euclaise/mathqa_programs huggingface dataset:
Problem: a mixture contains milk and water in the ratio 7 : 3 . on adding 20 liters of water , the ratio of milk to water becomes 7 : 5 . total quantity of milk & water before adding water to it ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 140
Rationale: "milk : water = 7 : 3 7 x : 3 x + 20 = 7 : 5 5 [ 7 x ] = 7 [ 3 x + 20 ] 35 x = 21 x + 140 35 x - 21 x = 140 14 x = 140 x = 10 the quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10 10 x = 100 option ' b '"
Answer: b
Python program:
a = 3 / 7
b = 20 * a
c = 7 + 3 
d = 7 / c
e = 7 + 3 
f = 3 / e
g = 3 / 7
h = f * g
i = d - h
j = b / i
Problem: the average age of a class of 20 students is 14 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 36 years
Rationale: "if age of the teacher was 14 , average would not have changed . since average increased by 2 , age of the teacher = 14 + 22 × 1 = 36 answer : e"
Answer: e
Python program:
a = 20 + 2 
b = 14 + 2 
c = a * b
d = 20 * 14
e = c - d
Problem: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points w that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points w for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Python program:
a = 12 * 7
b = 100 - a
c = b + 7
Problem: the average length of 6 strings is 80 cm . if the average length of one third of the strings is 70 cm , what is the average of the other strings ?
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 strings is 70 . that means out 6 / 3 = 2 strings . let the avg length of two strings 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 strings . imo correct option is b .
Answer: b
Python program:
a = 80 * 6
b = 6 / 3
c = b * 70
d = a - c
e = 6 / 3
f = 6 - e
g = d / f
Problem: a can do a piece of work in 24 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 11 , e ) 15
Rationale: "2 / 24 + 4 / 15 + x / 20 = 1 x = 13 answer : c"
Answer: c
Python program:
a = 4 - 2
b = 1/(15)
c = 1/(20)
d = b + c 
e = a * d
f = 1/(20)
g = 1/(24)
h = 1/(15)
i = g + h 
j = f + i 
k = j * 2
l = e + k 
m = 1 - l
n = 1/(15)
o = m / n
p = o + 4
Problem: a palindrome is a number that reads the same forward and backward , such as 242 . how many even 9 - digit numbers are palindromes ?
Options: a ) 40 , b ) 40000 , c ) 500 , d ) 5,000 , e ) 100,000
Rationale: if the palindrome must be even , it must begin and end in 2,4 6 and 8 ( 4 ways ) e . g 222212222,444414444 . the middle number in the nine - digit could be 0 - 9 ( 10 ways ) , e . g 22522 , 22822 the 2 nd and fourth numbers , the 3 rd and 5 th and 4 th and 6 th could must also be same i . e 0 - 9 ( 10 ways ) e . g 242343242 , 648565846 we thus have , 4 * 10 * 10 * 10 * 10 = 40000 b
Answer: b
Python program:
a = 9 / 2
b = math.floor(a)
c = 10 ** b
d = 4 * c
Problem: a cube is divided into 64 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30
Rationale: "each side of the cube has 4 x 4 = 16 cubelets . only the interior cubelets are painted one colour . on each side , 2 x 2 = 4 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 4 = 24 the answer is d ."
Answer: d
Python program:
a = 4 * 2
b = a * 3
c = 64 - b
d = c / 2
Problem: what is the probability of getting a sum of 12 when rolling 3 dice simultaneously ?
Options: a ) 10 / 216 , b ) 12 / 216 , c ) 21 / 216 , d ) 23 / 216 , e ) 25 / 216
Rationale: "sum of 12 can be achieved in following ways 6 , 5,1 - - - total cases = 3 ! = 6 6 , 4,2 - - - total cases = 3 ! = 6 6 , 3,3 - - - total cases = 3 ! / 2 ! = 3 5 , 5,2 - - - total cases = 3 ! / 2 ! = 3 5 , 4,3 - - - total cases = 3 ! = 6 4 , 4,4 - - - total cases = 3 ! / 3 ! = 1 total cases = 25 probability = 25 * ( 1 / 6 * 1 / 6 * 1 / 6 ) = 25 / 216 answer : e"
Answer: e
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 110 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 1 , b ) $ 27 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 110 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 54.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 11 . in any case , there is no necessity to know each item ' s price , just the sum . answer : a
Answer: a
Python program:
a = 164 - 5
b = 110 + a 
c = 164 - 5
d = c * 3
e = b - d
Problem: find the cost of fencing around a circular field of diameter 30 m at the rate of rs . 2 a meter ?
