euclaise/mathqa_programs huggingface dataset:
Problem: | 16 - 5 | - | 5 - 12 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 16 - 5 | - | 5 - 12 | = | 11 | - | - 7 | = 11 - 7 = 4 correct answer e"
Answer: e
Python program:
a = 16 - 5
b = 12 - 5
c = a - b
Problem: if two - third of a bucket is filled in 90 seconds then the time taken to fill the bucket completely will be .
Options: a ) 90 seconds , b ) 70 seconds , c ) 135 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: "2 / 3 filled in 90 seconds 1 / 3 filled in 45 seconds then 2 / 3 + 1 / 3 = 90 + 45 seconds = 135 seconds answer : c"
Answer: c
Python program:
a = 90 / 2
b = a * 3
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 120 km / h , what is the circumference of the tire ?
Options: a ) 7 meters
b ) 9 meters
c ) 8 meters
d ) 5 meters
e ) 3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 12,0000 m : c is the circumference c = 5 meters correct answer d
Answer: d
Python program:
a = 2 * 3
b = a * 10
c = b * 400
d = 120 / c
e = d * 1000
Problem: the population of a town increased from 1 , 75000 to 2 , 62500 in a decade . what is the average percent increase of population per year ?
Options: a ) 4 % , b ) 6 % , c ) 5 % , d ) 50 % , e ) none of these
Rationale: explanation : increase in the population in 10 years = 2 , 62500 - 1 , 75000 = 87500 % ncrease in the population in 10 years = ( 87500 / 175000 ) × 100 = 8750 / 175 = 50 % average % increase of population per year = 50 % / 10 = 5 % answer : option c
Answer: c
Python program:
a = 1000 * 100
b = 62500 / a
c = 2 + b 
d = 1000 * 100
e = 75000 / d
f = 1 + e 
g = c - f
h = g / 10
i = 1000 * 100
j = 75000 / i
k = 1 + j 
l = h / k
m = l * 100
Problem: 10 men do a work in 10 days . how many men are needed to finish the work in 2 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 2 days = 10 * 10 / 2 = 50 answer is a"
Answer: a
Python program:
a = 10 * 10
b = a / 2
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 38 students ?
Options: a ) 14 years , b ) 7 years , c ) 19 years , d ) 21 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 38 = 7 years . answer b"
Answer: b
Python program:
a = 35 * 16
b = a + 21 
c = b + 35 
d = 35 * 16
e = c - d
Problem: a man can row 8 kmph in still water . if the velocity of the current is 2 kmph and it takes him 2 hours to row to a place and come back . how far is the place ?
Options: a ) 5.5 , b ) 8.5 , c ) 6.5 , d ) 9.5 , e ) 7.5
Rationale: man ' s rate down stream = 8 + 2 = 10 kmph man ' s rate upstream = 8 - 2 = 6 kmph let the required distance be x km then x / 10 + x / 6 = 2 3 x + 5 x = 60 8 x = 60 x = 7.5 km answer is e .
Answer: e
Python program:
a = 8 - 2
b = 8 + 2 
c = a * b
d = c * 2
e = 8 + 2 
f = 8 - 2
g = e + f 
h = d / g
Problem: if x is equal to the sum of the integers from 20 to 40 , inclusive , and y is the number of even integers from 20 to 40 , inclusive , what is the value of x + y ?
Options: a ) 601 , b ) 611 , c ) 621 , d ) 631 , e ) 641
Rationale: "x = 20 + 21 + . . . + 40 = 21 ( 30 ) = 630 y = 11 x + y = 641 the answer is e ."
Answer: e
Python program:
a = 20 + 40 
b = a / 2
c = 40 - 20
d = c + 1 
e = b * d
f = 40 - 20
g = f / 2
h = g + 1 
i = e + h
Problem: the hiker walking at a constant rate of 5 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 15 , b ) 10 , c ) 20 , d ) 30 , e ) 35
Rationale: "after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 5 / 12 miles . so the hiker still has to cover 15 / 12 miles to meet the waiting cyclist . the hiker will need 1 / 4 hours or 15 mins to cover the remaining 15 / 12 miles . so the answer is a ."
