euclaise/mathqa_programs huggingface dataset:
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 18 ) both lie on the line defined by the equation x = ( y / 6 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 6 ) - ( 2 / 5 ) , and so y = 6 x + 12 / 5 . the slope is 6 . ( n + 18 - n ) / ( m + p - m ) = 6 p = 3 the answer is c ."
Answer: c
Python program:
a = 18 / 6
Problem: if w is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of w ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: w = 30 ! 8 w = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )
Answer: c
Python program:
a = 30 - 2
b = a / 2
Problem: a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . what will be b ' s share in the total profit of rs . 25000 earned at the end of 2 years from the starting of the business ?
Options: a ) rs . 7500 , b ) rs . 9000 , c ) rs . 9500 , d ) rs . 10,000 , e ) none
Rationale: solution a : b : c = ( 20000 × 24 ) : ( 15000 × 24 ) : ( 20000 × 18 ) = 4 : 3 : 3 b ' s share = rs . ( 25000 × 3 / 10 ) = rs . 7500 . answer a
Answer: a
Python program:
a = 12 * 2
b = 15000 * a
c = 12 * 2
d = 20000 * c
e = 12 * 2
f = 15000 * e
g = d + f 
h = 12 * 2
i = h - 6
j = 20000 * i
k = g + j 
l = b / k
m = l * 25000
Problem: length of a rectangular plot is 14 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m , b ) 57 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 14 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 14 ) + x ] = 200 2 x + 14 = 100 2 x = 86 x = 43 . hence , length = x + 14 = 57 m b"
Answer: b
Python program:
a = 5300 / 26
b = 2 * 14
c = a + b 
d = c / 4
Problem: 9 log 9 ( 7 ) = ?
Options: a ) 1 , b ) 2 , c ) 7 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 7 ) = 7 correct answer c"
Answer: c
Python program:
a = 9 * 9
b = math.log(a)
c = math.log(10)
d = b / c
Problem: if ( a + b ) = 4 , ( b + c ) = 5 and ( c + d ) = 3 , 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 = 5 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 5 + 3 = 2 . option d . . ."
Answer: d
Python program:
a = 4 + 3 
b = a - 5
Problem: indu gave bindu rs . 6500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 12.8 , b ) 20 , c ) 10.4 , d ) 11.6 , e ) 15
Rationale: "6500 = d ( 100 / 4 ) 2 d = 10.4 answer : c"
Answer: c
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 6500 * c
e = d - 6500
f = 4 / 100
g = 6500 * f
h = g * 2
i = e - h
Problem: if the product of two numbers is 84942 and their h . c . f . is 33 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1365 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 84942 , because we know product of two numbers = product of hcf and lcm lcm = 84942 / 33 = 2574 option a"
Answer: a
Python program:
a = 84942 / 33
Problem: if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by
Options: a ) 6 only , b ) 6 and 12 both , c ) 12 only , d ) 18 only , e ) 12 and 18 both
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is divisible by both 6 and 12 , since n ( n + 1 ) is always even . answer b ."
Answer: b
Python program:
a = 6 * 100
b = 2 * 6
c = a + b
Problem: express the ratio 3 2 / 3 : 7 1 / 3 in its simplest form .
Options: a ) 1 : 21 , b ) 1 : 1 , c ) 2 : 1 , d ) 1 : 2 , e ) 2 : 11
Rationale: solution we first convert the mixed numbers 3 2 / 3 and 7 1 / 3 into fractions 3 2 / 3 = 3 * 3 / 3 + 2 / 3 = 11 / 3 7 1 / 3 = 7 * 3 / 3 + 1 / 3 = 22 / 3 the ratio 3 2 / 3 : 7 1 / 3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 simplify = 11 / 22 = 1 / 2 the ratio is 1 / 2 or 1 : 2 answer is d
Answer: d
Python program:
a = 3 * 3
b = a + 2 
c = b / 3
d = 3 * 7
e = d + 1 
f = e / 3
g = c / f
Problem: a runs twice as fast as b and gives b a start of 64 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 128 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 64 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 64 m is 64 / 1 = 64 m so the total time taken by a and b to reach = 2 * 64 = 128 m answer : b"
Answer: b
Python program:
a = 64 * 2
Problem: on a map , 2.5 inches represent 25 miles . how many miles approximately is the distance if you measured 55 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 212.5 , b ) 213.5 , c ) 214.5 , d ) 215.5 , e ) 216.5
Rationale: "1 inch = 2.54 cm 2.5 inch = 2.54 * 2.5 cm 6.35 cm = 25 miles 55 cms = 25 / 6.35 * 55 = 216.5 miles answer : e"
Answer: e
Python program:
a = 55 / 2
b = 25 / 2
c = a * b
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 920 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 50 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 920 - 640 = 280 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 280 / 28 = 70 / 7 = 10 total hrs = 40 + 10 = 50 answer d 50"
Answer: d
Python program:
a = 16 * 40
b = 920 - a
c = 100 + 75 
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 2 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005
b ) 0.002
c ) 0.001
d ) 0.0005
e ) 0.0002
Rationale: it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 2 then x = 2 / 1000 = 0.002 . the answer is b
Answer: b
Python program:
a = 2 / 1000
Problem: the average age of a class of 20 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 42 , d ) 45 , e ) 43
Rationale: "total age of all students = 20 ã — 21 total age of all students + age of the teacher = 21 ã — 22 age of the teacher = 21 ã — 22 â ˆ ’ 21 ã — 20 = 21 ( 22 â ˆ ’ 20 ) = 21 ã — 2 = 42 answer is c ."
