euclaise/mathqa_programs huggingface dataset:
Problem: a worker is paid a regular rate of rs . 10 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 30 % higher than her regular rate . if she completed 60 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 180 , b ) 1180 , c ) 280 , d ) 580 , e ) 2080
Rationale: "amount earned using her cell phone = 60 * 13 = 780 earned for remaining surveys = 40 * 10 = 400 total earning = 1180 answer : b"
Answer: b
Python program:
a = 10 * 100
b = 30 / 100
c = 10 * b
d = 60 * c
e = a + d
Problem: if the price of sugar rises from rs . 2 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 60 %
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 2 = x × 5 = x = 40 kg . ∴ reduction in consumption = 60 % . answer e"
Answer: e
Python program:
a = 1 * 2
b = a / 5
c = 1 - b
d = c * 100
Problem: what is the 124 th digit to the right of the decimal point in the decimal form of 24 / 44 ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 4 , e ) 2
Rationale: "to solve this question , we first have to use some long division . this long division allows us to get 24 / 44 in decimal form , which is 0.545454 … where “ 54 ” is repeating . we can see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 5 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 4 . in other words , each odd - positioned digit is a 5 , and each even - positioned digit is a 4 . then the 124 digit to the right of the decimal point and we see that 124 is even , we know that the 124 th digit is a 4 . answer d ."
Answer: d
Python program:
a = 24 / 44
Problem: a palindrome is a number that reads the same forward and backward , such as 145 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 80 , d ) 90 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 16 = 80 ways c"
Answer: c
Python program:
a = 4 / 2
b = 10 ** a
c = b / 2
Problem: when n is divided by 25 , the remainder is 4 . what is the remainder when n + 15 is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 29 remainder ( n / 24 ) = 4 n + 15 = 44 remainder ( 44 / 5 ) = 4 option c"
Answer: c
Python program:
a = 4 - reminder
Problem: find the 25 % of rs . 500 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 125 , e ) s . 60
Rationale: "explanation : 25 % of 500 = > 25 / 100 * 500 = rs . 125 answer : d"
Answer: d
Python program:
a = 25 / 100
b = 500 * a
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 200 inclusive ?
Options: a ) 190 , b ) 105 , c ) 200 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 200 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 20 ( 10 ) = 200 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 200 = 210 20 + 190 = 210 30 + 180 = 210 etc . since there are 20 total terms , this pattern will create 10 ' pairs ' of 210 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 10 ) ( 210 ) / ( 20 ) = 105 answer : b"
Answer: b
Python program:
a = 10 + 200 
b = 200 - 10
c = b / 10
d = c + 1 
e = a * d
f = e / 2
g = 200 - 10
h = g / 10
i = h + 1 
j = f / i
Problem: the ages of two persons differ by 12 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,8 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 12 ) years . 5 ( x - 5 ) = ( x + 12 - 5 ) or 4 x = 32 or x = 8 . their present ages are 20 years and 8 years option b"
Answer: b
Python program:
a = 12 * 5
b = 5 - 1
c = a / b
d = c + 5 
e = d - 12
Problem: if n is the smallest integer such that 54 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 1 , c ) 6 , d ) 12 , e ) 24
Rationale: "54 can written as = 2 * 3 * 3 * 3 - - > 2 ^ 1 * 3 ^ 3 - - - ( 1 ) so for 54 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 1 in ( 1 ) even option b is correct"
Answer: b
Python program:
a = 54 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 3
f = e / 3
Problem: two trains a and b are 150 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 150 + 150 = 300 m . time taken = 300 / 25 = 12 s . correct answer e ."
Answer: e
Python program:
a = 150 + 150 
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e 
g = a / f
Problem: if 4 a = 5 b = 30 , then 40 ab =
Options: a ) 900 , b ) 1800 , c ) 2250 , d ) 1650 , e ) 1250
Rationale: "4 a * 5 b = 30 * 30 = 900 20 ab = 900 i . e . 30 ab = 1800 answer : option b"
Answer: b
Python program:
a = 30 / 4
b = 30 / 5
c = a * b
d = 40 * c
Problem: if a train , travelling at a speed of 18 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 281 m , b ) 25 m , c ) 50 m , d ) 125 m , e ) 75 m
Rationale: "b b = 18 * 5 / 18 * 5 = 25 m"
Answer: b
Python program:
a = 18 * const_0_2778
b = a * 5
Problem: a train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds . what is the length of the train ?
Options: a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) 165 m
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 110 = 25 * ( x / 15 ) 10 x = 1650 x = 165 meters the answer is e ."
Answer: e
Python program:
a = 2 - 1
b = 110 * a
Problem: a train covers a distance at a speed of 150 kmph in 3 hours . to cover the same distance in 1 hours , it must travel at a speed of ?
