euclaise/mathqa_programs huggingface dataset:
Problem: what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?
Options: a ) 1 or 7
b ) 3 or 21
c ) 4 or 28
d ) 2 or 14
e ) 5 or 14
Rationale: since the chord length = 2 sqrrt ( r ^ 2 - d ^ 2 ) chord length = 32 , r = 20 then we get d = 12 chord length = 24 , r = 20 then we get d = 16 then we add / subtract we get option c ) 4 or 28 answer : c
Answer: c
Python program:
a = 20 ** 2
b = 32 / 2
c = b ** 2
d = a - c
e = math.sqrt(d)
f = 20 ** 2
g = 24 / 2
h = g ** 2
i = f - h
j = math.sqrt(i)
k = e + j 
l = 20 ** 2
m = 24 / 2
n = m ** 2
o = l - n
p = math.sqrt(o)
q = 20 ** 2
r = 32 / 2
s = r ** 2
t = q - s
u = math.sqrt(t)
v = p - u
w = max(k)
Problem: one boss decided to increase the salary of an employee by 5 % . how much will he get if his salary was rs . 2000 ?
Options: a ) 2200 , b ) 2000 , c ) 2100 , d ) 2300 , e ) none
Rationale: solution : actual salary is 2000 rupees 5 % of 2000 = 2000 * 5 / 100 = 100 so 100 rupees increased = 2000 + 100 = 2100 he will get salary of 2100 answer c
Answer: c
Python program:
a = 5 / 100
b = 2000 * a
c = 2000 + b
Problem: a ratio between two numbers is 7 : 9 and their l . c . m . is 189 . the second number is
Options: a ) 35 , b ) 25 , c ) 20 , d ) 27 , e ) none
Rationale: "sol . let the required numbers be 7 x and 9 x . then , their l . c . m . is 63 x . ∴ 63 x = 189 ⇔ x = 3 . hence , the second number is 27 . answer d"
Answer: d
Python program:
a = 7 * 9
b = 189 / a
c = b * 7
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 80 % , what was the average score for the entire class ?
Options: a ) 64 % , b ) 66 % , c ) 68 % , d ) 70 % , e ) 72 %
Rationale: 70 % of the class scored 60 % and 30 % of the class scored 80 % . the difference between 60 % and 80 % is 20 % . the average will be 60 % + 0.3 ( 20 % ) = 66 % . the answer is b .
Answer: b
Python program:
a = 70 * 60
b = 100 - 70
c = 80 * b
d = a + c 
e = d / 100
Problem: if p ( 32 , 6 ) = kc ( 32 , 6 ) , then what is the value of k ?
Options: a ) 6 , b ) 32 , c ) 120 , d ) 720 , e ) 820
Rationale: solution since 32 p 6 = k 32 c 6 ⇒ 32 ! / ( 32 - 6 ) ! = k 32 ! / ( 32 - 6 ) ! ⇒ k = 6 ! = 720 . answer d
Answer: d
Python program:
a = math.factorial(32)
b = 32 - 6
c = math.factorial(b)
d = a / c
e = math.factorial(32)
f = math.factorial(6)
g = 32 - 6
h = math.factorial(g)
i = f * h
j = e / i
k = d / j
Problem: for how many values of q , is | | | q - 5 | - 10 | - 5 | = 2 ? ( those ls are mods )
Options: a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8
Rationale: i think its 8 | | | q - 5 | - 10 | - 5 | = 2 let | q - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; q has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d
Answer: d
Python program:
a = 10 - 5
b = a + 5 
c = b - 2
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts three hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 6 , d ) d ) 5.5 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 3 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 3 + t ) = 40 * t t = 9 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 9 / 60 = 6 hrs time taken by a = 3 + t = 3 + 9 = 12 hrs time taken by k = 6 hrs so k starts 12 - 6 = 6 hrs after a . ( answer c )"
Answer: c
Python program:
a = 40 - 30
Problem: at joes steakhouse the hourly wage for a chef is 25 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 3.19 , e ) $ 5.40
Rationale: "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 25 % greater than dishwasher wages - - > 25 % of $ 4.25 = ( 25 * ( $ 4.25 ) ) / 100 - - > ( $ 106.25 ) / 100 - - > $ 1.06 therefore , chef wages per hour = $ 4.25 + $ 1.06 = = > $ 5.31 difference of wages between manager and chef = $ 8.50 - $ 5.31 = = > $ 3.19 answer : d"
Answer: d
Python program:
a = 100 + 25 
b = a / 100
c = 1 / 2
d = b * c
e = 1 - d
f = e * 8
Problem: a manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18 % . the wholesaler sells the same to retailer at a profit of 20 % . the retailer in turn sells them to a customer for rs . 30.09 , there by earning a profit of 25 % . the cost price for the manufacturer is ?