Answer: c
Python program:
a = 20 + 1 
b = 21 + 1 
c = a * b
d = 20 * 21
e = c - d
Problem: when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 71.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 80
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"
Answer: e
Python program:
a = 71 * 2
b = a - 2
c = b / 10
d = 2 / 10
e = 11 / d
f = c * e
g = f + 11 
h = 2 / 10
i = 11 / h
j = g / i
Problem: if a and b are integers and ( a * b ) ^ 5 = 128 y , y could be :
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 16
Rationale: distribute the exponent . a ^ 5 * b ^ 5 = 128 y find the prime factorization of 96 . this is 2 ^ 5 * 2 ^ 2 . we need 2 ^ 3 ( or some other power of 2 that will give us a multiple of 2 ^ 5 as our second term ) . 2 ^ 3 = 8 the answer is d .
Answer: d
Python program:
a = 2 ** 5
b = 128 / a
c = b * 2
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed t of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = t ans = c"
Answer: c
Python program:
a = 24 * 4
b = a / 3
c = b - 24
d = 35 - 25
e = d + 50 
f = 35 - 25
g = e / f
h = c * g
Problem: jacob is now 12 years younger than michael . if 5 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 11 , d ) 21 , e ) 25
Rationale: "jacob = x years , mike = x + 12 years 5 years from now , 2 ( x + 5 ) = x + 17 2 x + 10 = x + 17 x = 7 x + 4 = 11 years answer c"
Answer: c
Python program:
a = 12 + 5 
b = 2 * 5
c = a - b
d = 4 + c
Problem: ( 1000 ) 7 ÷ ( 10 ) 19 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 19 = ( 10 ) 21 / ( 10 ) 19 = 10 ( 2 ) = 100 option b"
Answer: b
Python program:
a = 1000 * 10
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 143 per kg , the price of the third variety per kg will be
Options: a ) rs . 165.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 143 / 22.50 = 1 = â € º x - 143 = 22.50 = â € º x = 165.50 . hence , price of the third variety = rs . 165.50 per kg . answer a"
Answer: a
Python program:
a = 1 + 1 
b = a + 2 
c = 143 * b
d = 126 + 126 
e = c - d
f = e / 2
Problem: 3 numbers are in the ratio 3 : 5 : 7 . the largest number is 56 . what is the difference between smallest and largest number ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: the three numbers are 3 x , 5 x , and 7 x . the largest number is 56 = 7 * 8 , so x = 8 . the smallest number is 3 * 8 = 24 . 56 - 24 = 32 the answer is d .
Answer: d
Python program:
a = 56 / 7
b = 3 * a
c = 56 - b
Problem: mixture a is 20 % oil and 80 % material b by weight . if 2 more kilograms of oil are added to the 8 kilograms mixture a , how many kilograms of mixture a must be added to make a 70 % material b in the new mixture ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: old mix has 20 % oil . you add 2 kgs of 100 % oil . you get new mix with 30 % oil ( 70 % material b ) . w 1 / w 2 = ( 100 - 30 ) / ( 30 - 20 ) = 70 / 10 = 7 / 1 for every 7 parts of mix a , you have added 1 part of oil . since you have added 2 kgs oil , mix a must be 7 * 2 = 14 kgs . you already had 8 kgs of mix a , so extra mix a added must be 14 - 8 = 6 kgs . answer ( a )
Answer: a
Python program:
a = 100 - 70
b = a - 20
c = 70 / b
d = c * 2
e = d - 8
Problem: kanul spent $ 5000 in buying raw materials , $ 200 in buying machinery and 30 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 7456.00 , b ) $ 7500.55 , c ) $ 7428.57 , d ) $ 7852.56 , e ) $ 7864.00
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 5000 + 200 70 % of x = 5200 70 x / 100 = 5200 x = $ 52000 / 7 x = $ 7428.57 answer is c"
Answer: c
Python program:
a = 5000 + 200 
b = 30 / 100
c = 1 - b
d = a / c
Problem: there is 60 % increase in an amount in 6 yrs at si . what will be the ci of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2354 , b ) 2450 , c ) 2540 , d ) 2650 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 12000 . t = 3 years and r = 10 % p . a . c . i . = rs . 12000 x 1 + 10 3 - 1 100 = rs . 12000 x 331 1000 = 3972 . e"
Answer: e
Python program:
a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 60 / 6
g = f / 100
h = 1 + g 
i = 60 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.8 km ?
