euclaise/mathqa_programs huggingface dataset:
Problem: each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 9 . we need to remove 15 of the 20 - pound boxes . the answer is c .
Answer: c
Python program:
a = 20 * 30
b = 30 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 30
h = 30 * 18
i = g - h
j = 20 - 10
k = i / j
l = 30 - k
m = 20 * l
n = f + m 
o = 30 * 16
p = n - o
q = 20 - 16
r = p / q
Problem: two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 54 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 17 minutes , c ) 15 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 54 = ( 15 + 18 - 5 ) / 270 = 28 / 270 = 14 / 135 so , the tank becomes full in 6 minutes . answer : d"
Answer: d
Python program:
a = 1 / 18
b = 1 / 15
c = a + b 
d = 1 / 54
e = c - d
Problem: how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m
Options: a ) 5600 , b ) 600 , c ) 6400 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c"
Answer: c
Python program:
a = 8 * 6
b = a * 22
c = 25 * 11
d = c * 6
e = d / 100
f = e / 100
g = b / f
Problem: a prize of $ 500 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 160 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 300 - 140 = $ 160 , hence a is the correct answer .
Answer: a
Python program:
a = 500 * 2
b = a / 5
c = 500 - b
d = 20 * 3
e = d / 5
f = 20 - e
g = f - 1
h = g * 20
i = c - h
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ? a . 30 km / hr b . 45 km / hr
Options: a ) 11 , b ) 78 , c ) 60 , d ) 28 , e ) 81
Rationale: let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c
Answer: c
Python program:
a = 100 + 100 
b = a / 8
c = b / 3
d = c * 2
e = d / const_0_2778
Problem: a car going at 40 miles per hour set out on an 90 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 90
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 90 mins = 3 / 2 hour speed of car b = 60 / ( 3 / 2 ) = 90 miles per hour answer e"
Answer: e
Python program:
a = 10 - 9
b = a * const_60
c = 40 - 10
d = b + c 
e = d / const_60
f = 90 / e
Problem: how many bricks each measuring 30 cm x 12 cm x 10 cm , will be needed to build a wall 6 m x 4 m x 20.5 m
Options: a ) 5655 , b ) 1366 , c ) 6444 , d ) 7266 , e ) none of these
Rationale: explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 600 x 400 x 20.5 ) / ( 30 x 12 x 10 ) = 1366 answer : b
Answer: b
Python program:
a = 6 * 4
b = a * 20
c = 30 * 12
d = c * 10
e = d / 100
f = e / 100
g = b / f
Problem: a , b and c can do a work in 6 , 8 and 12 days respectively doing the work together and get a payment of rs . 1800 . what is b ’ s share ?
Options: a ) 300 , b ) 245 , c ) 600 , d ) 743 , e ) 215
Rationale: c 600 wc = 1 / 6 : 1 / 8 : 1 / 12 = > 4 : 3 : 2 3 / 9 * 1800 = 600
Answer: c
Python program:
a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d 
f = b + e 
g = a / f
h = 1800 * g
Problem: how many positive integers less than 50 have a reminder 01 when divided by 4 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 4 . so , there are total of 13 numbers . answer : a ."
Answer: a
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the proportion of water to alcohol in solution a is 2 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 46.7 % , b ) 47.3 % , c ) 48.4 % , d ) 50.6 % , e ) 51.8 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 3 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 6 + 3 v / 10 = 14 v / 30 = 7 v / 15 . the concentration of alcohol is 7 / 15 = 46.7 % the answer is a ."
Answer: a
Python program:
a = 1 + 3 
b = 2 + 2 
c = 1 + 3 
d = b + c 
e = a / d
f = e * 100
Problem: a worker makes a toy in every 2 h . if he works for 100 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 50 , d ) 39 , e ) none
Rationale: "no . of toys = 100 / 2 = 50 answer : c"
Answer: c
Python program:
a = 100 / 2
Problem: a book is bought for $ 32 and sold for $ 56 . what is the profit in percentage ?
Options: a ) 15 , b ) 35 , c ) 75 , d ) 25 , e ) 85
Rationale: 56 / 32 = 1.75 the answer is c .
Answer: c
Python program:
a = 56 - 32
b = a / 32
c = b * 100
Problem: an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 90 / 100 = > x = 48 . answer is e ."