Answer: a
Python program:
a = 20 - 5
b = 5 / const_60
c = a * b
d = c / 5
e = d * const_60
Problem: a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 8 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 1440 , b ) 2340 , c ) 3240 , d ) 4320 , e ) 5420
Rationale: "the tank is emptied at this rate : 9 + 8 - 5 = 12 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 12 = 4320 minutes . the answer is d ."
Answer: d
Python program:
a = 9 ** 5
b = 30 * a
c = 12 + 8 
d = c - 5
e = b / d
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 9 seconds . due to some problem , three boggies were detached . the train now crosses a telegraph post in
Options: a ) 6.75 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 9 = 20 m / s now , length of train = 9 ã — 15 = 135 m â ˆ ´ required time = 135 â  „ 20 = 6.75 sec . answer a"
Answer: a
Python program:
a = 12 * 15
b = a - 15
c = 12 * 15
d = c / 9
e = b / d
Problem: a 90 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 410 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 90 / 9 = 500 / 9 = > x + 90 = 500 = > x = 410 so the length of the train is 410 meters option d"
Answer: d
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 90
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 2 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 ) 240 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 2 2 x / 15 - x / 8 = 2 = > x = 240 km . answer : d"
Answer: d
Python program:
a = 1 / 2
Problem: a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 30 percent of the store ’ s cost for the computer . what selling price would yield a profit of 40 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2412 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: "1.3 x = 2240 x = 2240 / 1.3 so , 1.4 x = 2240 * 1.4 / 1.3 = 2412 answer : - b"
Answer: b
Python program:
a = 100 + 40 
b = 100 + 30 
c = a / b
d = 2240 * c
Problem: three table runners have a combined area of 220 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 220 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 220 - 24 - 140 all three = 28 answer : d"
Answer: d
Python program:
a = 220 - 24
b = 80 / 100
c = 175 * b
d = a - c
e = d / 2
Problem: the youngest of 4 children has siblings who are 2 , 7 , and 11 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 25 , what is the age of the youngest sibling ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "x + ( x + 2 ) + ( x + 7 ) + ( x + 11 ) = 100 4 x + 20 = 100 4 x = 80 x = 20 the answer is d ."
Answer: d
Python program:
a = 4 * 0
b = 4 + 7 
c = b + 11 
d = a - c
e = d / 4
Problem: addison high school ’ s senior class has 300 boys and 240 girls . if 60 % of the boys attended the college then 60 % of the total class attended college , what percentage of the girls class attended college ?
Options: a ) 60 , b ) 50 , c ) 46 , d ) 55.56 , e ) 65
Rationale: "number of boys attending the party : 0.60 * 300 = 180 total students = 300 + 240 = 540 number of students attending the party : 0.60 * 540 = 324 number of girls attending = 324 - 180 = 144 % of girls attending = 144 / 240 = 60 % . a is the correct answer"
Answer: a
Python program:
a = 60 / 100
b = a * 300
c = 60 / 100
d = 1 - c
e = d * 240
f = b + e 
g = 300 + 240 
h = f / g
i = h * 100
Problem: if 6 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 2 is allowed . imo a ."
Answer: a
Python program:
a = 6 / 3
b = 6 / 3
c = 3 / b
d = a + c
Problem: a person walking at 10 kmph reaches his office 10 minutes late . if he walks at 15 kmph , he reaches there 10 minutes earlier . how far is the office from his house ?
Options: a ) 5 km , b ) 15 km , c ) 8 km , d ) 10 km , e ) 20 km
Rationale: formula = s 1 * s 2 / s 2 - s 1 * t 1 + t 2 / 60 = 10 * 15 / 5 * 20 / 60 = 30 * 20 / 60 = 10 km answer is d
Answer: d
Python program:
a = 10 / const_60
b = 10 * a
c = 10 / const_60
d = 15 * c
e = b + d 
f = 15 - 10
g = e / f
h = 10 / const_60
i = g + h 
j = i * 10
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 18 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 3360 , c ) 7560 , d ) 50400 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 18 machine produce 560 * 6 * ( 18 / 8 ) in 6 minutes 560 * 6 * 18 / 8 = 7560 answer is c ."
