euclaise/mathqa_programs huggingface dataset:
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 12 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 14 %
Rationale: "total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 12 = 14 gallons - - - > 2 / 14 = 14 % of the fuel used . e is the correct answer ."
Answer: e
Python program:
a = 40 * 60
b = 80 * 60
c = a / b
d = 40 * 60
e = 80 * 60
f = d / e
g = f + 12 
h = c / g
Problem: the ratio of flour to water to sugar in a recipe is 11 : 5 : 2 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 7.5 cups of water , how much sugar is required ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: the ratio of flour to water is 22 : 5 . the ratio of flour to sugar is 5.5 : 2 = 22 : 8 . the new ratio of flour to water to sugar is 22 : 5 : 8 if we need 7.5 cups of water , then we need 12 cups of sugar . the answer is e .
Answer: e
Python program:
a = 7 / 5
b = 4 * 2
c = a * b
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 5 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 297 km , e ) 600 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 5 2 x / 15 - x / 8 = 5 = > x = 600 km . answer : e"
Answer: e
Python program:
a = 1 / 2
Problem: a merchant marks goods up by 60 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 20 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.6 p ) * x = 1.2 p x = 1.2 / 1.6 = 0.75 which is a discount of 25 % . the answer is b ."
Answer: b
Python program:
a = 60 / 100
b = 1 + a 
c = b - 1
d = 20 / 100
e = c - d
f = 60 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: a student scored an average of 65 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 165 , c ) 76 , d ) 125 , e ) 26
Rationale: "given m + p + c = 65 * 3 = 195 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 195 = 125 answer : d"
Answer: d
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 65 * 3
e = c - d
Problem: find the number of trailing zeros in the product of ( 1 ^ 1 ) * ( 5 ^ 5 ) * ( 10 ^ 10 ) * ( 15 ^ 15 ) * ( 20 ^ 20 ) * ( 25 ^ 25 ) … … … . * ( 50 ^ 50 ) .
Options: a ) 150 , b ) 200 , c ) 250 , d ) 245 , e ) 225
Rationale: looking at the numbers it looks like ( 1 x 5 ) ^ 5 ( 2 x 5 ) ^ 10 . . . ( 10 x 5 ) ^ 50 1 . determine the limiting factor . is it 2 or is it 5 ? we know that all the numbers are multiple of 5 but not of 2 . thus , the limiting factor in this case is 2 . let ' s drop all the 5 . then , we count factors of 2 of even multiples . 2 ^ 10 = 10 4 ^ 20 = 20 + 20 6 ^ 30 = 30 8 ^ 40 = 40 + 40 + 40 10 ^ 50 = 50 250 answer : c
Answer: c
Python program:
a = 15 * 15
b = a + 25
Problem: how many numbers from 2 to 8 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 8 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : b"
Answer: b
Python program:
a = 8 / 2
b = math.floor(a)
c = b * 2
d = 2 / 2
e = math.floor(d)
f = e + 1 
g = f * 2
h = c - g
i = h / 2
j = i + 1
Problem: the length of a bridge in meters , which a train 80 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 215 , b ) 235 , c ) 255 , d ) 275 , e ) 295
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 80 = 375 meters x = 295 meters the answer is e ."
Answer: e
Python program:
a = 45 * 1000
b = a / 3600
c = b * 30
d = c - 80
Problem: find the smallest number which should be divided with 3872 to make it a perfect square .
