euclaise/mathqa_programs huggingface dataset:
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 36 .
Options: a ) 5 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 36 , remainder will be - 4 i . e . n will be 4 less than a multiple of 36 . so you must add 5 to n to make it a multiple of 36 a"
Answer: a
Python program:
a = 36 - reminder
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on october 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 difference between stock on october 1 than were in stock on january 1 will be - c - ( c - 36 ) = 36 hence answer will be ( e )
Answer: e
Python program:
a = 10 - 1
b = a * 4
Problem: when positive integer n is divided by positive integer j , the remainder is 5 . if n / j = 105.20 , what is value of j ?
Options: a ) 10 , b ) 50 , c ) 30 , d ) 15 , e ) 25
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 105.20 here 105 is the quotient . given that remainder = 5 so , 105.20 = 105 + 5 / j so , j = 25 answer : e"
Answer: e
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 105 - 20
e = 5 / d
Problem: the speed at which a man can row a boat in still water is 9.5 kmph . if he rows downstream , where the speed of current is 8.5 kmph , what time will he take to cover 45.5 metres ?
Options: a ) 18 seconds , b ) 8.4 seconds , c ) 5 seconds , d ) 9.1 seconds , e ) 9.5 econds
Rationale: "speed of the boat downstream = 9.5 + 8.5 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 45.5 m = 45.5 / 5 = 9.1 seconds . answer : d"
Answer: d
Python program:
a = 9 + 5 
b = a * const_0_2778
c = 45 / 5
Problem: in what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 7 sec , c ) 2 sec , d ) 6.5 sec , e ) 9 sec
Rationale: "t = 65 / 36 * 18 / 5 = 6.5 sec answer : d"
Answer: d
Python program:
a = 36 * const_0_2778
b = 65 / a
Problem: of 70 players on a football team , 46 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 62
Rationale: "total = 70 thrower = 46 rest = 70 - 46 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 46 + 16 = 62 so e . 62 is the right answer"
Answer: e
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 46
d = b * c
e = d + 46
Problem: how many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards ? ( 1 mile = 1,160 yards )
Options: a ) 2 , b ) 5 , c ) 4 , d ) 3.61 , e ) 4.3
Rationale: speed = 9 miles / hr = 4.4 yard / s = 29.33 yards / min distance = 106 yards time = distance / speed = 106 / 29.33 = 3.61 minutes ans - d
Answer: d
Python program:
a = 3 + 4 
b = a * 100
c = 2 * 3
d = c * 10
e = b + d 
f = e + 1000 
g = 106 / f
h = g * const_60
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 8 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 8 = 4 / 9 ( t - 8 ) 10 t = 792 - 352 = > t = 44 . answer : b"
Answer: b
Python program:
a = 6 / 5
b = a * 5
c = b - 4
d = 8 / c
e = 5 * d
f = 6 / 5
g = f * 5
h = g - 4
i = 8 / h
j = e + i 
k = j + 8
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 800 m ?
Options: a ) 122.9 m , b ) 170 m . , c ) 122.2 m , d ) 222.9 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 800 m , the number of meters by which a beats c = ( 800 * 212.5 ) / 1000 = 170 m . answer : b"
Answer: b
Python program:
a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
Problem: 5 ^ 100 is divided by 18 then what is the remainder ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c
Answer: c
Python program:
a = 18 - 5
Problem: if ( a + b ) = 4 , ( b + c ) = 7 and ( c + d ) = 5 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 4 b + c = 7 c + d = 5 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 7 + 5 = 2 . option d . . ."
Answer: d
Python program:
a = 4 + 5 
b = a - 7
Problem: the average of 45 results is 8 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 470 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 8 * 45 - 15 * 22 + 20 * 22 = 360 - 330 + 440 = 470 answer is b"
Answer: b
Python program:
a = 45 * 8
b = 22 * 20
c = a - b
d = 22 * 15
e = c - d
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 20 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 4200 , b ) 5400 , c ) 6600 , d ) 7800 , e ) 8900
Rationale: "the distance the sound traveled to the man is 20 * 330 = 6600 meters the answer is c ."
Answer: c
Python program:
a = 330 * 20
Problem: in the set of positive integers from 1 to 70 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 240 , d ) 200 , e ) 190
Rationale: "reduce 1 - 70 5 - 15 - 25 - 35 - 45 + 55 + 65 are valid multiples 0 f 5 . add them - - > 245 b"
Answer: b
Python program:
a = 3 * 5
b = 70 * a
c = b / 5
Problem: if the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm , then the altitude of the triangle is
Options: a ) 12 cm
b ) 10 cm
c ) 11 cm
d ) 15 cm
e ) 20 cm
Rationale: area of square = 6 ^ 2 = 36 area of triangle = 36 1 / 2 bh = 36 h = 12 cm answer a
Answer: a
Python program:
a = square_area * (
b = a / 2
Problem: a train 600 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 298 m , b ) 279 m , c ) 500 m , d ) 289 m , e ) 700 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 600 + x ) / 60 = 65 / 3 x = 700 m . answer : e"
Answer: e
Python program:
a = 78 - 1
b = a * const_0_2778
c = 600 / b
Problem: walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?
