euclaise/mathqa_programs huggingface dataset:
Problem: albert buys 4 horses and 9 cows for rs . 13,400 . if he sells the horses at 10 % profit and the cows at 20 % profit , then he earns a total profit of rs . 1880 . the cost of a horse is ?
Options: a ) 1299 , b ) 2788 , c ) 2000 , d ) 2981 , e ) 2881
Rationale: explanation : let c . p . of each horse be rs . x and c . p . of each cow be rs . y . then , 4 x + 9 y = 13400 - - ( i ) and , 10 % of 4 x + 20 % of 9 y = 1880 2 / 5 x + 9 / 5 y = 1880 = > 2 x + 9 y = 9400 - - ( ii ) solving ( i ) and ( ii ) , we get : x = 2000 and y = 600 . cost price of each horse = rs . 2000 . answer : c
Answer: c
Python program:
a = 20 * 100
Problem: when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 76.4 , what is the value of y ?
Options: a ) 20 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 76.4 - - > x = 76 y + 0.4 y ( so q above equals to 76 ) ; 0.4 y = 8 - - > y = 20 . answer : a ."
Answer: a
Python program:
a = math.floor(76, 4)
b = 76 - 4
c = 8 / b
Problem: a family pays $ 850 per year for an insurance plan that pays 80 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,250 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 850 $ family needs to pay 20 % of first 1000 $ in expense = 200 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 850 + 200 = 1050 $ total amount paid by insurance plan for first 1000 $ = 850 $ total amount paid by family will equal amount paid by plan when medical expense = 1250 $ ( since insurance plan will pay 100 % of amount that exceeds 1050 $ ) answer b"
Answer: b
Python program:
a = 1 - 0
Problem: in a group of 120 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 60 / 120 , b ) 15 / 120 , c ) 30 / 120 , d ) 80 / 120 , e ) 40 / 120
Rationale: "number of people whose age is less than 20 is given by 120 - 90 = 30 probability p that a person selected at random from the group is less than 20 is gieven by 30 / 120 = 0.25 correct answer c"
Answer: c
Python program:
a = 120 - 90
b = a / 120
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 70 % , e ) 81 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 10 % , price = 81 - 8.1 = 72.9 which is 72.9 / 90 * 100 of the sale price on day 1 = ~ 81 % answer e"
Answer: e
Python program:
a = 10 / 100
b = 1 / 10
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: given that 268 x 74 = 19432 , find the value of 2.68 x . 74 .
Options: a ) 1.9432 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9432 answer a"
Answer: a
Python program:
a = 268 / 100
b = 74 / 100
c = a * b
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 22 percent alcohol by volume ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "22 % is 12 % - points higher than 10 % but 8 % - points lower than 30 % . thus there should be 2 parts of solution x for 3 parts of solution y . we should add 450 ml of solution y . the answer is d ."
Answer: d
Python program:
a = 22 - 10
b = 30 - 22
c = a / b
d = c * 300
Problem: walking at 5 / 6 of its usual speed , a train is 10 minutes too late . find its usual time to cover the journey .
Options: a ) 50 min , b ) 20 min , c ) 1 hour , d ) 30 min , e ) 45 min
Rationale: "new speed = 5 / 6 of the usual speed new time taken = 6 / 5 of the usual time taken so , ( 6 / 5 of the usual time ) - ( usual time ) = 10 min 1 / 5 of the usual time = 10 min usual time = 10 * 5 = 50 min correct option is a"
Answer: a
Python program:
a = 5 / 6
b = 1/(a)
c = b - 1
d = 10 / c
Problem: in the rectangle below , the line mn cuts the rectangle into two regions . find x the length of segment nb so that the area of the quadrilateral mnbc is 40 % of the total area of the rectangle .
