Cheukting/mathqa huggingface dataset:
Question (general): last year department store x had a sales total for december that was 3 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 3 / 14 , d ) 4 / 11 , e ) 4 / 5
Rationale: let avg for 11 mos . = 10 therefore , dec = 30 year total = 11 * 10 + 30 = 140 answer = 30 / 140 = 3 / 14 = c
Answer: c
Question (general): if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 = > ab = 10 . answer : a"
Answer: a
Question (gain): the ratio of the cost price and selling price is 4 : 5 . the profit percent is ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 15 %
Rationale: "let the c . p . = $ 4 x then s . p . = $ 5 x then , gain = 5 x - 4 x = $ x gain % = x / 4 x * 100 = 25 % answer is b"
Answer: b
Question (general): farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: only trick n this question is to ignore 50 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % and the answer is not there in the options . the correct answer is ( b ) .
Answer: b
Question (general): the difference between the local value and the face value of 7 in the numeral 32675149 is
Options: a ) 69990 , b ) 69993 , c ) 70000 , d ) 77000 , e ) 78000
Rationale: "explanation : ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 b )"
Answer: b
Question (general): how many even 4 - digit numbers can be formed , so that the numbers are divisible by 4 and no two digits are repeated ?
Options: a ) 336 , b ) 784 , c ) 1120 , d ) 1804 , e ) 1936
Rationale: number is divisible by 4 if the last two digits form a number divisible by 4 . therefore last two digits can be : 00 ; 04 ; 08 ; 12 16 ; . . . 96 . basically multiples of 4 in the range 0 - 96 , inclusive . multiples of 4 in a range 0 - 96 , inclusive are last multiple in the range − first multiple in the range 4 + 1 = 25 last multiple in the range − first multiple in the range 4 + 1 = 25 but 3 numbers out of these 25 are not formed with distinct digits : 00 , 44 , and 88 . hence the numbers we are looking for can have only 22 endings . if there is 0 in the ending ( 04 , 08 , 20 , 40 , 60 , 80 - total 6 such numbers ) , then the first and second digit can take 8 and 7 choices each = 56 choices total . as there are 6 numbers with 0 in ending , hence total 6 * 56 = 336 . if there is no 0 in the ending ( total 22 - 6 with zero = 16 such numbers ) , then the first digit can take 7 choices ( 10 - 2 digits in the ending and zero , so total 3 digits = 7 , as 4 - digit number can not start with zero ) and the second digit can take 7 choices too ( 10 digits - 3 digits we ' ve already used ) = 7 * 7 = 49 choices total . as there are 16 numbers without zero in ending , hence total 16 * 49 = 784 . total : 336 + 784 = 1120 answer : c .
Answer: c
Question (general): 317 x 317 + 283 x 283 = ?
Options: a ) 79698 , b ) 80578 , c ) 80698 , d ) 180578 , e ) none of them
Rationale: "= ( 317 ) ^ 2 + ( 283 ) ^ 2 = ( 300 + 17 ) ^ 2 + ( 300 - 17 ) ^ 2 = 2 [ ( 300 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 90000 + 289 ] = 2 x 90289 = 180578 answer is d"
Answer: d
Question (physics): two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 36 seconds , the speed of each train ( in km / hr ) is
Options: a ) 12 , b ) 36 , c ) 28 , d ) 20 , e ) 24
Rationale: explanation : distance covered = 120 + 120 = 240 m time = 36 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 36 = 6.667 m / s speed of each train = v = 6.667 / 2 = 3.33 m / s = 3.33 × 36 / 10 km / hr = 12 km / hr answer : option a
Answer: a
Question (physics): two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer r between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) r = 18 , e ) 20
Rationale: since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 1112 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 1113 ) , ( 717 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 1517 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 1317 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 1819 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 2023 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) .
Answer: d
Question (physics): pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 2 hours ; pumps a and c , operating simultaneously , can fill the tank in 3 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 2 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6
Rationale: a + b = 2 ; a + c = 3 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 4 + 3 / 2 = 11 / 2 a + b + c = 11 / 4 hrs c
Answer: c
Question (general): how many even number in the range between 8 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 32 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 47 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 47 - 15 = 32 . hence , answer c"
Answer: c
Question (other): in a group of 100 people , 50 like reading books , 20 like both reading books and listening songs . how many like listening songs ?