Options: a ) 2 hr , b ) 1 hr , c ) 3 hr , d ) 1.5 hr , e ) 2.5 hr
Rationale: let the original speed be s and time be t if new speed = s ã — 3 / 4 , then new time would be t ã — 4 / 3 ( d = st = constant ) . given , 3 t / 4 â ˆ ’ t = 20 t / 3 â ‡ ’ t = 60 minutes = 1 hour answer : a
Answer: a
Python program:
a = 20 * 3
b = a / 4
c = b * 4
d = c * 2
e = d / const_60
Problem: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.86 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.86 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.86 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.86 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Python program:
a = 1 + 75 
b = a + 1 
c = b + 2 
d = c + 1 
e = d + 2 
f = e + 1 
g = f / 7
h = min(g)
Problem: how many odd numbers between 10 and 1,100 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 15 numbers . answer : d ."
Answer: d
Python program:
a = 10 + 4
Problem: a pump can fill a tank with water in 6 hours . because of a leak , it took 12 hours to fill the tank . the leak can drain all the water in ?
Options: a ) 12 hr , b ) 11 hr , c ) 13 hr , d ) 14 hr , e ) 16 hr
Rationale: work done by the leak in 1 hour = 1 / 6 - 1 / 12 = 1 / 12 leak will empty the tank in 12 hours answer is a
Answer: a
Python program:
a = 6 * 12
b = 12 - 6
c = a / b
Problem: if 10 x = 8 y = 14 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 166 , c ) 84 , d ) 122 , e ) 168
Rationale: "10 x = 8 y = 14 z 5 x = 4 y = 7 z 5 ( 4 * 7 ) = 4 ( 5 * 7 ) = 7 ( 5 * 4 ) addition = 28 + 20 + 35 = 83 answer would be multiple of 83 which is 166 answer : b"
Answer: b
Python program:
a = 8 * 14
b = a * 10
c = b / 4
Problem: if x and y are positive integers and 9 + x + y + xy = 23 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 9 + 3 + xy = 23 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 9 + 5 + xy = 23 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 9 + 6 + xy = 23 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 9 + 8 + xy = 23 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 9 + 9 + xy = 23 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Python program:
a = 23 + 1
Problem: a container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 16
Rationale: container 1 has 15 ounces in the ratio 1 : 2 or , x + 2 x = 15 gives x ( alcohol ) = 5 and remaining water = 10 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 5 + 2 and water = 10 + 6 ratio thus alcohol / water = 7 / 16 answer e
Answer: e
Python program:
a = 1 + 2 
b = 1 / a
c = 15 * b
d = 1 + 3 
e = 1 / d
f = 8 * e
g = c + f 
h = 15 + 8 
i = 1 + 2 
j = 1 / i
k = 15 * j
l = 1 + 3 
m = 1 / l
n = 8 * m
o = k + n 
p = h - o
q = g / p
Problem: how many plants will be there in a circular bed whose outer edge measure 31 cms , allowing 4 cm 2 for each plant ?
Options: a ) 19
b ) 750
c ) 24
d ) 120
e ) none of these
Rationale: circumference of circular bed = 31 cm area of circular bed = ( 31 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 31 ) 2 â  „ 4 ï € ã · 4 = 19.11 = 19 ( approx ) answer a
Answer: a
Python program:
a = 2 * math.pi
b = 31 / a
c = circle_area / (
Problem: 3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1 - . 06 = . 94
Options: a ) 0.06 , b ) 0.12 , c ) 0.21 , d ) 0.29 , e ) 0.28
Rationale: the probability that eachdoesn ' thit is : 0.5 , 0.8 , and 0.7 . when we have multiple independent events , we multiply the probabilities : . 5 * . 8 * . 7 = 0.28 . option : e
Answer: e
Python program:
a = 1 - 0
b = 1 - 0
c = a * b
d = 1 - 0
e = c * d
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 18 years investment will become $ 5,000 * 2 = $ 10,000 and in another 18 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Python program:
a = 5000 * 2
b = a * 2
Problem: 2 / 5 of 3 / 7 of 23 / 11 of ? = 64 × 3
Options: a ) 511 , b ) 419 , c ) 616 , d ) 636 , e ) 686
Rationale: "explanation : 2 / 5 & time ; 3 / 7 & time ; 20 / 11 & time ; x = 192 x = 192 & time ; 11 & time ; 7 & time ; 5 / 2 & time ; 3 & time ; 20 = 616 answer : option c"
Answer: c
Python program:
a = 2 / 5
b = 3 / 7
c = a * b
d = 7 / 11
e = c * d
f = e * 64
Problem: the annual interest rate earned by an investment increased by 11 percent from last year to this year . if the annual interest rate earned by the investment this year was 22 percent , what was the annual interest rate last year ?