Options: a ) 320 , b ) 250 , c ) 560 , d ) 400 , e ) 450
Rationale: distance = 150 * 3 = 450 km required speed = 450 / 1 = 450 km / hr answer is e
Answer: e
Python program:
a = 150 * 3
b = a / 1
Problem: find the quotient : 0.63 / 9
Options: a ) 0.5 , b ) 0.3 , c ) 0.9 , d ) 0.1 , e ) 0.7
Rationale: "63 / 9 = 7 . dividend contains 2 places decimal . 0.63 / 9 = 0.7 answer is e ."
Answer: e
Python program:
a = 0 / 63
Problem: the ratio of boys to girls in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the boys and two - third of the girls in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 272 degree
e ) e ) 192 degree
Rationale: let the common ratio be x . . so b = 2 x and g = 3 x and total = 5 x 1 / 3 of m = 2 x / 3 and 2 / 3 of f = 2 x . . total preferring that carrer = 2 x / 3 + 2 x = 8 x / 3 . . now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 ans 192 e
Answer: e
Python program:
a = 2 + 3 
b = 2 / a
c = b / 3
d = 2 + 3 
e = 3 / d
f = e * 2
g = f / 3
h = c + g 
i = h * 360
Problem: x , y , and z are different prime numbers . the product x ^ 2 * y * z is divisible by how many different positive numbers ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: the exponents of x ^ 2 * y * z are 2 , 1 , and 1 . the number of factors is ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 the answer is e .
Answer: e
Python program:
a = 2 ** 4
b = a - 4
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 13.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 25 = 10 * 12 / 5 = 24 time difference = 13.1 ans : b"
Answer: b
Python program:
a = 55 + 10 
b = a - 1
c = 10 / 25
d = 10 / 55
e = c - d
f = b * e
g = max(f)
Problem: a 120 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 72 , e ) 112
Rationale: "s = 120 / 6 * 18 / 5 = 72 kmph answer : d"
Answer: d
Python program:
a = 120 / 6
b = a * const_3_6
Problem: peter takes a loan of $ 100000 with 12 % annual interest : the interest is paid once , at the end of the year . martha takes a loan of $ 100000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to peter ' s loan interest , approximately how much more does martha have to repay ?
Options: a ) $ 68.25 , b ) zero , c ) $ 6825.00 , d ) $ 6.82 , e ) $ 682.50
Rationale: peters interest = $ 100000 * 0.12 = $ 12000 or $ 1000 each month . martha ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 100000 * 0.01 = $ 1000 ; for the 2 nd month = $ 1000 + 1 % of 1000 = $ 1010 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1010 + 1 % of 1010 = ~ $ 1020 ; for the 4 th month = $ 1020 + 1 % of 1020 = ~ $ 1030 ; . . . for the 12 th month = $ 1100 + 1 % of 1100 = ~ $ 1110 . the difference between peters interest and martha ’ s interest = ~ ( 10 + 20 + . . . + 110 ) = $ 660 . answer : e .
Answer: e
Python program:
a = const_0_25 * 1000
b = 12 / 12
c = b / 100
d = 100000 * c
e = 12 / 12
f = e / 100
g = d * f
h = 12 / 12
i = h / 100
j = 100000 * i
k = 12 / 12
l = k / 100
m = j * l
n = m + 1 
o = g * n
p = 3 * 100
q = o + p 
r = a + q
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 15 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48 , d ) 56.8 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 63.75 . 4 ) now 63.75 has to be added byx % in order to equal the original price . 63.75 + ( x % ) 63.75 = 100 . solving this eq for x , we get x = 56.8 ans is d ."
Answer: d
Python program:
a = 100 - 25
b = 100 - 25
c = 15 / 100
d = b * c
e = a - d
f = 100 - e
g = 100 - 25
h = 100 - 25
i = 15 / 100
j = h * i
k = g - j
l = f / k
m = 100 * l
Problem: 3 numbers are randomly selected , with replacement , from the set of integers { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . if the first number selected is w , the second number selected is x , and the third number is y , what is the probability that w < x < y ?
Options: a ) 3 / 40 , b ) 28 / 243 , c ) 3 / 25 , d ) 33 / 100 , e ) 64 / 125
Rationale: solution : total possible ways = 10 * 10 * 10 = 1000 case 1 : w = 0 . if x = 1 , then y can have 8 ways . if x = 2 , then y can have 7 ways and so on . so , no . of ways = 8 + 7 + . . + 1 case 2 : w = 1 . if x = 2 , then y can have 7 ways . if x = 3 , then y can have 6 ways and so on . so , no . of ways = 7 + 6 + . . + 1 there will be 8 cases in this way and they will follow a pattern which looks like this : no . of ways for case 1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 no . of ways for case 2 : 1 + 2 + 3 + 4 + 5 + 6 + 7 no . of ways for case 3 : 1 + 2 + 3 + 4 + 5 + 6 no . of ways for case 4 : 1 + 2 + 3 + 4 + 5 no . of ways for case 5 : 1 + 2 + 3 + 4 no . of ways for case 6 : 1 + 2 + 3 no . of ways for case 7 : 1 + 2 no . of ways for case 8 : 1 ____________________________________________________________ total number of ways : 8 ( 1 ) + 7 ( 2 ) + 6 ( 3 ) + 5 ( 4 ) + 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) = 2 ( 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) ) = 2 ( 60 ) = 120 therefore , ans is 120 / 1000 = 3 / 25 . option c .