Options: a ) 1 meter , b ) 2 meter , c ) 3 meter , d ) 4 meter , e ) 5 meter
Rationale: solution we first note that mc = 20 - 5 = 15 the quadrilateral mnbc is a trapezoid and its area a is given by a = ( 1 / 2 ) × 10 × ( x + mc ) = 5 ( x + 15 ) 40 % of the area of the rectangle is equal to 40 % × ( 20 × 10 ) = ( 40 / 100 ) × 200 = 80 since the area of mnbc is equal to 40 % the area of the rectangle , we can write 5 ( x + 15 ) = 80 5 x + 75 = 80 5 x = 5 x = 1 meter answer is a
Answer: a
Python program:
a = 40 / 12
b = a - const_0_33
c = b - 2
Problem: two trains of equal lengths take 15 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 15 = 8 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 8 + 6 = 14 m / sec . required time = ( 120 + 120 ) / 14 = 17 sec . answer : c"
Answer: c
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: 3,7 , 12,18 , 25,33 , . . . . . . . . . . . . . . 7 th terms
Options: a ) 43 , b ) 42 , c ) 63 , d ) 65 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 answer : b"
Answer: b
Python program:
a = negate - (
Problem: the floor of a rectangular room is 20 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 144 m 2 , b ) 120 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 24 ã — 16 = 384 m 2 area of the inner rectangle = 20 ã — 12 = 240 m 2 required area = ( 304 â € “ 180 ) = 144 m 2 answer a"
Answer: a
Python program:
a = 2 * 2
b = a + 20 
c = 2 * 2
d = 12 + c 
e = rectangle_area - (
Problem: the average weight of a class is x pounds . when a new student weighing 90 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 99
Rationale: when the student weighs 90 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 90 = 20 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 20 / 5 = 4 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 90 = 6 ( x - 1 ) - - > x = 96 pounds . answer : e .
Answer: e
Python program:
a = 90 + 4 
b = 4 + 1 
c = a + b
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 200 more . what was the sum ?
Options: a ) s . 550 , b ) s . 1000 , c ) s . 600 , d ) s . 200 , e ) s . 400
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 200 ( given ) so , at 5 % more rate , the increase in si for 1 year = 200 / 10 = rs . 20 / - i . e . rs . 20 is 5 % of the invested sum so , 1 % of the invested sum = 20 / 5 therefore , the invested sum = 20 × 100 / 5 = rs . 400 answer : e"
Answer: e
Python program:
a = 5 / 100
b = a * 10
c = 200 / b
Problem: the sum of a certain number and its reciprocal is equal to 29 . what is the absolute value of the difference of this number and its reciprocal ?
Options: a ) 22 , b ) 12 , c ) 03 , d ) 04 , e ) 21
Rationale: x + 1 / x = 2.9 x - 1 / x = y add two equations 2 x = 2.9 + y so when 2.9 and correct answer choice are added , the final digit should be even so eliminate a , b and d substitute y = 0.3 x = 1.6 1.6 + 1 / 1.6 is not equal to 2.9 substitute y = 2.1 so x = 2.5 2.5 + 1 / 2.5 = 2.9 answer : e
Answer: e
Python program:
a = 29 / 10
b = 2 ** 3
c = b / 10
d = a - c
Problem: what is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1 ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400
Rationale: since 500 = 2 ^ 2 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500 . we then need to eliminate the 50 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 495 . there are a total of 250 - 50 = 200 such numbers between 1 and 500 . the answer is c .
Answer: c
Python program:
a = 500 - 1
b = 500 - 2
c = b - 2
d = c / 2
e = d + 1 
f = 500 / 100
g = 500 - f
h = 500 / 100
i = g - h
j = 500 / 100
k = i / j
l = k + 1 
m = e + l 
n = 500 - 10
o = n - 10
p = o / 10
q = p + 1 
r = m - q
s = a - r
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 7.5 , b ) 7.4 , c ) 7.9 , d ) 7.2 , e ) 8.0
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 9 ) = 1 / 8 the cistern will be filled in 8 / 1 hrs i . e . , 8 hrs . answer : e"
Answer: e
Python program:
a = 1 / 4
b = 1 / 8
c = a - b
d = 1 / c
Problem: in a simultaneous throw of pair of dice . find the probability of getting the total more than 7 .