Options: a ) 660 m , b ) 650 m , c ) 570 m , d ) 670 m , e ) 680 m
Rationale: "distance covered by amar = ( 18 / 48 ) * 1800 = 670 m answer : d"
Answer: d
Python program:
a = 1 * 8
b = 18 * a
c = b / 48
Problem: find the value of x from the below equation : x ^ 2 − 7 x + 10 = 0
Options: a ) 5 , b ) 7 , c ) 6 , d ) 11 , e ) 12
Rationale: "here we need to find out a and b such that a + b = - 7 and ab = + 10 a = - 5 and b = - 2 satisfies the above condition . hence x ^ 2 − 7 x + 10 = ( x − 5 ) ( x − 2 ) x 2 − 7 x + 10 = ( x − 5 ) ( x − 2 ) x ^ 2 − 7 x + 10 = 0 ⇒ ( x − 5 ) ( x − 2 ) = 0 x 2 − 7 x + 10 = 0 ⇒ ( x − 5 ) ( x − 2 ) = 0 step 3 : equate each factor to 0 and solve the equations ( x − 5 ) ( x − 2 ) = 0 ⇒ ( x − 5 ) = 0 or ( x − 2 ) = 0 ⇒ x = 5 or 2 a"
Answer: a
Python program:
a = 7 ** 2
b = 10 * 10
c = a - b
d = math.sqrt(c)
e = 7 - d
f = e / 2
Problem: find the largest 7 digit number which is exactly divisible by 88 ?
Options: a ) 9998765 , b ) 9998907 , c ) 9999944 , d ) 9999954 , e ) 9999968
Rationale: "largest 7 digit number is 9999999 after doing 9999999 ÷ 88 we get remainder 31 hence largest 7 digit number exactly divisible by 88 = 9999999 - 31 = 9999968 e"
Answer: e
Python program:
a = 100 * 100
b = 100 * 10
c = a + b 
d = 100 * 3
e = c + d 
f = 7 * 10
g = e + f 
h = g + 3 
i = h * 88
Problem: in a theater , the first row has 15 seats and each row has 2 more seats than previous row . if the last row has 53 seats , what is the total number of seats in the theater ?
Options: a ) 600 , b ) 640 , c ) 680 , d ) 720 , e ) 760
Rationale: "the number of seats in the theater is 15 + ( 15 + 2 ) + . . . + ( 15 + 38 ) = 20 ( 15 ) + 2 ( 1 + 2 + . . . + 19 ) = 20 ( 15 ) + 2 ( 19 ) ( 20 ) / 2 = 20 ( 15 + 19 ) = 20 ( 34 ) = 680 the answer is c ."
Answer: c
Python program:
a = 15 + 53 
b = a / 2
c = 53 - 15
d = c + 2 
e = d / 2
f = b * e
Problem: evaluate : 20 - 12 ÷ 12 × 2 =
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 12 , d ) d ) 16 , e ) e ) 20
Rationale: "according to order of operations , 12 ÷ 12 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 12 × 2 = 1 × 2 = 2 hence 20 - 12 ÷ 12 × 2 = 20 - 12 = 8 correct answer is b ) 8"
Answer: b
Python program:
a = 12 * 12
b = a * 2
c = 20 - b
Problem: shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5,000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12,000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15,000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16,000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60,000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15
Rationale: for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e
Answer: e
Python program:
a = 2 + 3 
b = a * 3
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 276 . what is their h . c . f . ?
Options: a ) 18 , b ) 23 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 276 x = 23 hcf of 2 x , 3 x and 4 x = x = 23 the answer is b ."