Answer: c
Python program:
a = 1 / 8
Problem: two trains a and b are 200 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 14 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 200 + 150 = 350 m . time taken = 350 / 25 = 14 s . correct answer c ."
Answer: c
Python program:
a = 200 + 150 
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e 
g = a / f
Problem: if 20 % of a class averages 80 % on a test , 50 % of the class averages 60 % on the test , and the remainder of the class averages 40 % on the test , what is the overall class average ?
Options: a ) 80 % , b ) 74 % , c ) 58 % , d ) 56 % , e ) 50 %
Rationale: 2 students scored 80 % 5 students scored 60 % 3 students scored 40 % ( 2 ) ( 80 ) + 5 ( 60 ) + 3 ( 40 ) = 160 + 300 + 120 = 580 580 / 10 students = 58 - - > 58 % average answer : c
Answer: c
Python program:
a = 20 * 80
b = 50 * 60
c = a + b 
d = 20 + 50 
e = 100 - d
f = e * 40
g = c + f 
h = g / 100
Problem: a man whose bowling average is 12.4 , takes 6 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 113 , b ) 114 , c ) 115 , d ) 116 , e ) 117
Rationale: "12.4 * x + 26 = ( 6 + x ) 12 solve equation x = 115 answer : c"
Answer: c
Python program:
a = math.floor(12, 4)
b = a * 6
c = b - 26
d = math.floor(12, 4)
e = 12 - 4
f = c / e
Problem: of the 200 stamps in a collection , 90 are foreign and 70 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 150
Rationale: 20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 50 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 50 ) = 60 the answer is a .
Answer: a
Python program:
a = 90 + 70 
b = a - 20
c = 200 - b
Problem: the average age of 20 students in a class is 5 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 28 , b ) 24 , c ) 20 , d ) 22 , e ) 18
Rationale: "total age of 50 students = 20 * 5 = 100 total age of 51 persons = 20 * 6 = 120 age of teacher = 120 - 100 = 20 years answer is c"
Answer: c
Python program:
a = 20 * 5
b = a + 1 
c = b + 20 
d = 20 * 5
e = c - d
Problem: how many zeroes are there at the end of the number n , if n = 80 ! + 160 ! ?
Options: a ) 15 , b ) 19 , c ) 23 , d ) 27 , e ) 31
Rationale: "the number of zeroes at the end of 80 ! will be less than the number of zeroes at the end of 160 ! hence it is sufficient to calculate the number of zeroes at the end of 80 ! the number of zeroes = [ 80 / 5 ] + [ 80 / 25 ] + [ 80 / 125 ] = 16 + 3 + 0 = 19 the answer is b ."
Answer: b
Python program:
a = 4 + 1 
b = 80 / a
c = b + 2
Problem: the principal that amounts to rs . 4913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) 288 , b ) 267 , c ) 200 , d ) 4096 , e ) 2771
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4096 . answer : d"
Answer: d
Python program:
a = 1 / 4
b = 6 + a 
c = b / 100
d = 1 + c 
e = d ** 3
f = 4913 / e
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by c are ?
Options: a ) 11 , b ) 18 , c ) 45 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 75 = 45 answer : c"
Answer: c
Python program:
a = 2 / 3
b = 5 / 2
c = a + b 
d = c + 2 
e = 75 / d
f = e * 5
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 9 , what is the least possible value of n ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 12 , e ) 7
Rationale: we need at least 2 factors of three , which means n must be at least 6 , so b is the correct answer .
Answer: b
Python program:
a = 9 / 2
Problem: √ 289 - √ 625 ÷ √ 25 is equal to ?
Options: a ) 17 , b ) 15 , c ) 12 , d ) - 8 / 5 , e ) none
Rationale: answer √ 289 - √ 625 ÷ √ 25 = √ 17 x 17 - √ 25 x 25 ÷ √ 5 x 5 = 17 - 25 ÷ 5 = 17 - 5 = 12 correct option : c
Answer: c
Python program:
a = math.sqrt(289)
b = math.sqrt(625)
c = math.sqrt(625)
d = math.sqrt(c)
e = b / d
f = a - e
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 83 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 28
Rationale: total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 83 thus m = 664 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 664 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 28 ans : e
Answer: e
Python program:
a = 90 * 8
b = 83 * 8
c = a - b
d = 92 - 90
e = c / d
Problem: what is the compound interest on rs . 9500 at 6 % p . a . compounded half - yearly for 1 1 / 2 years .