Options: a ) 5 / 19 , b ) 5 / 12 , c ) 5 / 28 , d ) 5 / 10 , e ) 5 / 11
Rationale: "explanation : here n ( s ) = ( 6 x 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } therefore , p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 . answer : b ) 5 / 12"
Answer: b
Python program:
a = 7 + 4 
b = a + 4 
c = 4 + 2 
d = 4 + 2 
e = c * d
f = b / e
Problem: krishan and nandan jointly started a business . krishan invested 6 times as nandan did and invested his money for double time as compared to nandan . nandan earned rs . 6000 . if the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
Options: a ) rs . 78000 , b ) rs . 48000 , c ) rs . 6000 , d ) rs . 82000 , e ) rs . 32000
Rationale: 6 : 1 2 : 1 - - - - - - 12 : 1 1 - - - - - 6000 13 - - - - - ? = > rs . 78,000 answer : a
Answer: a
Python program:
a = 6 * 2
b = a + 1 
c = 6000 * b
Problem: consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes
Options: a ) 1700 , b ) 7570 , c ) 1576 , d ) 17576 , e ) 500
Rationale: the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 ã — 26 = 67626 ã — 26 = 676 ways having chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 ã — 26 = 17576676 ã — 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer d
Answer: d
Python program:
a = 10 + 10 
b = a + 3 
c = b + 3 
d = 5 - 2
e = c ** d
Problem: a glass was filled with 25 ounces of water , and 0.04 ounce of the water evaporated each day during a 10 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.4 % , d ) 1.6 % , e ) 20 %
Rationale: "in 10 days 10 * 0.04 = 0.4 ounces of water evaporated , which is 0.4 / 25 â ˆ — 100 = 1.6 of the original amount of water . answer : d ."
Answer: d
Python program:
a = 0 * 4
b = a / 25
c = b * 100
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 37.5 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 180 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 37.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 37.5 miles in 150 mins so answer 30 + 150 = 180 mins . ( answer c )"
Answer: c
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: vijay lent out an amount rs . 10000 into two parts , one at 8 % p . a . and the remaining at 10 % p . a . both on simple interest . at the end of the year he received rs . 850 as total interest . what was the amount he lent out at 8 % pa . a ?
Options: a ) rs . 15000 , b ) rs . 6000 , c ) rs . 25000 , d ) rs . 10000 , e ) rs . 18000
Rationale: let the amount lent out at 8 % p . a . be rs . a = > ( a * 8 ) / 100 + [ ( 10000 - a ) * 10 ] / 100 = 850 = > a = rs . 15000 . answer : a
Answer: a
Python program:
a = 10 / 100
b = a * 10000
c = 8 / 100
d = b + c 
e = d - 850
f = e * 100
Problem: find k if 64 ÷ k = 4 .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 36 , e ) 40
Rationale: "since 64 ÷ k = 4 and 64 ÷ 16 = 4 , then k = 16 correct answer b"
Answer: b
Python program:
a = 64 / 4
Problem: the mean of 50 observations is 200 . but later he found that there is decrements of 9 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 190 , d ) 191 , e ) 199
Rationale: "191 answer is d"
Answer: d
Python program:
a = 200 - 9
Problem: a couple spent $ 184.80 in total while dining out and paid this amount using a credit card . the $ 184.80 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 124 , b ) $ 132 , c ) $ 140 , d ) $ 148 , e ) $ 156
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 184.80 x = 140 the correct answer is c ."
Answer: c
Python program:
a = 184 * 80
b = 100 + 20 
c = a / b
d = c * 100
e = 100 + 10 
f = d / e
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 5 * / 6 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 1 / 4 d"
Answer: d
Python program:
a = 1 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 30 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 3360 , c ) 8400 , d ) 12600 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 30 machine produce 560 * 6 * ( 30 / 8 ) in 6 minutes 560 * 6 * 30 / 8 = 12600 answer is d ."
Answer: d
Python program:
a = 30 / 8
b = 560 * a
c = b * 6
Problem: abel can complete a work in 10 days , ben in 12 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 5 days before the completion of the work . how long did the work last ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 8 1 / 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 5 days before the completion , this means that carla had to work alone for these 5 days in which she completed 1 / 3 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 7 / 15 3 / 20 ( t ) = 7 / 15 - - - > t = 3 1 / 9 therefore , these 3 1 / 9 days worked plus the 5 days that carla had to work by herself add to 8 1 / 9 days answer : d"
Answer: d
Python program:
a = 2 + 5 
b = a * 5
Problem: a man can do a piece of work in 5 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 13 / 2 , b ) 7 , c ) 15 / 2 , d ) 8 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 5 ) = 2 / 5 the son alone can do the work in 15 / 2 days answer is c"
Answer: c
Python program:
a = 5 * 3
b = 5 - 3
c = a / b
Problem: annika hikes at a constant rate of 10 minutes per kilometer . she has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 45 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "set up two r x t = d cases . 1 . 1 / 10 km / min x t = 2.75 from which t = 27.5 mins . we know total journey time now is 45 + 27.5 = 72.5 the rate is the same ie 1 / 10 km / min . set up second r x t = d case . 1 / 10 km / min x 72.5 = 7.25 km now the total journey would be halved as distance would be same in each direction . 7.25 / 2 = 3.625 . a ."