Options: a ) 100.5 , b ) 188.5 , c ) 190.5 , d ) 168.5 , e ) 175.5
Rationale: "2 * 22 / 7 * 15 = 94.25 94.25 * 2 = rs . 188.5 answer : b"
Answer: b
Python program:
a = 30 / 2
b = circumface * (
Problem: what is the ratio whose term differ by 40 and the measure of which is 2 / 7 ?
Options: a ) 32 : 23 , b ) 16 : 56 , c ) 71 : 85 , d ) 32 : 39 , e ) 41 : 52
Rationale: let the ratio be x : ( x + 40 ) then , x / ( x + 40 ) = 2 / 7 x = 16 required ratio = 16 : 56 answer is b
Answer: b
Python program:
a = 40 * 2
b = 7 - 2
c = a / b
d = 40 * 2
e = 7 - 2
f = d / e
g = 40 + f 
h = c / g
Problem: in how many ways 4 boys and 2 girls can be seated in a row so that they are alternate .
Options: a ) 48 , b ) 288 , c ) 12 , d ) 256 , e ) none
Rationale: "solution : let the arrangement be , b g b g b b 4 boys can be seated in 4 ! ways . girl can be seated in 2 ! ways . required number of ways , = 4 ! * 2 ! = 48 answer : option a"
Answer: a
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = a * b
Problem: find the ones digit of 73 ^ 352
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 352 will be the same as the units digit of 3 ^ 352 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 352 = ( multiple of 4 ) + 0 , since 3 is an odd number , the units digit of 3 ^ 352 will be 1 . answer : a ."
Answer: a
Python program:
a = 3 + 4 
b = a * 10
c = 73 - b
d = 352 / 4
e = math.floor(d)
f = e * 4
g = 352 - f
h = c ** g
i = 2 * 10
j = h - i
Problem: the difference between the compound interest and simple interest on a certain sum of money at 5 % per annum for 2 years is 45 . then the original sum is ?
Options: a ) rs . 16500 / - , b ) rs . 17000 / - , c ) rs . 18000 / - , d ) rs . 19000 / - , e ) rs . 20000 / -
Rationale: "for 2 years = ( 1002 d ) / r 2 = ( 1002 × 45 ) / ( 5 × 5 ) = ( 10000 × 45 ) / 25 = rs . 18000 / - c"
Answer: c
Python program:
a = 100 * 100
b = a * 45
c = b / 100
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 13 is :
Options: a ) 448 , b ) 553 , c ) 542 , d ) 548 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 13 = 540 + 13 = 553 . answer : b"
Answer: b
Python program:
a = 54 * 10
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 4 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 7 / 12 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 4 x = 3 / 4 x so if gold card balance is transferred then the rest unspent will be 3 / 4 x - x / 6 = 7 / 12 x so the ans is a"
Answer: a
Python program:
a = 1/(3)
b = 1/(2)
c = a * b
d = 1/(4)
e = c + d 
f = 1 - e
Problem: at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 30 of which were white and 5 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 30 short - stemmed pink = 5 = > short - stemmed red = 5 5 / p = 5 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 30 ( as no long stemmed white ) = > r + r + 30 = 120 = > 2 r = 90 and r = 45 long stemmed r = 45 - 5 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - e"
Answer: e
Python program:
a = 120 / 3
b = 120 - a
c = 120 / 3
d = c - 30
e = d - 5
f = b * e
g = 120 / 3
h = g - 30
i = h - 5
j = 5 + i 
k = f / j
l = 120 / 3
m = 120 - l
n = k / m
o = n * 100
Problem: a car is running at a speed of 108 kmph . what distance will it cover in 15 sec ?
Options: a ) 300 m , b ) 150 m , c ) 200 m , d ) 450 m , e ) 500 m
Rationale: "speed = 108 kmph = 108 * 5 / 18 = 30 m / s distance covered in 15 sec = 30 * 15 = 450 m answer is d"
Answer: d
Python program:
a = 108 / const_3_6
b = a * 15
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 60 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 12.9 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 60 = 140 * 5 / 18 = 350 / 9 t = 500 * 9 / 350 = 12.9 sec answer : option d"
Answer: d
Python program:
a = 80 * const_0_2778
b = 250 / a
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 52 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 44 ¢ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: if the average price is 52 , then mary has 6 oranges and 4 apples ( a ratio of 3 : 2 ) . for the average price to be 44 , the ratio should be 1 : 4 . mary must put back 5 oranges . the answer is e .