Options: a ) 810.91 , b ) 840.91 , c ) 880.91 , d ) 887.91 , e ) 980.91
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 10 , 380.91 c . i . > > 10 , 380.91 - 9500 > > rs . 880.91 answer : c"
Answer: c
Python program:
a = 6 / 2
b = a + 100 
c = b / 100
d = 1 * 2
e = c ** d
f = e - 1
g = 9500 * f
Problem: a and b ’ s salaries together amount to rs . 4,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 2777 , b ) 1000 , c ) 2789 , d ) 2776 , e ) 2881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 1000 4 b = 1000 = > b = 1000 answer b"
Answer: b
Python program:
a = 2 + 3 
b = 4 * a
c = 2 * b
d = c * 100
e = 85 / 100
f = 1 - e
g = d * f
h = 95 / 100
i = 1 - h
j = 85 / 100
k = 1 - j
l = i + k 
m = g / l
Problem: the population of a bacteria culture doubles every 6 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 54 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 6 minutes so answer is 9 * 6 = 54 minutes answer ( d )"
Answer: d
Python program:
a = 4 + 1 
b = a * 1
c = b * 100
d = c / 1
e = math.log(d)
f = e * 6
Problem: can you solve it ? 2 + 3 = 8 , 3 + 7 = 27 , 4 + 5 = 32 , 5 + 8 = 60 , 6 + 7 = 72 , 7 + 8 = ? ?
Options: a ) 68 , b ) 78 , c ) 88 , d ) 98 , e ) 56
Rationale: 2 + 3 = 2 * [ 3 + ( 2 - 1 ) ] = 8 3 + 7 = 3 * [ 7 + ( 3 - 1 ) ] = 27 4 + 5 = 4 * [ 5 + ( 4 - 1 ) ] = 32 5 + 8 = 5 * [ 8 + ( 5 - 1 ) ] = 60 6 + 7 = 6 * [ 7 + ( 6 - 1 ) ] = 72 therefore 7 + 8 = 7 * [ 8 + ( 7 - 1 ) ] = 98 x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x correct answer is d ) 98
Answer: d
Python program:
a = 7 - 1
b = a + 8 
c = b * 7
Problem: if the remainder is 10 when positive integer n is divided by 14 , what is the remainder when n is divided by 7 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "assume x is quotient here , n = 14 x + 7 - - - - - - - - - - ( 1 ) and n = 7 x + ? we can also write equation ( 1 ) as : n = ( 14 x + 7 ) + 3 . ie 7 ( 2 x + 1 ) + 3 ie the first term is perfectly divisible by 7 . so , the remainder left is 3 . so , answer ( d ) is right choice ."
Answer: d
Python program:
a = 14 / 7
Problem: if x ^ 2 + 1 / x ^ 2 = 2 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 2 , c ) 4 , d ) 16 , e ) 18
Rationale: important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 2 andsquareboth sides : ( x ² + 1 / x ² ) ² = 4 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 4 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 4 simplify : x ⁴ + 1 / x ⁴ = 2 answer : b
Answer: b
Python program:
a = 2 ** 2
b = a - 2
Problem: a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 12 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 12 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 443 , b ) 450 , c ) 460 , d ) 468 , e ) 475
Rationale: "total number of installments = 52 payment per installment for the first 12 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 12 * 410 + 40 * 475 ) / 52 = 460 answer c"
Answer: c
Python program:
a = 12 * 410
b = 410 + 65 
c = 52 - 12
d = b * c
e = a + d 
f = e / 52
Problem: at what rate percent of simple interest will a sum of money double itself in 22 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 22 ) = 100 / 22 = 4.54 % answer : b"
Answer: b
Python program:
a = 100 / 22
Problem: consider a square of diagonal length d . let another square be formed with d as its side . find the ratio of the area of the bigger square to that of the smaller square .
Options: a ) 2
b ) 3
c ) 4
d ) 16
e ) 41
Rationale: d ^ 2 / ( 1 / 2 ) * d ^ 2 = 2 answer : a
Answer: a
Python program:
a = 1 ** 2
b = 1 + 1 
c = 1 / b
d = math.sqrt(c)
e = d ** 2
f = a / e
Problem: find the missing value : ? - 1936248 = 1635773
Options: a ) 3572021 , b ) 3570221 , c ) 3572012 , d ) 3752012 , e ) none of them
Rationale: "let x - 1936248 = 1635773 . then , x = 1635773 + 1936248 = 3572021 answer is a ."
Answer: a
Python program:
a = 1936248 / 100
b = 1635773 / a