Answer: c
Python program:
a = 18 / 8
b = 560 * a
c = b * 6
Problem: two pipes a and b can fill a tank in 25 hours and 35 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 14 6 / 11 hours , c ) 10 hours , d ) 12 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 25 part filled by b in 1 hour = 1 / 30 part filled by ( a + b ) in 1 hour = 1 / 25 + 1 / 30 = 11 / 150 both the pipes together fill the tank in 150 / 11 = 14 6 / 11 hours answer is b"
Answer: b
Python program:
a = 1 / 25
b = 1 / 35
c = a + b 
d = 1 / c
Problem: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many w kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Python program:
a = 14 + 2 
b = a / 2
c = b - 2
d = c / 2
e = 52 - d
f = 14 + 2 
g = f / 2
h = g - 2
i = 14 + 2 
j = i / 2
k = h + j 
l = e / k
m = 1 / 2
n = l + m
Problem: jolene entered an 14 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 506.00 answer : a ."
Answer: a
Python program:
a = 3 / 100
b = 2 / 100
c = 100 ** 2
d = b * c
e = 100 ** 2
f = d + e 
g = a * f
h = 2 / 100
i = 100 ** 2
j = h * i
k = 100 ** 2
l = j + k 
m = g + l 
n = 4 / 100
o = m * n
p = 3 / 100
q = 2 / 100
r = 100 ** 2
s = q * r
t = 100 ** 2
u = s + t 
v = p * u
w = o + v
Problem: an isosceles triangle with sides 13 13 10 and there is a circle inscribed it . find the radius of circle ?
Options: a ) 1.32
b ) 3.33
c ) 3.58
d ) 4.34
e ) 5.18
Rationale: height of triangle = √ ( 13 ^ 2 - ( 10 / 2 ) ^ 2 ) = 12 area of triangle = r * s where , r = radius of inscribed circle & s = ( a + b + c ) / 2 area of triangle = 1 / 2 * b * h = 1 / 2 * 10 * 12 = 60 s = ( 13 + 13 + 10 ) / 2 = 18 r = area of triangle / s = 60 / 18 = 10 / 3 = 3.33 answer : b
Answer: b
Python program:
a = triangle_area_three_edges * (
b = a / 2
Problem: in a can , there is a mixture of milk and water in the ratio 1 : 5 . if it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 3 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 8 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 3 / 8 t . 3 t / 8 - 2 = 1 / 6 = ( t - 2 ) 10 t = 96 - 16 = > t = 8 answer : d"
Answer: d
Python program:
a = 3 / 5
b = a * 5
c = b - 1
d = 2 / c
e = 5 * d
f = 3 / 5
g = f * 5
h = g - 1
i = 2 / h
j = e + i 
k = j + 2
Problem: each child has 6 crayons and 12 apples . if there are 12 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 72 , d ) 78 , e ) 90
Rationale: 6 * 12 = 72 . answer is c
Answer: c
Python program:
a = 12 * 6
Problem: in a certain school , the ratio of boys to girls is 5 to 17 . if there are 72 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 72 , e ) 108
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 72 . . . looking at the ratio we can say that the 12 ( 17 - 5 ) extra parts caused this diff of 72 . so 1 part corresponds to 72 / 8 = 9 and so 5 parts correspond to 12 * 9 = 108 . e"
Answer: e
Python program:
a = 5 / 17
b = 1 - a
c = 72 / b
d = c - 72
Problem: a car takes 8 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 10 kmph , b ) 45 kmph , c ) 60 kmph , d ) 55 kmph , e ) 30 kmph
Rationale: "time = 8 distence = 540 3 / 2 of 8 hours = 8 * 3 / 2 = 12 hours required speed = 540 / 12 = 45 kmph b )"
Answer: b
Python program:
a = 8 * 3
b = a / 2
c = 540 / b
Problem: in a room with 7 people , 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "( 4 / 7 ) ( 5 / 6 ) + ( 3 / 7 ) ( 4 / 6 ) if you choose one of the 4 with one other friend , then you have a 5 / 6 chance of not picking their friend 2 nd . if you choose one of the 3 with 2 friends , you have a 4 / 6 chance of not picking one of their friends second . add them up . 20 / 42 + 12 / 42 32 / 42 = 16 / 21 e . 16 / 21"
Answer: e
Python program:
a = 7 - 1
b = a - 1
c = b - 1
d = 7 - 1
e = c / d
Problem: assisants are needed to prepare for preparation . each helper can make either 2 large cakes or 35 small cakes / hour . the kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed . how many helpers are required ?