Answer: e
Python program:
a = 60 * 10
b = 52 * 10
c = a - b
d = 60 - 40
e = c / d
f = e * 40
g = 60 * 10
h = 52 * 10
i = g - h
j = 60 - 40
k = i / j
l = 10 - k
m = l * 60
n = f + m 
o = 44 * 10
p = n - o
q = 60 - 44
r = p / q
Problem: there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ?
Options: a ) rs . 450 , b ) rs . 320 , c ) rs . 550 , d ) rs . 420 , e ) none
Rationale: "solution : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 42 . = > 7 x = 84 = > x = 12 therefore original expenditure , = rs . ( 35 × 12 ) = rs . 420 . answer : option d"
Answer: d
Python program:
a = 35 + 7 
b = 42 + a 
c = b / 7
d = c * 35
Problem: excluding stoppages , the speed of a bus is 54 km / hr and including stoppages , it is 45 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 10 , c ) 99 , d ) 77 , e ) 29
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 9 km = 9 / 54 * 60 = 10 min . answer : b"
Answer: b
Python program:
a = 54 - 45
b = a / 54
c = const_60 * b
Problem: a man two flats for $ 675958 each . on one he gains 15 % while on the other he loses 15 % . how much does he gain or lose in the whole transaction ?
Options: a ) 2 % , b ) 2.25 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 15 / 10 ) ^ 2 = 9 / 4 = 2.25 % answer is b"
Answer: b
Python program:
a = 100 + 15 
b = 100 / a
c = b * 675958
d = 100 - 15
e = 100 / d
f = e * 675958
g = c + f 
h = 675958 + 675958 
i = g - h
j = 100 + 15 
k = 100 / j
l = k * 675958
m = 100 - 15
n = 100 / m
o = n * 675958
p = l + o 
q = i / p
r = q * 100
Problem: the product of three consecutive numbers is 990 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 19 , d ) 38 , e ) 56
Rationale: "product of three numbers = 990 990 = 9 * 10 * 11 . so , the three numbers are 9 , 10 and 11 . and sum of smallest of these two = 9 + 10 = 19 . answer : option c"
Answer: c
Python program:
a = 2 ** 4
b = math.factorial(990)
c = a * b
Problem: 61 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 62 , e ) 21
Rationale: "61 + 5 * 12 / ( 180 / 3 ) = 61 + 5 * 12 / ( 60 ) = 61 + ( 5 * 12 ) / 60 = 61 + 1 = 62 . answer : d"
Answer: d
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 61 + c
Problem: the area of a triangle will be when a = 5 m , b = 7 m , c = 8 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 10
Rationale: s = ( 5 + 7 + 8 ) / 2 = e answer : e
Answer: e
Python program:
a = 5 + 7 
b = a + 8 
c = b / 7
Problem: there is enough provisions for 600 men in an army camp for 25 days . if there were 100 men less , how long will the provision last ?
Options: a ) 10 days , b ) 50 days , c ) 100 days , d ) 150 days , e ) 200 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 100 * d 2 d 2 = 600 * 25 / 100 = 150 days . answer : d"
Answer: d
Python program:
a = 600 * 25
b = a / 100
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 34 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 890 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? b"
Answer: b
Python program:
a = 1000 / 11
b = 1000 / 34
c = a + b 
d = 11 * 34
e = 1000 / d
f = c - e
g = 1000 - f
Problem: veena ranks 79 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 82 , d ) 90 , e ) 93
Rationale: total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 79 + 1 = 82 answer : c
Answer: c
Python program:
a = 182 - 22
b = 79 - 1
c = a - b
d = c - 4
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 4 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 76 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 4 = 72 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 72 + 4 = 76 a"
Answer: a
Python program:
a = 80 * 4
b = 79 * 4
c = 80 * 4
d = 84 * 4
e = c - d
f = 4 + e 
g = b - f
h = a - g
Problem: a certain telescope increases the visual range at a particular location from 100 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 50 %
Rationale: "original visual range = 100 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 100 ) / 100 * 100 % = 1 / 2 * 100 % = 50 % answer e"
Answer: e
Python program:
a = 150 - 100
b = a / 100
c = b * 100
Problem: what is the area of a square field whose diagonal of length 10 m ?
Options: a ) 50 , b ) 70 , c ) 60 , d ) 20 , e ) 25
Rationale: "d 2 / 2 = ( 10 * 10 ) / 2 = 50 answer : a"
Answer: a
Python program:
a = square_area / (
Problem: if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 10 : 1 / 11 : 1 / 15 : 1 / 16 , then find the total number of items the wholesaler distributes ?