Options: a ) 33 , b ) 29 , c ) 17 , d ) 10 , e ) 16
Rationale: "explanation : let the cost price for the manufacturer be rs . x . then , 125 % of 120 % of 118 % of x = 30.09 . 125 / 100 * 120 / 100 * 118 / 100 * x = 3009 / 100 177 / 100 x = 3009 / 100 = > x = 17 answer : c"
Answer: c
Python program:
a = 1 + 2 
b = 20 / 2
c = a * b
d = 3 * 3
e = d / 100
f = c + e 
g = 100 + 25 
h = g / 100
i = f / h
j = 20 + 100 
k = j / 100
l = i / k
m = 100 + 18 
n = m / 100
o = l / n
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 11 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 477 , b ) 384 , c ) 279 , d ) 276 , e ) 291
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 11 + 21 = 32 t = 12 d = 32 * 12 = 384 . answer : b"
Answer: b
Python program:
a = 21 - 11
b = 60 / a
c = b * 11
d = 21 - 11
e = 60 / d
f = e * 21
g = c + f
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is ?
Options: a ) 39 yr , b ) 42 yr , c ) 45 yr , d ) 32 yr , e ) 50 yr
Rationale: "let b ' s present age = x years then a ' s present age = x + 9 years x + 9 + 10 = 2 ( x - 10 ) x + 19 = 2 x - 20 x = 39 years answer is a"
Answer: a
Python program:
a = 2 * 10
b = a + 10 
c = b + 9
Problem: if 89 / 99 = 0.898 , what is the 83 rd digit to the right of the decimal point of the fraction ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 7 , e ) 9
Rationale: "we are not concerned what 89 / 99 means . . we have to look at the decimal . . 0.898 means 0.898989 . . . . so right of decimal , all odd numbered are 8 and all even numbered are 9 . . here 83 is odd , so ans is 8 answer is c"
Answer: c
Python program:
a = 2 + 3
Problem: little krish had $ 200.50 . he spent $ 35.25 on sweets and gave to his two friends $ 25.20 each . how much money was left ?
Options: a ) $ 220.85 , b ) $ 214.85 , c ) $ 114.85 , d ) $ 314.85 , e ) $ 104.85
Rationale: krish spent and gave to his two friends a total of 35.25 + 25.20 + 25.20 = $ 85.65 money left 200.50 - 85.65 = $ 114.85 correct answer is c ) $ 114.85
Answer: c
Python program:
a = 200 - 5
b = 25 * 2
c = a - b
Problem: pat , kate , and mark charged a total of 117 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 65
Rationale: "65 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 117 = > x = 13 26 : 13 : 78 78 - 13 = 65 answer e"
Answer: e
Python program:
a = 1 / 3
b = 1 + a 
c = 3 * 2
d = 1 / c
e = b + d 
f = 117 / e
g = 1 / 3
h = 1 + g 
i = 3 * 2
j = 1 / i
k = h + j 
l = 117 / k
m = 3 * 2
n = l / m
o = f - n
Problem: what is the probability of getting at least one six in a single throw of three unbiased dice ?