Options: a ) 9 , b ) 10 , c ) 13 , d ) 16 , e ) 18
Rationale: 20 large cakes will require the equivalent of 10 helpers working for one hour . 700 small cakes will require the equivalent of 20 helpers working for one hour . this means if only one hour were available we would need 30 helpers . but since three hours are available we can use 10 helpers . b
Answer: b
Python program:
a = 20 / 2
b = 700 / 35
c = a + b 
d = c / 3
Problem: if the perimeter of a rectangular park is 1000 m , its length when its breadth is 200 m is ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400
Rationale: 2 ( l + 200 ) = 1000 = > l = 300 m answer : d
Answer: d
Python program:
a = 1000 / 2
b = a - 200
Problem: a boat running upstream takes 640 min to cover a certain distance , while it takes 280 min to cover the same distance running down stream . what is the ratio between the speed of the boat and speed of water current respectively ?
Options: a ) 23 : 7 , b ) 22 : 9 , c ) 23 : 8 , d ) 23 : 9 , e ) 23 : 11
Rationale: let the speed of the boat = x and speed of the current = y relative speed in upstream = x - y and in downstream = x + y let the distance ' d ' is to be covered in downstream and upstream , then time taken in upstream = d / ( x - y ) = 640 or d = 640 ( x - y ) - - - - ( i ) and time taken in downstream = d / ( x + y ) = 280 or d = 280 ( x + y ) - - - - ( ii ) comparing ( i ) & ( ii ) , 640 ( x - y ) = 280 ( x + y ) = > 16 ( x - y ) = 7 ( x + y ) = > 16 x - 16 y = 7 x - 7 y = > 9 x = 23 y = > x / y = 23 / 9 answer : d
Answer: d
Python program:
a = 640 + 280 
b = a / 2
c = 640 + 280 
d = c / 2
e = 640 - d
f = b / e
Problem: f ( 1 ) = 1 , where f ( x + y ) = f ( x ) + f ( y ) + 8 xy - 2 . then f ( 7 ) = ?
Options: a ) 162 , b ) 163 , c ) 164 , d ) 165 , e ) 166
Rationale: f ( 1 ) = 1 f ( 2 ) = f ( 1 + 1 ) = 1 + 1 + 8 - 2 = 8 f ( 3 ) = f ( 2 + 1 ) = 8 + 1 + ( 8 * 2 * 1 ) - 2 = 23 f ( 6 ) = f ( 3 + 3 ) = 23 + 23 + ( 8 * 3 * 3 ) - 2 = 116 f ( 7 ) = f ( 6 + 1 ) = 116 + 1 + ( 8 * 6 * 1 ) - 2 = 163 thus ans is 163 answer : b
Answer: b
Python program:
a = 1 + 1 
b = a + 8 
c = b - 2
d = c + 1 
e = 8 * 2
f = d + e 
g = f - 2
h = g + 1 
i = 8 * 3
j = h + i 
k = j - 2
l = k + 1 
m = 8 * 4
n = l + m 
o = n - 2
p = o + 1 
q = 3 + 2 
r = 8 * q
s = p + r 
t = s - 2
u = t + 1 
v = 3 + 3 
w = 8 * v
x = u + w 
y = x - 2
Problem: what is the largest possible value of cc if 5 c + ( d − 12 ) ^ 2 = 235 ?
Options: a ) 17 , b ) 25 , c ) 35 , d ) 42 , e ) 47
Rationale: to maximize c , we should minimize ( d - 12 ) ^ 2 . ( d - 12 ) ^ 2 is a square of a number , thus its smallest possible value is 0 ( for d = 12 ) . in this case we ' d have 5 c + 0 = 235 - - > c = 47 . answer : e .