Options: a ) 17 % , b ) 19 % , c ) 18 % , d ) 20 % , e ) 22 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.11 i ( last year ) = 1.11 i ( last year ) 22 = 1.11 x i ( last year ) i ( last year ) = 22 / 1.1 = 220 / 11 = 20 % answer : d"
Answer: d
Python program:
a = 22 * 100
b = 22 + 100 
c = a / b
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: there are 3 single digit multiple of 3 , that is , 3 , 69 . there are 8 prime nos less than 20 - 23 , 57 , 1113 , 1719 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability = 1 / 24 . answer c .
Answer: c
Python program:
a = 20 + 4 
b = 1 / a
Problem: if p ^ 2 – 13 p + 40 = h , and p is a positive integer between 1 and 10 , inclusive , what is the probability that h < 0 ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10
Rationale: p 2 – 13 p + 40 = h so ( p – 8 ) ( p – 5 ) = h for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b .
Answer: b
Python program:
a = 2 / 10
Problem: abcd is a square where ab = â ˆ š 4004 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4004 / 2 = 2002 . correct answer b"
Answer: b
Python program:
a = 4004 / 2
Problem: two - third of a positive number and 16 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 1 / 3 , d ) 144 / 25 , e ) 146 / 25
Rationale: let the number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 = 1 / 9 x = 1 / 3 answer : c
Answer: c
Python program:
a = 16 * 3
b = 216 * 2
c = a / b
d = math.sqrt(c)
Problem: if x < y < z and y - x > 9 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10
Rationale: we have : 1 ) x < y < z 2 ) y - x > 9 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 9 , the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 13 ( y - 2 = 11 , y = 13 ) 2 < 13 < z , since z is odd , the least possible value for z is 15 z - x = 15 - 2 = 13 answer d
Answer: d
Python program:
a = 9 + 2 
b = a + 2
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are marketing majors ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 11 , e ) 17
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 7 . the answer is c ."
Answer: c
Python program:
a = 2 + 3 
b = 2 + 3 
c = b + 2 
d = a * c
e = 10 + 3 
f = d * e
g = 1365 / f
Problem: if x = 8 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.007 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.007 answer : b"
Answer: b
Python program:
a = 2 / 2
b = a / 1000
Problem: a train running at the speed of 60 km / hr crosses a pole in 5 seconds . find the length of the train .
Options: a ) 83.33 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 5 = 83.33 meter . answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 5
Problem: on a purchase of $ 118 , a store offered a payment plan consisting of a $ 18 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 16.7 % , b ) 16.2 % , c ) 16.5 % , d ) 15.5 % , e ) 15.3 %
Rationale: "12 * 10 + 18 = 138 ( 18 / 118 ) * 100 = 15.3 answer : e"
Answer: e
Python program:
a = 10 * 12
b = a + 18 
c = 10 * 12
d = b - c
e = d / 118
f = e * 100
Problem: if 70 honey bees make 70 grams of honey in 70 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 70
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 70 : : 70 : x honey 70 : 1 = > 1 x 70 x x = 70 x 1 x 70 = > x = 70 . answer : e"
Answer: e
Python program:
a = 1 / 70
b = 1 / a
Problem: 3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 26
Rationale: let the three integers be x , x + 2 and x + 4 . then , 3 x = 2 ( x + 4 ) + 3 x = 11 . third integer = x + 4 = 15 . option a
Answer: a
Python program:
a = 2 * 4
b = a + 3 
c = b + 4
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 10 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 76 km / hr , b ) 66 km / hr , c ) 48 km / hr , d ) 67 km / hr , e ) 22 km / hr
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 ) / 10 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 48 km / hr . answer : c
Answer: c
Python program:
a = 100 + 100 
b = 1 + 2 
c = 10 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
Problem: if a certain number is divided by 9 , the quotient , dividend , and divisor , added together , will amount to 69 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 54
Rationale: let x = the number sought . then x / 9 + x + 9 = 69 . and x = 54 . e
Answer: e
Python program:
a = 69 - 9
b = a * 9
c = 9 + 1 
d = b / c
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did b get in a profit of rs . 2400 ?
Options: a ) s . 532 , b ) s . 600 , c ) s . 822 , d ) s . 812 , e ) s . 810
Rationale: "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 b ' s share in the profit of rs . 2400 = 15 ( 2400 / 60 ) = rs . 600 . answer : b"
Answer: b
Python program:
a = 1 / 3
b = 2400 * a
Problem: if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "50 * 10 = 500 66 * 5 = 330 830 / 15 = 55.33 answer : d"
Answer: d
Python program:
a = 10 * 50
b = 5 * 66
c = a + b 
d = 10 + 5 
e = c / d
Problem: if the price of a book is first decreased by 25 % and then increased by 20 % , then the decrease in the price will be ?
Options: a ) 20 % , b ) 10 % , c ) 25 % , d ) 18 % , e ) 30 %
Rationale: "let the original price be $ 100 new final price = 120 % of ( 75 % of $ 100 ) = 120 / 100 * 75 / 100 * 100 = $ 90 decrease is 10 % answer is b"
Answer: b
Python program:
a = 100 * 25
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 20
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j