Options: a ) 945 , b ) 745 , c ) 845 , d ) 145 , e ) 345
Rationale: "here , a : b : c : d = 1 / 10 : 1 / 11 : 1 / 15 : 1 / 16 1 ) l . c . m of 10 , 11 , 15,16 is 2640 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 10 ) x 2640 = 264 b = ( 1 / 11 ) x 2640 = 240 c = ( 1 / 15 ) x 2640 = 176 d = ( 1 / 16 ) x 2640 = 165 3 ) total number of toys = ( 264 x + 240 x + 176 x + 165 x ) = 845 x minimum number of pens ( x ) = 1 therefore , total number of items = 845 items . correct option : c"
Answer: c
Python program:
a = 100 * 4
b = a + 100 
c = 15 * 4
d = 4 + 3 
e = c + d 
f = b + e
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 9 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , and 3 ^ 2 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 = 2520 the answer is d ."
Answer: d
Python program:
a = math.lcm(1, 9)
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 36 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 36 kg joins the group , total weight of boys = 20 x + 36 so 20 x + 36 = 21 ( x + 1 ) = > x = 15 answer : b"
Answer: b
Python program:
a = 20 + 1 
b = 36 - a
c = b + 1
Problem: if 2994 ã · 14.5 = 175 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 175 in the place of 2994 / 14.5 ] = 175 / 10 = 17.5 answer is c ."
Answer: c
Python program:
a = 14 / 5
b = 175 / a
Problem: what is the remainder when the number y = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus y = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Python program:
a = 5 / 5
Problem: there are 50 students in a class . if 2 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 49 , e ) 11
Rationale: "number of students absent on a particular day = 1 % of 50 i . e . , 2 / 100 × 50 = 1 therefore , the number of students present = 50 - 1 = 49 students . answer : d"
Answer: d
Python program:
a = 2 / 50
b = 1 - a
c = b * 50
Problem: if k and w are the dimensions of a rectangle that has area 40 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: "kw = 40 = 40 * 1 = 20 * 2 = 10 * 4 = 8 * 5 = - - > k can take 4 values , namely : 8 , 10,20 and 40 answer : c ."
Answer: c
Python program:
a = 3 * 1
Problem: jim drove 215 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 432 miles , c ) 456 miles , d ) 887 miles , e ) 985 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 215 = 985 miles correct answer e"
Answer: e
Python program:
a = 1200 - 215
Problem: for a certain alarm system , each code is comprised of 5 digits , but no digit can be used more than twice . how many codes can be made ?
Options: a ) 30240 , b ) 60480 , c ) 91440 , d ) 98240 , e ) 101040
Rationale: case 1 : all digits distinct select 5 digits out of 10 in 10 c 5 ways and arrange them in 5 ! ways which gives us 10 c 5 x 5 ! = 30240 case 2 : two digits are same , other 3 are distinct e . g . 45722 select a digit which is to be repeated in 10 c 1 ways , select other 3 digits in 9 c 3 ways and arrange them in 5 ! / 2 ! ways to get 10 c 1 x 9 c 3 x 5 ! / 2 ! = 50400 ways case 3 : two digits repeated and one other digit e . g . 33448 select 2 digits to be repeated in 10 c 2 ways , select the single digit in 8 c 1 ways and arrange them all in 5 ! / 2 ! . 2 ! ways to get 10 c 2 x 8 c 1 x 5 ! / 2 ! . 2 ! = 10800 sum of all = 30240 + 50400 + 10800 = 91440 ways ans : c
Answer: c
Python program:
a = math.factorial(10)
b = 10 - 5
c = math.factorial(b)
d = a / c
e = 10 - 1
f = math.factorial(e)
g = math.factorial(3)
h = 10 - 1
i = h - 3
j = math.factorial(i)
k = g * j
l = f / k
m = 10 * l
n = math.factorial(5)
o = n / 2
p = m * o
q = d + p 
r = math.factorial(10)
s = 10 - 2
t = math.factorial(s)
u = math.factorial(2)
v = t * u
w = r / v
x = 10 - 2
y = w * x
z = math.factorial(5)
A = z / 4
B = y * A
C = q + B
Problem: in the rectangular coordinate system , if the line x = 3 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) - 2 , b ) 0 , c ) 1 / 2 , d ) 1 , e ) 2 / 3
Rationale: x = 3 y + 5 , and thus y = x / 3 - 5 / 3 the slope is 1 / 3 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 3 and thus p = 2 / 3 the answer is e .
Answer: e
Python program:
a = 2 / 3
Problem: what decimal fraction is 30 ml of a litre ?
Options: a ) . 3 , b ) . 0003 , c ) . 003 , d ) 0.03 , e ) none of these
Rationale: "answer required fraction = 30 / 1000 = 3 / 100 = . 03 correct option : d"
Answer: d
Python program:
a = 30 / 1000