Answer: e
Python program:
a = 235 / 5
Problem: find the cost of fencing around a circular field of diameter 35 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 132 , c ) 156 , d ) 115.5 , e ) 267
Rationale: "2 * 22 / 7 * 17.5 = 110 110 * 1 1 / 2 = rs . 115.5 answer : d"
Answer: d
Python program:
a = 35 / 2
b = circumface * (
Problem: the sum of all two digit numbers divisible by 5 is
Options: a ) 945 , b ) 3487 , c ) 28 , d ) 279 , e ) 1287
Rationale: "required numbers are 10,15 , 20,25 , . . . , 95 this is an a . p . in which a = 10 , d = 5 and l = 95 . let the number of terms in it be n . then t = 95 so a + ( n - 1 ) d = 95 . 10 + ( n - 1 ) * 5 = 95 , then n = 18 . required sum = n / 2 ( a + l ) = 18 / 2 ( 10 + 95 ) = 945 . answer : a ) 945"
Answer: a
Python program:
a = 10 + 1 
b = 5 * a
c = 1 * 5
d = b - c
e = 5 * 2
f = 1 * 5
g = e - f
h = d / g
i = h / 2
j = 5 * 2
k = 10 + 1 
l = 5 * k
m = j + l 
n = i * m
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 222 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 404 , b ) 452 , c ) 444 , d ) 468 , e ) 422
Rationale: "312 + 222 - 112 ( since 112 is counted twice ) = 422 e is the answer"
Answer: e
Python program:
a = 112 / 2
b = 312 - a
c = 112 / 2
d = 222 - c
e = b + d
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1700 . the difference between the profit shares of a and c is ?
Options: a ) 288 , b ) 266 , c ) 155 , d ) 680 , e ) 441
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1700 = > 5 parts out of 15 parts is rs . 1700 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1700 ) = rs . 680 answer : d"
Answer: d
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 1700
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 2 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 the answer is b ."
Answer: b
Python program:
a = 2 ** 4
b = 2 ** 2
c = a / b
d = 2 ** c
e = 2 ** 2
f = d / e
Problem: if x , y , and z are positive integers , and 2 x = 5 y = 7 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 28 , c ) 37 , d ) 42 , e ) 59
Rationale: "take lcm of 2,5 and 7 = 70 now 2 x = 70 = > x = 35 5 y = 70 = > y = 14 7 z = 70 = > z = 10 35 + 14 + 10 = 59 . option e ."
Answer: e
Python program:
a = 2 * 5
b = a * 7
c = b / 2
d = c / 2
e = 2 * 5
f = e * 7
g = f / 2
h = g / 5
i = d + h 
j = 2 * 5
k = j * 7
l = k / 2
m = l / 7
n = i + m
Problem: on a trip , a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles . if the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "the time to go 32 miles was 16 / 8 + 16 / 10 = 2 + 1.6 = 3.6 hours . the average speed for the return trip was 32 miles / 3.2 hours = 10 mph . the answer is b ."
Answer: b
Python program:
a = 16 + 16 
b = 16 / 8
c = 16 / 10
d = b + c 
e = 6 - 8
f = a / e
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 235 true ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 7 , e ) 9
Rationale: "answer b ( a + b ) ( a - b ) = 235 2 cases for ( a + b ) , ( a - b ) 235 , 1 47 , 5 answer b"
Answer: b
Python program:
a = math.log(235)
b = 4 + 1 
c = math.log(b)
d = a / c
Problem: on dividing a number by 999 , the quotient is 366 and the remainder is 103 . the number is :
Options: a ) 364724 , b ) 365387 , c ) 365737 , d ) 366757 , e ) none of these
Rationale: "required number = 999 * 366 + 103 = ( 1000 - 1 ) * 366 + 103 = 366000 - 366 + 103 = 365737 . answer : c"
Answer: c
Python program:
a = 366 ** 2
b = a / 999
c = 366 ** 2
d = c / 999
e = math.floor(d)
f = b - e
g = f * 999
Problem: one - third less than 20 % of 180 is equal to :
Options: a ) 24 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 20 % of 180 = 36 1 / 3 of 36 = 12 so , 1 / 3 , less than 36 is equal to 36 - 12 = 24 answer : a"
Answer: a
Python program:
a = 20 / 100
b = a * 180
c = 1 / 3
d = 20 / 100
e = d * 180
f = c * e
g = b - f