Options: a ) 1 / 6 , b ) 125 / 216 , c ) 1 / 36 , d ) 81 / 216 , e ) 91 / 216
Rationale: "find the number of cases in which none of the digits show a ' 6 ' . i . e . all three dice show a number other than ' 6 ' , 5 * 5 * 5 = 125 cases . total possible outcomes when three dice are thrown = 216 . the number of outcomes in which at least one die shows a ' 6 ' = total possible outcomes when three dice are thrown - number of outcomes in which none of them show ' 6 ' . = 216 - 125 = 91 . the required probability = 91 / 216 . answer : e"
Answer: e
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: in the coordinate plane a slope of the line k is 3 / 2 times the x - intercept of the line k . what is the y - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) 1 / 4 , e ) 2 / 3
Rationale: as 3 / 2 y = mx + c , from 3 / 2 y = 0 + m we get y = 2 / 3 . hence , the correct answer choice is e .
Answer: e
Python program:
a = 1 / 3
Problem: a wooden box of dimensions 8 m x 10 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 5 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 4000000 , e ) none of these
Rationale: explanation : number = ( 800 * 1000 * 600 ) / 4 * 5 * 6 = 4000000 answer : d
Answer: d
Python program:
a = 8 * 100
b = 5 * 100
c = a * b
d = 4 * 0
e = c * d
f = 8 * 10
g = f * 10
h = e / g
Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of both the cards being kings ?
Options: a ) 1 / 15 , b ) 25 / 57 , c ) 35 / 256 , d ) 1 / 221 , e ) 2 / 15
Rationale: "let s be the sample space . then , n ( s ) = 52 c 2 = ( 52 x 51 ) / ( 2 x 1 ) = 1326 . let e = event of getting 2 kings out of 4 . n ( e ) = 4 c 2 = ( 4 x 3 ) / ( 2 x 1 ) = 6 . p ( e ) = n ( e ) / n ( s ) = 6 / 1326 = 1 / 221 . option d"
Answer: d
Python program:
a = 52 / 4
b = 52 / 4
c = a * b
d = math.comb(52, 2)
e = c / d
Problem: a school has 4 section of chemistry in class x having 65 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.25 , b ) 52.25 , c ) 51.95 , d ) 53.25 , e ) none of the above
Rationale: required average marks = 65 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 65 + 35 + 45 + 42 = 3250 + 2100 + 2475 + 1890 / 187 = 9715 â  „ 187 = 51.95 answer c
Answer: c
Python program:
a = 65 * 50
b = 35 * 60
c = a + b 
d = 45 * 55
e = c + d 
f = 42 * 45
g = e + f 
h = 65 + 35 
i = h + 45 
j = i + 42 
k = g / j
Problem: the speed at which a girl can row a boat in still water is 75 kmph . if he rows downstream , where the speed of current is 15 kmph , what time will he take to cover 300 metres ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "speed of the boat downstream = 75 + 15 = 90 kmph = 90 * 5 / 18 = 25 m / s hence time taken to cover 400 m = 400 / 25 = 16 seconds . answer : a"
Answer: a
Python program:
a = 300 * const_3_6
b = 75 + 15 
c = a / b
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 16 , b ) 3 / 11 , c ) 13 / 20 , d ) 3 / 10 , e ) 1 / 10
Rationale: "p ( x is prime ) = 1 / 4 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 4 * 1 / 4 = 1 / 16 the answer is a ."
Answer: a
Python program:
a = 1 / 2
b = 1 / 4
c = a * b
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: if 1430 is divisible by anyone of the answer choices . a . 1430 / 20 = 143 / 2 b 1430 / 21 = 1430 / 21 c 1430 / 22 = 65 if 1430 apple was divided among 65 people , each would have received 22 . after addition of 45 people the answer should be 13 . 1430 / 110 = 13 . c is the answer .