Answer: e
Python program:
a = 90 / 100
b = a * 24
c = 70 / 100
d = b / c
Problem: the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 20 , what is the age of the youngest sibling ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "x + ( x + 3 ) + ( x + 5 ) + ( x + 8 ) = 80 4 x + 16 = 80 4 x = 64 x = 16 the answer is c ."
Answer: c
Python program:
a = 4 * 20
b = 4 + 5 
c = b + 8 
d = a - c
e = d / 4
Problem: on a map the distance between two mountains is 310 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.91 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 310 inch = 136 km so 1 inch = 136 / 310 km so 34 inch = ( 136 ã — 34 ) / 310 = 14.91 km answer : c"
Answer: c
Python program:
a = 34 * 136
b = a / 310
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 100 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 100 meters , thus the circumference is 200 + 100 = 300 meters . answer : b ."
Answer: b
Python program:
a = 2 * 100
b = a + 100
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 3 ” 3 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "3 ” 3 = 9 - 3 = 6 answer : a"
Answer: a
Python program:
a = 3 ** 2
b = a - 3
Problem: a river 3 m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 3200 , c ) 3400 , d ) 2761 , e ) 2882
Rationale: "( 2000 * 3 * 32 ) / 60 = 3200 m 3 answer : b"
Answer: b
Python program:
a = 3 * 32
b = 2 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: a factory produces 7500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 6113 toys , d ) 1875 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 7500 / 4 = 1875 toys correct answer d"
Answer: d
Python program:
a = 7500 / 5
Problem: if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 140 %
b ) 350 %
c ) 450 %
d ) 600 %
e ) 700 %
Rationale: the area a of the large cube is 7 * 7 * 6 = 294 square cm . the area of the 343 small cubes is 7 * 7 * 7 * 6 = 7 a , an increase of 600 % . the answer is d .
Answer: d
Python program:
a = surface_cube * (
b = a / surface_cube
c = 100 * b
Problem: a student chose a number , multiplied it by 4 , then subtracted 142 from the result and got 110 . what was the number he chose ?
Options: a ) 58 , b ) 59 , c ) 60 , d ) 62 , e ) 63
Rationale: "let x be the number he chose , then 4 ⋅ x − 142 = 110 4 x = 252 x = 63 correct answer e"
Answer: e
Python program:
a = 110 + 142 
b = a / 4
Problem: a merchant purchased a jacket for $ 56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 8 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "actual cost = $ 56 sp = actual cost + mark up = actual cost + 30 % sp = 56 * 100 / 70 on sale sp = 80 / 100 ( 56 * 100 / 70 ) = 64 gross profit = $ 8 answer is b"
Answer: b
Python program:
a = 30 / 100
b = 1 - a
c = 56 / b
d = 20 / 100
e = 1 - d
f = c * e
g = f - 56
Problem: a and b can do a piece of work in 3 days , b and c in 4 days , c and a in 6 days . how long will c take to do it ?
Options: a ) 33 , b ) 77 , c ) 24 , d ) 55 , e ) 71
Rationale: "2 c = ¼ + 1 / 6 – 1 / 3 = 1 / 12 c = 1 / 24 = > 24 days answer : c"
Answer: c
Python program:
a = 3 * 3
b = 3 * 3
c = b / 6
d = 3 * 3
e = d / 3
f = 3 * 3
g = f / 4
h = e + g 
i = c + h 
j = i / 2
k = 3 * 3
l = k / 3
m = j - l
n = a / m
Problem: how many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr
Options: a ) 25 seconds , b ) 28 seconds , c ) 30 seconds , d ) 35 seconds , e ) 40 seconds
Rationale: "explanation : relative speed = 63 - 3 = 60 km / hr = 60 * ( 5 / 18 ) = 50 / 3 m / sec time taken to pass the man will be 500 â ˆ — 3 / 50 = 30 seconds answer is c"
Answer: c
Python program:
a = 63 - 3
b = a * const_0_2778
c = 500 / b
d = c - 1
e = d * 10
f = e * 2
Problem: the current in a river is 3 mph . a boat can travel 21 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 102.8 miles , e ) 112 miles
Rationale: "upstream speed = 21 - 3 = 18 mph downstream speed = 21 + 3 = 24 mph d / 18 + d / 24 = 10 hours solving for d we get d = 102.8 answer : d"
Answer: d
Python program:
a = 21 - 3
b = 21 + 3 
c = a * b
d = c * 10
e = 21 + 3 
f = 21 - 3
g = e + f 
h = d / g
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 180 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: l + k = 180 and so k = 180 - l l + 10 = 1.5 k = 1.5 ( 180 - l ) 2.5 l = 260 l = 104 the answer is e .