Options: a ) 40 , b ) 50 , c ) 70 , d ) 60 , e ) none
Rationale: make a venn diagram , and enter your data . let the number of people who like listening songs be x x + 20 + 30 = 100 x = 50 so number who like listening songs = 20 + 50 = 70 answer c
Answer: c
Question (physics): a man rows his boat 90 km downstream and 72 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 5 , c ) 7 , d ) 3 , e ) 2
Rationale: "speed downstream = d / t = 90 / 3 = 30 kmph speed upstream = d / t = 72 / ( 3 ) = 24 kmph the speed of the stream = ( 30 - 24 ) / 2 = 3 kmph answer : d"
Answer: d
Question (other): there are 97 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 29 , b ) 49 , c ) 39 , d ) 59 , e ) 69
Rationale: editing my solution : number of switches = 97 number of switches turned on by a : 3 , 6 , . . . 96 = 32 number of switches turned on by b : 5 , 10 , . . . . 95 = 19 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 32 - 6 ) + ( 19 - 6 ) = 39 answer : c
Answer: c
Question (general): the product of two consecutive odd no is - 1 , then what is the value of the sum of them .
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "two odd numbers are - 1 and + 1 . - 1 + 1 = 0 answer : c"
Answer: c
Question (physics): to fill a tank , 10 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifth of its present ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 10 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 10 x ) / ( 2 x / 5 ) = ( 10 x ) x 5 / 2 x = 50 / 2 = 25 answer is a ."
Answer: a
Question (physics): if 30 oxen can plough 1 / 7 th of a field in 2 days , how many days 18 oxen will take to do the remaining work ?
Options: a ) 30 days , b ) 20 days , c ) 15 days , d ) 18 days , e ) 21 days
Rationale: solution : we will use work equivalence method , 30 / 18 = ( 1 / 7 ) / ( 6 / 7 ) * x / 2 ; 5 / 3 = ( 1 / 6 ) * x / 2 ; or , x = 60 / 3 = 20 days . answer : option b
Answer: b
Question (general): how many two - element subsets of { 6,7 , 8,9 } are there that do not contain the pair of elements 8 and 9 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 6 , e ) 7
Rationale: required subsets are = { 6,7 } , { 6,8 } , { 6,9 } , { 7,8 } , { 7,9 } = 5 answer : a
Answer: a
Question (gain): one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 14 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 64 % , c ) 42 % , d ) 28 % , e ) 26 %
Rationale: say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.14 - - > x = 0.26 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.14 - - > x = 0.26 . answer : e .
Answer: e
Question (gain): two - fifth of one - third of 3 - seventh of a number is 15 . what is 40 % of that number ?
Options: a ) 72 , b ) 84 , c ) 136 , d ) 140 , e ) none of these
Rationale: explanation : let the number be x . then , 2 / 5 of 1 / 3 of 3 / 7 of x = 15 = > x = ( 15 * 5 / 3 * 3 * 5 / 2 ) = 525 / 2 40 % of 525 / 2 = ( 40 / 100 * 525 / 2 ) = 105 answer is e
Answer: e
Question (general): when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 522.416 is divided by 0.0168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 7
Rationale: "for the 1 st no . there are 3 digits after decimal for the 2 nd no . there are 5 digits after decimal total no . of decimals = 8 req . no . of digits = ( n - 1 ) = ( 8 - 1 ) = 7 answer : e"
Answer: e
Question (general): there are 69 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 39 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 69 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 69 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 39 answer : d"
Answer: d
Question (general): an employee ’ s annual salary was increased $ 25,000 . if her new annual salary now equals $ 90,000 , what was the percent increase ?
Options: a ) 15 % , b ) 162 ⁄ 3 % , c ) 20 % , d ) 38.46 % , e ) 24 %
Rationale: new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d .
Answer: d
Question (physics): 30 men can do a work in 40 days . when should 15 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 10 days , c ) 15 days , d ) 44 days , e ) 22 days
Rationale: total work to be done = 30 * 40 = 1200 let 15 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 15 * 40 ) = 1200 40 p = 600 = > p = 15 days answer : c
Answer: c
Question (general): a car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let the time for which car averages 60 mph = t 65 * ( t + 4 ) = 70 * 4 + 60 t = > 5 t = 20 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a"
Answer: a
Question (physics): the speed of the boat in still water in 12 kmph . it can travel downstream through 39 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 3.5 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 39 / 3 = 13 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 13 / 2 = 11 km / hr so time taken in upstream = 39 / 11 = 3.5 hrs answer : a"
Answer: a
Question (general): if n = 7 ^ 11 – 7 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 7 ^ 3 - 7 . now 7 ^ 3 has last digit 3 . since 7 ^ 11 ( or for that matter 7 ^ 3 ) is greater than 7 , we subtract 7 from 13 ( the 10 + 3 - - > 10 has come from carry over from the tenth place ) . thus 13 - 7 = 6 is the answer . option d
Answer: d
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 525 $ , d ) 456 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 14 ) + ( 0.65 * 14 * 55 ) = 24.5 + 500.5 = > 525 hence answer will be ( c ) 525"
Answer: c
Question (geometry): in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 14 feet between each tree . how many trees can be planted if the road is 151 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 14 feet spaces will be t - 1 . then , the length of sidewalk required for 14 feet spaces will be 14 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 14 ( t - 1 ) + t = 151 or 14 t - 14 + t = 151 or 15 t = 165 or t = 11 answer : - d"
Answer: d
Question (probability): the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability q that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . q = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Question (general): the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is :
Options: a ) 23 , b ) 20 , c ) 12 , d ) 128 , e ) 171
Rationale: "let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a"
Answer: a
Question (physics): when tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? .