Answer: c
Python program:
a = 10 + 10 
b = a + 2 
c = 1430 / b
d = c + 45 
e = 1430 / d
f = e + 9
Problem: a merchant purchased a jacket for $ 42 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 6 , d ) $ 12 , e ) $ 15
Rationale: actual cost = $ 42 sp = actual cost + mark up = actual cost + 30 % sp = 42 * 100 / 70 on sale sp = 80 / 100 ( 42 * 100 / 70 ) = 48 gross profit = $ 6 answer is c
Answer: c
Python program:
a = 30 / 100
b = 1 - a
c = 42 / b
d = 20 / 100
e = 1 - d
f = c * e
g = f - 42
Problem: if two positive numbers are in the ratio 1 / 9 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: "given ratio = 1 / 9 : 1 / 5 = 5 : 9 let first number be 5 x and the second number be 9 x . the second number is more than first number by 4 x . required percentage = 4 x / 5 x * 100 = 80 % . answer : e"
Answer: e
Python program:
a = 1 / 5
b = a * 100
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 25 million in sales of and then $ 9 million in royalties on the next $ 130 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 25 million in sales to the next $ 130 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 35 % , d ) 42 % , e ) 56 %
Rationale: "( 9 / 130 ) / ( 3 / 25 ) = 15 / 26 = 57.7 % it means that 9 / 130 represents only 57.7 % . therefore a decrease of 42 % . answer d"
Answer: d
Python program:
a = 3 / 25
b = a * 100
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 5 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 30 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 30 days to doing 5 w widgets . answer : d"
Answer: d
Python program:
a = 5 * 2
b = a * 3
Problem: two employees x and y are paid a total of rs . 616 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 300
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 616 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 616 ⇒ y [ 12 / 10 + 1 ] = 616 ⇒ 22 y / 10 = 616 ⇒ 22 y = 6160 ⇒ y = 6160 / 22 = 560 / 2 = rs . 280 b"
Answer: b
Python program:
a = 1 + 4 
b = a * 2
c = 616 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 22 , d ) 15 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 8 w = 120 = > w = 15 answer d"
Answer: d
Python program:
a = rectangle_area / (
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 546 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 546 = > x = ( 546 * 100 ) / 65 = 840 answer d"
Answer: d
Python program:
a = 546 * 100
b = 100 - 35
c = a / b
Problem: jacob is now 14 years younger than michael . if 9 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 ) 9 , d ) 21 , e ) 25
Rationale: "jacob = x years , michael = x + 14 years 9 years from now , 2 ( x + 9 ) = x + 23 2 x + 18 = x + 23 x = 5 x + 4 = 9 years answer c"
Answer: c
Python program:
a = 14 + 9 
b = 2 * 9
c = a - b
d = 4 + c
Problem: a bag consists of 60 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 11 / 12 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: bag consists of 60 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 60 - 5 - 9 = 46 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 60 + 46 / 60 = 55 / 60 = 11 / 12 hence , answer will be a .
Answer: a
Python program:
a = 5 + 9 
b = 60 - a
c = b + 9 
d = c / 60
Problem: if 6 women can color 360 m long cloth in 3 days , then 5 women can color 100 m long cloth in ?
Options: a ) 2 days , b ) 3 days , c ) 2.5 days , d ) 4 days , e ) 1 day
Rationale: "the length of cloth painted by one woman in one day = 360 / 6 × 3 = 20 m no . of days required to paint 100 m cloth by 5 women = 100 / 5 × 20 = 1 day answer : e"
Answer: e
Python program:
a = 6 * 3
b = 360 / a
c = 5 * b
d = 100 / c
Problem: ram sold two bicycles , each for rs . 990 . if he made 10 % profit on the first and 10 % loss on the second , what is the total cost of both bicycles ?
Options: a ) 2000 , b ) 2888 , c ) 2667 , d ) 2999 , e ) 2122
Rationale: ( 10 * 10 ) / 100 = 1 % loss 100 - - - 99 ? - - - 1980 = > rs . 2000 answer : a
Answer: a
Python program:
a = 10 / 100
b = 990 * a
c = 990 + b 
d = 10 / 100
e = 990 * d
f = 990 - e
g = c + f
Problem: the simple form of the ratio 7 / 6 : 3 / 2 is ?
