d . e"
Answer: e
Python program:
a = negate + ( 
b = a + 1
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.7 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8000 = 1 / 16 = 6.25 % the answer is c ."
Answer: c
Python program:
a = 100 * 100
b = 5 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: a tank is filled in 10 hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?
Options: a ) 56 hours , b ) 28 hours , c ) 35 hours , d ) 66 hours , e ) 47 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 10 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 10 = > ( 1 + 2 + 4 ) / 2 b = 1 / 10 = > 2 b / 7 = 10 = > b = 35 hours . answer : c
Answer: c
Python program:
a = 3 + 4 
b = 2 / a
c = 10 / b
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum e of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : e = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Python program:
a = 200 + 102 
b = a / 2
c = 200 - 102
d = c / 2
e = d + 1 
f = b * e
Problem: a , b and c rents a pasture for rs . 928 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 288 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 928 = 288 answer : c"
Answer: c
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 928 / e
g = 16 * 9
h = f * g
Problem: in a class of 28 students in an examination in maths 4 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47.3 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 4 * 95 + 3 * 0 + 21 * 45 = 1325 average marks of whole class = 1325 / 28 = 47.3 answer : option a"
Answer: a
Python program:
a = 3 + 4 
b = 28 - a
c = 45 * b
d = 95 * 4
e = c + d 
f = e / 28
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 65 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 65 . thus , 3434 ( 90 + x ) = 65 + x or 270 + 3 x = 260 + 4 x or x = 10 answer : d"
Answer: d
Python program:
a = 90 - 65
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
Problem: the temperature of a certain cup of coffee 30 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 120 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 30 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 30 a ) + 60 60 = 120 * ( 2 ^ - 30 a ) 60 / 120 = 2 ^ - 30 a 1 / 2 = 2 ^ - 30 a 2 ^ - 1 = 2 ^ - 30 a - 1 = - 30 a 1 / 30 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 30 * 30 ) + 60 f = 120 * ( 2 ^ - 1 ) + 60 f = 120 * ( 1 / 2 ^ 1 ) + 60 f = 120 * 1 / 2 + 60 f = 60 + 60 = 120 answer b !"
Answer: b
Python program:
a = 60 / 30
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: the sum of three consecutive even numbers is 246 . what are the numbers ?
Options: a ) 80 , 82,84 , b ) 65 , 68,71 , c ) 45 , 47,42 , d ) 100 , 102,49 , e ) 87 , 88,89
Rationale: "first x make the first x second x + 2 even numbers , sowe add 2 to get the next third x + 4 add 2 more ( 4 total ) to get the third f + s + t = 246 summeansaddfirst ( f ) plussecond ( s ) plusthird ( t ) ( x ) + ( x + 2 ) + ( x + 4 ) = 246 replace each f , s , and t withwhatwe labeled them x + x + 2 + x + 4 = 246 here the parenthesis are not needed 3 x + 6 = 246 combine like terms x + x + x and 2 + 4 − 6 − 6 subtract 6 fromboth sides 3 x = 240 the variable ismultiplied by 3 3 3 divide both sides by 3 x = 80 our solution for x first 80 replace x in the origional listwith 80 . second ( 80 ) + 2 = 82 the numbers are 80 , 82 , and 84 . third ( 80 ) + 4 = 84 correct answer a"
Answer: a
Python program:
a = 246 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 246 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 246 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 246 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: two pipes a and b can separately fill a cistern in 60 minutes and 120 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 60 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 110 min , d ) 120 min , e ) 130 min
Rationale: "1 / 60 - ( 1 / 60 + 1 / 120 ) = - 1 / 120 third pipe can empty in 120 minutes answer : d"
Answer: d
Python program:
a = 1/(60)
b = 1/(120)
c = a + b 
d = 1/(60)
e = c - d
f = 1/(e)
Problem: if the average of 10 consecutive integers is 23.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 28 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 23 , integer 6 = 24 . counting up to the tenth integer we get 28 . answer : d"
Answer: d
Python program:
a = 10 * 2
b = 10 * 2
c = 23 - 5
d = c * 10
e = a + d
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 7.2 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 9 ) = 5 / 36 the cistern will be filled in 36 / 5 hrs i . e . , 7.2 hrs . answer : d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 9
c = a - b
d = 1 / c
Problem: the distance between west - town to east - town is 16 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 5 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 16 .
Rationale: "time taken by the birds to meet = 16 / ( 5 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : e"
Answer: e
Python program:
a = 5 * 5
Problem: which 2 digit number has its digits reversed when you double it and take 1 ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: reverse it and you get 73 which is 2 * 37 - 1 . answer : e
Answer: e
Python program:
a = 10 + 2 
b = a * 3
Problem: by selling 8 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 10 % ?
Options: a ) 6.54 , b ) 9.45 , c ) 7.34 , d ) 6.67 , e ) 5.09
Rationale: "90 % - - - 8 110 % - - - ? 90 / 110 * 8 = 6.54 answer : a"
Answer: a
Python program:
a = 100 + 10 
b = 100 - 10
c = 1 / b
d = a * c
e = 1 / d
f = e * 8
Problem: if the sum of a number and its square is 132 , what is the number ?
Options: a ) 15 , b ) 11 , c ) 28 , d ) 91 , e ) none of these
Rationale: let the number be x . then , x + x 2 = 132 ( x + 12 ) ( x - 11 ) = 0 x = 11 answer : b
Answer: b
Python program:
a = math.sqrt(132)
b = math.floor(a)
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 180 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 480
Rationale: "easy 480 is the answer . 3 / 4 ( x / 2 ) = 180 x = 180 * 8 / 3 = 480 . answer e"
Answer: e
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 4
d = b * c
e = a + d 
f = 1 - e
g = 180 / f
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 25 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 136.50 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 25 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 260 would be . . . . . ( $ 260 ) ( . 7 ) ( . 75 ) = ( $ 260 ) ( . 525 ) = 136.5 final answer : a
Answer: a
Python program:
a = 30 + 25 
b = a / 100
c = 260 * b
Problem: if 2464 / 1.12 = 2200 , then 246.4 / 11.2 is equal to ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 25
Rationale: "answer given expression 246.4 / 11.2 = 2464 / 112 = 2464 / ( 1.12 x 100 ) = 2200 / 100 = 22 correct option : c"
Answer: c
Python program:
a = 2200 * 1
b = a / 2464
Problem: if 4 men can paint 60 m long wall in 3 days , then 5 men can paint 50 m long wall in
Options: a ) 3 days , b ) 2 days , c ) 5 days , d ) 6 days , e ) 1 day
Rationale: the length of wall painted by one man in one day = 60 / 4 ã — 3 = 5 m no . of days required to paint 50 m wall by 5 men = 50 / 5 ã — 5 = 2 day . b
Answer: b
Python program:
a = 60 / 3
b = a / 4
c = b * 5
d = 50 / c
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 22.22 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 110 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 110 - 90 ) / 90 * 100 = ~ 22.22 % answer : d ."
Answer: d
Python program:
a = 100 + 10 
b = 100 - 10
c = a - b
d = c * 100
e = 100 - 10
f = d / e
Problem: a cricketer scored 152 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 60.52 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 152 - ( 12 x 4 + 2 x 6 ) = 152 - ( 60 ) = 92 now , we need to calculate 92 is what percent of 152 . = > 92 / 152 * 100 = 60.52 % answer : c"
Answer: c
Python program:
a = 12 * 4
b = 2 * 3
c = 2 * b
d = a + c 
e = 152 - d
f = e / 152
g = f * 100