Options: a ) 8 , b ) 6 , c ) 2 , d ) 4 , e ) 1
Rationale: "3872 = 11 * 11 * 2 * 2 * 2 * 2 * 2 required smallest number = 2 2 is the smallest number which should be divided with 3872 to make it a perfect square . answer : c"
Answer: c
Python program:
a = 3872 / 3
b = a / 3
c = b / 4
d = c / 4
e = d / 4
Problem: x and y are both integers . if x / y = 59.80 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 200 , e ) 1024
Rationale: "remainder = 0.80 = - - > 80 / 100 - - > can be written as ( 80 / 4 ) / ( 100 / 4 ) = 20 / 25 so remainders can be 20 , 40 , 60 , 80 we need the sum of only 2 digit remainders - - > 20 + 40 + 60 + 80 = 200 answer : d"
Answer: d
Python program:
a = 3 / 2
b = a * 100
c = 2 + 3 
d = c * 59
e = d + 3 
f = b + e
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 4 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 21 , b ) 26 , c ) 30 , d ) 18 , e ) 16
Rationale: "a - - - - - b - - - - c - - - - - - - - d - - - - e given : de = 4 - ( i ) ab = 5 - ( ii ) ac = 11 - ( iii ) bc = 2 cd - ( iv ) from ( ii ) and ( iii ) , bc = 6 from ( iv ) , cd = 3 length of ae = ac + cd + de = 11 + 3 + 4 = 18 correct option : d"
Answer: d
Python program:
a = 11 - 5
b = a / 2
c = 11 + b 
d = c + 4
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction t of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is t = 2 / 14 = 1 / 7 . answer : e
Answer: e
Python program:
a = math.lcm(2, 3)
b = a / 2
c = b - 2
Problem: a train leaves delhi at 9 a . m . at a speed of 35 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 600 , d ) 888 , e ) 1400
Rationale: "d = 35 * 5 = 175 rs = 40 – 35 = 5 t = 175 / 5 = 35 d = 40 * 35 = 1400 km answer : e"
Answer: e
Python program:
a = 3 + 2 
b = 35 * a
c = 40 - 35
d = b / c
e = d * 40
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 2000 . then his monthly salary is
Options: a ) rs . 10000 , b ) rs . 6000 , c ) rs . 8000 , d ) rs . 4000 , e ) rs . 2000
Rationale: sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 2000 â ‡ ” 20 / 100 x = 2000 â ‡ ” x = 2000 ã — 5 = 10000 . answer a
Answer: a
Python program:
a = 4 + 1 
b = 2000 * a
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 7.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 10 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.075 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 75 f - - > s = 9 f - - > f / s = 1 / 9 - - > f / ( s + f ) = 1 / ( 1 + 9 ) = 1 / 10 = 0.1 . answer : b ."
Answer: b
Python program:
a = 3 - 5
b = 7 - 5
c = a / b
d = c * 100
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 42 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 4 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 3 / 45 * 60 = 4 answer : b"
Answer: b
Python program:
a = 42 / 45
b = const_60 * a
c = const_60 - b
Problem: . 008 / ? = . 01
Options: a ) . 8 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: "let . 008 / x = . 01 ; then x = . 008 / . 01 = . 8 / 1 = . 8 answer is a"
Answer: a
Python program:
a = 8 / 1000
b = 1 / 100
c = a / b
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 17000 left with him . find salary . .
Options: a ) $ 10700 , b ) $ 17000 , c ) $ 180000 , d ) $ 1700 , e ) $ 170000
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 17000 , = [ 1 - 9 / 10 ] * total salary = $ 17000 , total salary = $ 17000 * 10 = $ 180000 , correct answer ( e )"
Answer: e
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 3 / 5
e = c + d 
f = 1 - e
g = 17000 / f
Problem: what is the lowest positive integer that is divisible by 8 through 11 , inclusive ?
Options: a ) 999 , b ) 7811 , c ) 6555 , d ) 9200 , e ) 7920
Rationale: "the integer should be divisible by : 8 , 9 , 10 and 11 . the least common multiple of these integers is lcm = 8 * 9 * 10 * 11 = 7920 answer : e"
Answer: e
Python program:
a = math.lcm(8, 11)
Problem: the sector of a circle has radius of 20 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 , b ) 87.1 , c ) 91.7 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 20 ) + 2 ( 20 ) = 47.1 + 40 = 87.1 cm answer : b"
Answer: b
Python program:
a = 20 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 20
Problem: tara bought 19 cartons of ice cream and 4 cartons of yoghurt . each carton of ice cream cost $ 7 and each carton of yoghurt cost $ 1 . how much more did tara spend on ice cream than on yoghurt ?
Options: a ) $ 144 , b ) $ 130 , c ) $ 80 , d ) $ 110 , e ) $ 129
Rationale: step 1 : find the cost of the ice cream . 19 × $ 7 = $ 133 step 2 : find the cost of the yoghurt . 4 × $ 1 = $ 4 step 3 : find how much more the ice cream cost than the yoghurt . $ 133 – $ 4 = $ 129 tara spent $ 129 more on ice cream . answer is e .
Answer: e
Python program:
a = 19 * 7
b = 4 * 1
c = a - b
Problem: if 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 36 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 9 * 8 / 2 = 36 answer : c"
Answer: c
Python program:
a = math.factorial(9)
b = 9 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 65 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 20 : 13 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 65 × 4 = 260 km the ratio is 400 : 260 = 40 : 26 = 20 : 13 the answer is c ."