Answer: a
Python program:
a = 45 / 10
b = a - 2
c = b / 2
d = c + 2
Problem: the average of 10 numbers is calculated as 20 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 12 , b ) 26 , c ) 16 , d ) 97 , e ) 20
Rationale: "10 * 20 + 36 – 26 = 200 / 10 = 20 answer : e"
Answer: e
Python program:
a = 36 - 26
b = a / 10
c = 20 + b
Problem: two trains 161 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 6.18 , b ) 7.12 , c ) 7.1 , d ) 8.09 , e ) 8.11
Rationale: "t = ( 161 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 8.09 answer : d"
Answer: d
Python program:
a = 161 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: there is 60 % increase in an amount in 6 years at s . i . what will be the c . i . of rs . 12,000 after 3 years at the same rate ?
Options: a ) rs . 3932 , b ) rs . 3972 , c ) rs . 3372 , d ) rs . 3942 , e ) rs . 3772
Rationale: "explanation : let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = ( 100 * 60 ) / ( 100 * 6 ) = 10 % p . a . now , p = rs . 12000 , t = 3 years and r = 10 % p . a . c . i . = [ 12000 * { ( 1 + 10 / 100 ) 3 - 1 } ] = 12000 * 331 / 1000 = rs . 3972 answer : option c"
Answer: c
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: in a mixed college 160 students are there in one class . out of this 160 students 1 / 2 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 1 / 2 = 80 total boys : 160 - 80 = 80 answer is c"
Answer: c
Python program:
a = 160 / 2
b = a * 3
Problem: the average weight of 8 person ' s increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 80 kg , e ) 98.6 kg
Rationale: "explanation : total increase in weight = 8 ã — 4.2 = 33.6 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 33.6 = x - 65 = > x = 33.6 + 65 = 98.6 answer : option e"
Answer: e
Python program:
a = 8 * 4
b = a + 65
Problem: on sunday morning , pugsley and wednesday are trading pet spiders . if pugsley were to give wednesday two of his spiders , wednesday would then have 9 times as many spiders as pugsley does . but , if wednesday were to give pugsley 6 of her spiders , pugsley would now have 6 fewer spiders than wednesday had before they traded . how many pet spiders does pugsley have before the trading game commences ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 20
Rationale: if pugsley were to give wednesday two of his spiders , wednesday would then have nine times as many spiders as pugsley does : ( w + 2 ) = 9 ( p - 2 ) if wednesday were to give pugsley six of her spiders , pugsley would now have six fewer spiders than wednesday had before they traded : p + 6 = w - 6 solving gives p = 4 and w = 16 . answer : a .
Answer: a
Python program:
a = 6 + 6 
b = a + 6 
c = 6 + 6 
d = c * 9
e = b + d 
f = e + 2 
g = 6 + 2 
h = f / g
i = 6 + 6 
j = h - i
Problem: rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1250 , b ) $ 1350 , c ) $ 1150 , d ) $ 1360 , e ) $ 1370
Rationale: "50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 30 ( 10 + 5 ) + 20 ( 10 + 5 + 5 ) = 500 + 450 + 400 = 1350 answer - b"
Answer: b
Python program:
a = 100 * 10
b = 30 * 5
c = a + b 
d = 20 * 5
e = d * 2
f = c + e
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 74 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 74 0.18 x = 234 x = 1300 then the amount invested at 8 % is $ 2000 - $ 1300 = $ 700 the answer is b ."
Answer: b
Python program:
a = 100 * 10
b = a * 2
c = 10 * 8
d = c * 2
e = d + 74 
f = 10 / 100
g = 8 / 100
h = f + g 
i = e / h
j = b - i