Options: a ) 5 : 8 , b ) 7 : 9 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 1
Rationale: "7 / 6 : 3 / 2 = 7 : 9 answer : b"
Answer: b
Python program:
a = 3 / 2
Problem: a company produces 72000 bottles of water everyday . if a case can hold 9 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 9 . number of cases required to hold 72000 bottles = 72000 / 9 = 8000 cases . so the answer is d = 8000"
Answer: d
Python program:
a = 72000 / 9
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 135 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 20 , d ) 15 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 135 6 x + 15 = 135 6 x = 120 x = 20 answer : c"
Answer: c
Python program:
a = 3 * 5
b = 135 - a
c = 3 * 2
d = b / c
Problem: on average , activated yeast cells divide once every 120 minutes ; that is , each individual cell divides into two individual cells over that time span . given that a certain yeast colony consisted of 310000 cells two hours ago , approximately how many cells will be populating the colony 12 hours from now ?
Options: a ) 77500 , b ) 1 , 860000 , c ) 2 , 480000 , d ) 3 , 720000 , e ) 39 , 680000
Rationale: 310000 × 2 × 2 × 2 × 2 x 2 × 2 × 2 = 310000 × 128 = e
Answer: e
Python program:
a = 120 / const_60
b = 12 / a
c = 2 ** b
d = 310000 * 2
e = c * d
f = e / 1000
g = 3 * 3
h = g * 1000
i = f + h 
j = i / 1000
k = math.floor(j)
l = k * 100
m = l * 100
Problem: the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 1 years ?
Options: a ) 5100 , b ) 5120 , c ) 7200 , d ) 5400 , e ) 5500
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 = 7200 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 8000 * a
c = 8000 - b
d = 10 / 100
e = 8000 * d
f = 8000 - e
g = 10 / 100
h = f * g
i = c - h
Problem: the average ( arithmetic mean ) of 10 , 30 , and 50 is 8 more than the average of 20 , 40 , and x . what is x ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the average of 10 , 30 , and 50 is 30 . the average of 20 , 40 and x is 22 . then 20 + 40 + x = 66 . x = 6 . the answer is c ."
Answer: c
Python program:
a = 10 + 30 
b = a + 50 
c = 8 * 3
d = c + 20 
e = d + 40 
f = b - e
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 7 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 7 + 1 ) / ( 7 - 1 ) = 8 / 6 = 4 / 3 answer : a"
Answer: a
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 7
d = c / 100
Problem: what is the square root of 625 , divided by 5 ?
Options: a ) 9 , b ) 36 , c ) 5 , d ) 6 , e ) 1
Rationale: square root is a number times itself square root of 625 = 25 , 25 / 5 = 5 ( c ) 5
Answer: c
Python program:
a = math.sqrt(625)
b = a / 5
Problem: find the simple interest on rs . 350 for 10 months at 5 paisa per month ?
Options: a ) 277 , b ) 175 , c ) 288 , d ) 266 , e ) 121
Rationale: "i = ( 350 * 10 * 5 ) / 100 = 175 answer : b"
Answer: b
Python program:
a = 10 / 100
b = 350 * a
Problem: a and b can do a piece of work in 60 days and 60 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 60 + 1 / 60 ] = 10 [ 1 + 1 / 60 ] = 1 / 3 a complete remaining work in 1 / 3 * 60 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Python program:
a = 10 / 60
b = 10 / 60
c = a + b 
d = 10 - c
e = 10 / 60
f = d / e
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 9
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 9 + 2 ^ 9 , which will give you 2 ^ 10 answer b"
Answer: b
Python program:
a = 2 + 2 
b = 2 * a
c = b / 2
Problem: what is the ratio of 4 / 7 to the product 2 * ( 7 / 3 ) ?
Options: a ) 6 : 49 , b ) 1 : 3 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "4 / 7 / 14 / 3 = 6 / 49 . . . imo option a ."
Answer: a
Python program:
a = 4 / const_60
Problem: calculate the sum of first 39 natural numbers .
Options: a ) 780 , b ) 891 , c ) 812 , d ) 847 , e ) 890
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 39 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 39 ) = ( 39 × 40 / 2 ) = 780 . answer a"
Answer: a
Python program:
a = 39 + 1 
b = 39 / 2
c = a * b
Problem: operation # is defined as adding a randomly selected two digit multiple of 14 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 14 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Python program:
a = 10 + 3 
b = 14 + a 
c = b / 2