Answer: c
Python program:
a = 50 * 8
b = 65 * 4
c = a / b
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 48 inches by 60 inches . if the measurement of each soap box is 8 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 280 , d ) 320 , e ) 300
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 48 * 60 dimensions of the soap = 5 * 6 * 8 we get = 5 x 6 x 10 = 300 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( e )"
Answer: e
Python program:
a = 25 * 48
b = a * 60
c = 8 * 6
d = c * 5
e = b / d
Problem: what is the greatest 5 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 4 , 5 , 6 , 7 , and 9 respectively ?
Options: a ) 56780 , b ) 78910 , c ) 97479 , d ) 97918 , e ) 97920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 9 when we divide by 10 , so c is the only possible answer .
Answer: c
Python program:
a = 1000 * 1000
b = a / 10
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 5 each . if none of the 50 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 550 , b ) $ 600 , c ) $ 500 , d ) $ 400 , e ) $ 450
Rationale: "if 50 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 100 books amount received for sold books = 100 * 5 = $ 500 answer : c"
Answer: c
Python program:
a = 2 / 3
b = 50 * a
c = 1 / 3
d = b / c
e = 2 * 0
Problem: a rower can row 6 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.21 , b ) 2.45 , c ) 2.67 , d ) 2.83 , e ) 2.95
Rationale: "let x be the distance to big rock . time = x / 4 + x / 8 = 1 x = 32 / 12 = 2.67 km the answer is c ."
Answer: c
Python program:
a = 6 - 2
b = 6 + 2 
c = 6 - 2
d = b + c 
e = a / d
f = 6 + 2 
g = e * f
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 75 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 5 rs , e ) 1 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 75 rs . 5 m + 5 m + 5 m - - - - - 75 rs . 15 m - - - - - - 75 rs . = > 1 m = 5 rs . answer : d"
Answer: d
Python program:
a = 3 * 5
b = 75 / a
Problem: the value of ( 34.31 * 0.473 * 1.5 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.01 , d ) 2.06 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.5 ) / ( 0.0673 * 23.25 * 7.57 ) = 24.343 / 11.845 = 2.06 answer : d"
Answer: d
Python program:
a = 34 * 31
b = a * 1
c = 7 * 57
d = c * 0
e = b / d
f = e / 10
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 40 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 4 , e ) $ 28
Rationale: bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 40 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 40 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 40 i . e . x = 36 i . e . fixed monthly charge , y = 4 answer : option d
Answer: d
Python program:
a = 40 * 2
b = a - 76
Problem: how many seconds does puja take to cover a distance of 500 m , if she runs at a speed of 30 km / hr ?
Options: a ) 60 sec , b ) 82 sec , c ) 95 sec , d ) 100 sec , e ) 120 sec
Rationale: hint : time = distance / speed we see that the distance is given in metres while the speed is given in km / hr and the answer is asked in seconds . so , convert km / hr into m / s by multiplying 5 / 18 m / s to the given value of speed . 30 km / hr = 30 x 5 / 18 = 75 / 9 m / sec i . e . place these values in the formula : time = 500 x 9 / 75 = 60 sec answer is a
Answer: a
Python program:
a = 30 * const_0_2778
b = 500 / a
Problem: the l . c . m . of 2 numbers is 40 . the numbers are in the ratio 4 : 5 . find their sum ?
Options: a ) 18 , b ) 40 , c ) 48 , d ) 32 , e ) 56
Rationale: "let the numbers be 4 x and 5 x l . c . m . = 20 x 20 x = 40 x = 2 the numbers are = 8 and 10 required sum = 8 + 10 = 18 answer is a"
Answer: a
Python program:
a = 40 * 4
b = 2 / a
c = b * 4
d = 40 * 4
e = 2 / d
f = e * 40
g = c + f
Problem: the sum of the ages 4 members of a family 5 years ago was 94 . today , when the daughter has been married off and replaced by a daughter - in - law , the sum of their ages is 100 . assuming that there has been no other change in the family structure and all members are alive , what is the difference in the ages of daughter and daughter - in - law ?