Answer: e
Python program:
a = 100 + 50 
b = a / 100
c = 180 * b
d = c - 10
e = 100 + 50 
f = e / 100
g = f + 1 
h = d / g
Problem: if the perimeter of a rectangular garden is 1200 m , its length when its breadth is 240 m is ?
Options: a ) 338 m , b ) 778 m , c ) 200 m , d ) 276 m , e ) 360 m
Rationale: "2 ( l + 240 ) = 1200 = > l = 360 m answer : e"
Answer: e
Python program:
a = 1200 / 2
b = a - 240
Problem: the volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 7 : 5 , b ) 2 : 9 , c ) 7 : 2 , d ) 2 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 35 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 7 / 5 i . e . h 1 : h 2 = 7 : 5 answer : a"
Answer: a
Python program:
a = 1 / 35
b = 1 / 2
c = b ** 2
d = a / c
Problem: a jar of 144 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "144 = 16 * 9 = 18 * 8 there are 16 people in the group today . the answer is c ."
Answer: c
Python program:
a = 144 * 2
b = a * 4
c = 2 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 2
g = f / 2
Problem: how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr
Options: a ) 115 min , b ) 215 min , c ) 315 min , d ) 415 min , e ) none of these
Rationale: "explana ɵ on : we know that , time = distancespeedspeed = 20 km / hr = 20 ∗ 518 m / sec = 509 m / sec time = ( 400 ∗ 950 ) = 72 sec = 115 min answer : op ɵ on a"
Answer: a
Python program:
a = 20 * const_0_2778
b = 400 / a
c = b / const_60
Problem: a cyclist rides a bicycle 7 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 7 km / hr . what is the average speed for the entire trip ?
Options: a ) 7.59 , b ) 7.79 , c ) 7.99 , d ) 8.19 , e ) 8.39
Rationale: distance = 17 km time = 7 / 10 + 10 / 7 = ( 49 + 100 ) / 70 = 149 / 70 hours average speed = ( 17 * 70 ) / 149 = 7.99 km / h the answer is c .
Answer: c
Python program:
a = 7 + 10 
b = 7 / 10
c = 10 / 7
d = b + c 
e = a / d
Problem: a train 240 m long passed a pole in 24 sec . how long will it take to pass a platform 650 m long ? a . 65
Options: a ) 28 sec , b ) 89 sec , c ) 85 sec , d ) 16 sec , e ) 15 sec
Rationale: speed = 240 / 24 = 10 m / sec . required time = ( 240 + 650 ) / 10 = 89 sec . answer : b
Answer: b
Python program:
a = 240 + 650 
b = 240 / 24
c = a / b
Problem: if the radius of a circle that centers at the origin is 5 , how many k points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : k = c"
Answer: c
Python program:
a = 5 * 5
b = 5 + 4 
c = a - b
d = 2 ** 2
e = c - d
Problem: 1504 x 1504 = ?