Answer: b
Python program:
a = 2 * 4
Problem: if the length of a rectangle is increased by 10 % and the area is unchanged , then its corresponding breadth must be decreased by ?
Options: a ) 9 1 / 19
b ) 9 1 / 15
c ) 9 1 / 16
d ) 9 1 / 11
e ) 9 1 / 10
Rationale: suppose length = 100 m and breadth = x m area = 100 m new length = 110 m and breadth = ( x - y % of x ) then , \ inline 110 \ times ( x - \ frac { y } { 100 } x ) = 100 \ times x \ inline \ rightarrow \ inline 110 \ times ( 1 - \ frac { y } { 100 } ) = 100 \ inline \ rightarrow \ inline 1 - \ frac { y } { 100 } = \ frac { 100 } { 110 } \ inline \ rightarrow \ frac { y } { 100 } = 1 - \ frac { 100 } { 110 } = \ frac { 1 } { 11 } \ inline y = \ frac { 100 } { 11 } = 9 \ frac { 1 } { 10 } % answer : e
Answer: e
Python program:
a = 10 / 100
b = 1 + a 
c = 1 / b
d = c * 100
e = 100 - d
Problem: in a mayoral election , candidate x received 1 / 3 more votes than candidate y , and candidate y received 1 / 7 fewer votes than z . if z received 21,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: "z = 21 - - > y received 1 / 7 fewer votes than z - - > y = z - 1 / 7 * z = 18 ; x received 1 / 3 more votes than y - - > x = y + 1 / 3 * y = 24 . answer : c ."
Answer: c
Python program:
a = 3 / 7
b = 1 - a
c = const_0_25 * 100
d = c * 100
e = d * 10
f = b * e
g = 1 / 3
h = g + 1 
i = f * h
Problem: each factor of 200 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 9
Rationale: 200 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 9 . answer : e .
Answer: e
Python program:
a = math.comb(42, 1)
b = a / 42
c = 3 ** 2
d = b / c
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 18 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 32 , e ) 48
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 18 ) x solve for r , r = 66 66 - 18 = 48 mpg e"
Answer: e
Python program:
a = 462 - 336
b = a / 18
c = 336 / b
Problem: can v and can в are both right circular cylinders . the radius of can v is twice the radius of can b , while the height of can v is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can v with the same brand of gasoline ?
Options: a ) $ 1
b ) $ 2
c ) $ 4
d ) $ 8
e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of v = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Python program:
a = 2 ** 4
b = a * 2
c = b * 2
d = 2 ** 2
e = 2 * d
f = e * 4
g = f / 2
h = c / g
i = 4 * h
Problem: x can give y 100 meters start and z 200 meters start in x kilometer race . how much start can y give z in x kilometer race ?
Options: a ) 112.2 m , b ) 216.3 m , c ) 111.12 m , d ) 213.27 m , e ) 222.40 m
Rationale: c 111.12 m x runs 1000 m while y runs 900 m and z runs 800 m . the number of meters that z runs when y runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . y can give z = 1000 - 888.88 = 111.12 m .
Answer: c
Python program:
a = 200 - 100
b = 1000 * a
c = 1000 - 100
d = b / c
Problem: a sum of money deposited at c . i . amounts to rs . 1890 in 2 years and to rs . 2350 in 3 years . find the rate percent ?
Options: a ) 30 % , b ) 24 % , c ) 20 % , d ) 19 % , e ) 50 %
Rationale: "1890 - - - 460 100 - - - ? = > 24 % answer : b"
Answer: b
Python program:
a = 2350 - 1890
b = a / 1890
c = b * 100
Problem: what is the least number that should be added to 1053 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1053 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e ."
Answer: e
Python program:
a = 1053 / 23
b = math.floor(a)
c = 1 + b 
d = 1053 / 23
e = c - d
f = e * 23
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 16000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = rs . 9000 correct option : d"
Answer: d
Python program:
a = 8000 + 5000 
b = a + 16000 
c = b + 7000 
d = c + 9000 
e = 4 + 1 
f = d / e
Problem: find out the c . i on rs . 3000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 183.62 , b ) 106.07 , c ) 106.04 , d ) 106.03 , e ) 186.01
Rationale: "a = 3000 ( 51 / 50 ) 3 = 3183.62 3000 - - - - - - - - - - - 183.62 answer : a"
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 3000 * d
f = e - 3000
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 ) 65 , b ) 69 , c ) 30 , d ) 31 , e ) 32
Rationale: "let length of tunnel is x meter distance = 800 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 800 + x = ( 65 / 3 ) * 60 800 + x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters answer : option 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