Options: a ) 44 % , b ) 125 % , c ) 105 % , d ) 225 % , e ) 400 %
Rationale: tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : b
Answer: b
Question (gain): the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 3 years ?
Options: a ) 5100 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 5832
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 ã — 90 / 100 x 90 / 100 = 5832 answer : e"
Answer: e
Question (gain): a reduction of 30 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 2.5 , d ) 2.1 , e ) 4.3
Rationale: "100 * ( 30 / 100 ) = 30 - - - 10 ? - - - 1 = > rs . 3 100 - - - 70 ? - - - 3 = > rs . 4.3 answer : e"
Answer: e
Question (general): what is the sum of all the even numbers between 31 and 99 , inclusive ?
Options: a ) 3,000 , b ) 2,562 , c ) 2,500 , d ) 2,180 , e ) 2,766
Rationale: "to figure this problem out , you just have to add all the even numbers , starting with 32 . 32 + 34 + 36 + 38 and so on , all the way up to 98 . you ' ll get 2,180 , so final answer : d"
Answer: d
Question (geometry): a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 1080 feet by 605 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330 , b ) $ 3,360 , c ) $ 450 , d ) $ 360 , e ) $ 150
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 450 ( c )
Answer: c
Question (general): according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 25 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 13.88 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 25 = 57 - - > c = 5 / 9 * 25 = 13.88 . increase = 13.88 degrees . answer : b ."
Answer: b
Question (general): kamal obtained 76 , 60 , 72 , 65 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 71 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 60 + 72 + 65 + 82 / 5 ) = ( 355 / 5 ) = 71 . answer a"
Answer: a
Question (gain): a person buys an article at rs . 550 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 600 , b ) 715 , c ) 772 , d ) 662 , e ) 521
Rationale: "cost price = rs . 550 profit = 30 % of 550 = rs . 165 selling price = cost price + profit = 550 + 165 = 715 answer : b"
Answer: b
Question (gain): an article with cost price of 280 is sold at 30 % profit . what is the selling price ?
Options: a ) 198 , b ) 364 , c ) 369 , d ) 207 , e ) 210
Rationale: "sp = 1.30 * 280 = 364 answer : b"
Answer: b
Question (physics): john can type a set of pages in 5 hours at a constant rate . if john types for 3 hours and jack does the rest of the job , who works at 2 / 5 constant rate of john . how long will it take for jack alone to do the rest of the job ?
Options: a ) 1 hrs , b ) 3 hrs , c ) 4 hrs , d ) 5 hrs , e ) 7 hrs
Rationale: john will do 3 / 5 in 3 hrs , so john does 3 / 5 of the work . . therefore , jack will do the remaining 2 / 5 th work alone . . as the speed of jack is 2 / 5 rate of john , jack will do the 2 / 5 th work in same time that john takes to complete full job . . . ans 5 d
Answer: d
Question (gain): a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 30 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20.8 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 30 ) / 100 × 16 = 20.8 answer c"
Answer: c
Question (physics): two persons a and b can complete a piece of work in 15 days and 30 days respectively . if they work together , what part of the work will be completed in 5 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 15 b ' s one day ' s work = 1 / 30 ( a + b ) ' s one day ' s work = 1 / 15 + 1 / 30 = 1 / 10 the part of the work completed in 5 days = 5 ( 1 / 10 ) = 1 / 2 . answer : d"
Answer: d
Question (general): the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 50 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 63.75 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 50 minutes after it was poured is : f = 120 ( 2 ^ - 50 / 10 ) + 60 f = 120 * 1 / 32 + 60 f = 15 / 4 + 60 f = 255 / 4 = 63.75 a"
Answer: a
Question (physics): water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 40 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 85 ° f , b ) 92 ° f , c ) 96 ° f , d ) 99 ° f , e ) 104 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 40 ) / 5 + 32 = 104 ° f the answer is e ."
Answer: e
Question (general): the number of natural numbers n such that ( n + 1 ) ^ 2 / ( n + 7 ) is an integer , is ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: we can use ( n + 1 ) ^ 2 greater than ( n + 7 ) which gives n > 2 , - 3 . . . . . . . . now there are four integers - 2 . - 1 , 01 in between - 3 and 2 . so answer is 4 . answer : a
Answer: a
Question (general): total dinning bill of 8 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 11.84 , b ) 12.84 , c ) 23.84 , d ) 19.11 , e ) 10.12
Rationale: "dinner bill of 8 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 8 = $ 19.11 answer : d"
Answer: d
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 100 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 100 y / 100 * 4 y = 100 y = 50 and x = 200 answer - c"
Answer: c