Options: a ) 22 , b ) 11 , c ) 25 , d ) 14 , e ) 16
Rationale: solution : sum of ages of 4 members 5 years ago = 94 = > sum of present ages of 4 members = 94 + 4 * 5 = 114 difference in the sum of the ages = difference in the ages of daughter and daughter - in - law difference in the sum of the ages = 114 - 100 = 14 = > difference in the ages of daughter and daughter - in - law = 14 answer d
Answer: d
Python program:
a = 5 * 4
b = a + 94 
c = b - 100
Problem: 35 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 42 , d ) 16 , e ) 10
Rationale: "binders books days 35 1400 21 x 1600 20 x / 35 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 42 answer : c"
Answer: c
Python program:
a = 1600 / 20
b = 35 * 21
c = 1400 / b
d = a / c
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - sixth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 22 , c ) 3 , d ) 11 / 3 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 6 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 6 ( 11 + n ) 11 + 2 n / 10 = 11 + n / 6 = > 66 + 12 n = 110 + 10 n = > 2 n = 44 n = 22 answer : b"
Answer: b
Python program:
a = 12 - 1
b = 12 - 3
c = 1/(b)
d = 1/(10)
e = c - d
f = a * e
g = 1 + 4 
h = 1/(g)
i = 12 - 3
j = 1/(i)
k = h - j
l = f / k
Problem: what is the probability of getting exactly 4 heads in a single throw of five fair coins ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32
Rationale: "one possible case is hhhht . p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 4 = 5 possible cases . p ( 4 heads ) = 5 * 1 / 32 = 5 / 32 the answer is d ."
Answer: d
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: 40 × ? + ( 12 + 8 ) × 3 / 5 = 1212
Options: a ) a ) 7 , b ) b ) 5 , c ) c ) 4 , d ) d ) 18 , e ) e ) 30
Rationale: "explanation : = > 40 × ? + ( 12 + 8 ) × 3 / 5 = 1212 = > 40 × ? = 1212 - ( 12 + 8 ) × 3 / 5 = > 40 × ? = 1212 - 20 × 3 / 5 = > 40 × ? = 1212 - 20 × 3 / 5 = 1200 = > ? = 1200 / 40 = 30 answer : option e"
Answer: e
Python program:
a = 12 + 8 
b = 3 / 5
c = a * b
d = 1212 - c
e = d / 40
Problem: in how many ways 4 boys and 5 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) 2880
Rationale: "solution : let the arrangement be , g b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 3 ! ways . required number of ways , = 4 ! * 5 ! = 2880 . answer : option e"
Answer: e
Python program:
a = math.factorial(4)
b = math.factorial(5)
c = a * b
Problem: in a manufacturing plant , it takes 48 machines 4 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 48 machines take 4 hours to fill 8 standard orders . . in next eq we are doubling the machines from 48 to 72 , but the work is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 8 = 4 ans a"
Answer: a
Python program:
a = 48 * 12
b = a * 4
c = b / 72
d = c / 8
Problem: f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 )
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "f ( x ) + 3 f ( 8 - x ) = f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation correct answer c"
Answer: c
Python program:
a = 3 * 3
b = a * 2
c = 2 - b
d = 3 * 3
e = 1 - d
f = c / e
Problem: two cubes of their volumes in the ratio 64 : 1331 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 11 , e ) 4 : 5
Rationale: "the ratio of their surface area is 64 : 1331 4 : 11 answer is d ."
Answer: d
Python program:
a = 64 ** const_0_33
b = 1331 ** const_0_33
c = a / b
Problem: at joel ’ s bookstore , the current inventory is 30 % historical fiction . of the historical fiction books , 30 % are new releases , while 40 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 9 / 37 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 30 % of total = 30 other books = 70 new historic fiction = 30 % of 30 = 9 other new books = 40 % of 70 = 28 total new books = 37 fraction = 9 / 37 ans : b"
Answer: b
Python program:
a = 30 * 30
b = a / 100
c = 30 * 30
d = c / 100
e = 100 - 30
f = 40 * e
g = f / 100
h = d + g 
i = b / h
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student b answers each of the 100 questions on her test and receives a score of 73 , how many questions did student b answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 91
Rationale: "a score of 73 brings to mind that it is an odd number even though you are subtracting an even number ( twice the incorrect responses ) out of the correct responses score . so the correct responses score must be an odd number too ( odd - even = odd ) . since the overall score is 73 , the number of correct responses must be more than 73 since the student answered all questions . only 91 satisfies both these conditions . answer ( e )"
Answer: e
Python program:
a = 100 - 73
b = a / 3
c = 100 - b
Problem: a box measuring 30 inches long by 48 inches wide by 12 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 78 , b ) 80 , c ) 85 , d ) 88 , e ) 90
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 6 is the biggest number that could divide all three , 30 , 48 and 12 . thus side of cube must be 6 , and total number of cubes = 30 / 6 * 48 / 6 * 12 / 6 = 80 ans b ."
Answer: b
Python program:
a = 30 * 48
b = a * 12
c = 12 / 2
d = b / volume_cube