Options: a ) 2262016 , b ) 2250000 , c ) 12000 , d ) 2262000 , e ) 2250016
Rationale: "1504 x 1504 = ( 1504 ) 2 = ( 1500 + 4 ) 2 = ( 1500 ) 2 + ( 4 ) 2 + ( 2 x 1500 x 4 ) = 2250000 + 16 + 12000 = 2250016 + 12000 = 2262016 a"
Answer: a
Python program:
a = 1504 / 1504
b = a * 100
Problem: marcella has 23 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 18 , e ) 15
Rationale: marcella has 23 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 23 pairs of shoes minus the 5 ' destroyed ' pairs yields 20 pairs that still fulfill the requirements . answer : d
Answer: d
Python program:
a = 9 / 2
b = math.floor(a)
c = b + 1 
d = 23 - c
Problem: a room 3 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 27636 , b ) 27640 , c ) 27647 , d ) 27713 , e ) 27675
Rationale: "explanation : area of the room = ( 321 x 777 ) cm 2 . size of largest square tile = h . c . f . of 321 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 321 × 777 ) / ( 3 × 3 ) = 27713 answer : option d"
Answer: d
Python program:
a = 3 * 100
b = a + 21 
c = 7 * 100
d = c + 77 
e = b * d
f = 2 * 4
g = f + 2 
h = 21 - g
i = 2 * 4
j = i + 2 
k = 21 - j
l = h * k
m = e / l
Problem: a shopkeeper sold 15 articles at the cost price of 20 articles . then find the profit % or lost %
Options: a ) 30 % , b ) 31 % , c ) 20 % , d ) 33.33 % , e ) 40 %
Rationale: "here 15 articles selling price = 20 articles cost price so the difference = 20 - 15 = 5 % of profit = 5 * 100 / 15 = 33.33 % correct option is d"
Answer: d
Python program:
a = 20 - 15
b = a / 15
c = b * 100
Problem: the price of 2 saris and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) rs . 2400 , b ) rs . 2490 , c ) rs . 2500 , d ) rs . 2550 , e ) rs . 2600
Rationale: let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . a
Answer: a
Python program:
a = 6 * 2
b = a - 4
c = 1600 / b
d = 12 * c
Problem: two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is
Options: a ) 9 , b ) 15 , c ) 36 , d ) 45 , e ) none
Rationale: solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c
Answer: c
Python program:
a = 5 * 4
b = 180 / a
c = 4 * b
Problem: how many cubes of 25 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 177 cm
b ) 100 cm
c ) 86 cm
d ) 64 cm
e ) 87 cm
Rationale: number of cubes = 100 â ˆ — 100 â ˆ — 100 / 25 â ˆ — 25 â ˆ — 25 = 64 note : 1 m = 100 cm answer : d
Answer: d
Python program:
a = volume_cube / (
Problem: if an object travels at two feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 3778 , c ) 7200 , d ) 1800 , e ) 2881
Rationale: "explanation : if an object travels at 2 feet per second it covers 2 x 60 feet in one minute , and 2 x 60 x 60 feet in one hour . answer = 7200 answer : c ) 7200"
Answer: c
Python program:
a = 3 * const_60
b = a * const_60
Problem: an apple orchard grows red and green apples . on the first day of harvest , 496 apples are collected . there are 3 times as many red apples as there are green apples . how many green apples were harvested ?
Options: a ) 99 , b ) 112 , c ) 118 , d ) 124 , e ) 130
Rationale: let x be the number of green apples . there were 496 total apples ; there are three times as many red apples as green apples . therefore , x + 3 x = 496 4 x = 496 x = 124 answer : d
Answer: d
Python program:
a = 3 + 1 
b = 496 / a
Problem: 100 liters of a mixture contains milk and water in the ratio 7 : 3 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 7 : 8 , b ) 8 : 3 , c ) 3 : 8 , d ) 8 : 7 , e ) 7 : 1
Rationale: "quantity of milk in 100 liters if mix = 100 * 7 / 10 = 70 liters quantity of milk in 110 liters of new mix = 80 + 10 = 80 liters quantity of water in it = 110 - 80 = 30 liters ratio of milk and water in new mix = 80 : 30 = 8 : 3 answer is b"
Answer: b
Python program:
a = 10 - 1
b = a * 3
c = 7 * 3
d = b / c
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 16 : 5 , b ) 14 : 5 , c ) 16 : 7 , d ) 19 : 5 , e ) none of these
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres as 6 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5 . answer : d"
Answer: d
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 2 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k 
m = e / l
Problem: a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 36 / 49 . how many marbles are in the bag ?
Options: a ) 24 , b ) 48 , c ) 84 , d ) 72 , e ) 80
Rationale: ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 36 / 49 - - > ( x - 12 ) ^ 2 = 36 / 49 x ^ 2 square rooting u have x - 12 / x = 6 / 7 or 7 x - 6 x = 84 or x = 84 c
Answer: c
Python program:
a = 36 / 49
b = math.sqrt(a)
c = 1 - b
d = 12 / c
Problem: 288 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 32 , d ) 39 , e ) 43
Rationale: "explanation : 288 ã · ? ã — 15 = 405 - 270 = 135 ( 288 ã — 15 ) / ? = 135 ? = ( 288 ã — 15 ) / 135 = 32 answer : option c"
Answer: c
Python program:
a = 405 - 270
b = a + 15 
c = b * 2
d = c / 10
e = 405 - 270
f = e + 15 
g = f * 2
h = g / 10
i = h / 10
j = d + i 
k = j + 1