Cheukting/mathqa huggingface dataset:
Question (general): in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 338.50 , b ) $ 341.40 , c ) $ 344.30 , d ) $ 347.20 , e ) $ 350.10
Rationale: the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 10.50 = $ 347.20 the answer is d .
Answer: d
Question (general): following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 15 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 13 . , d ) 18 . , e ) 14.5
Rationale: price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 15 / 1.5 = 10 total price = 8 + 10 = 18 d is the answer
Answer: d
Question (physics): the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 11 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 4096 , d ) 2048 , e ) 1024
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 ans : e"
Answer: e
Question (general): in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 120 , b ) 190 , c ) 224 , d ) 298 , e ) 256
Rationale: "there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 14 * 16 = 224 . the answer is c ."
Answer: c
Question (physics): in what time will a train 135 m long cross an electric pole , it its speed be 140 km / hr ?
Options: a ) 3.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 140 * 5 / 18 = 38.8 m / sec time taken = 135 / 38.8 = 3.5 sec . answer : a"
Answer: a
Question (gain): a man buys a cycle for rs . 1200 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) s . 1080 , b ) s . 1140 , c ) s . 1090 , d ) s . 1202 , e ) s . 1092
Rationale: "s . p . = 90 % of rs . 1200 = rs . 90 x 1200 / 100 = rs . 1080 answer : option a"
Answer: a
Question (general): the average age of 30 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .
Options: a ) 43 , b ) 44 , c ) 45 , d ) 47 , e ) 48
Rationale: explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 30 ) = 45 years answer : c
Answer: c
Question (physics): john and lewis leave city a for city b simultaneously at 6 a . m in the morning driving in two cars at speeds of 40 mph and 60 mph respectively . as soon as lewis reaches city b , he returns back to city a along the same route and meets john on the way back . if the distance between the two cities is 240 miles , how far from city a did john and lewis meet ?
Options: a ) 150 miles , b ) 160 miles , c ) 140 miles , d ) 170 miles , e ) 200 miles
Rationale: time taken by lewis to reach city b = 240 / 60 = 4 hours in 4 hours , john travels 40 * 4 = 160 miles so distance at which they meet should be greater than 160 miles . only b satisfies . answer is b .
Answer: b
Question (general): a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 700 more than that by the previous schema , his sales were worth ?
Options: a ) s . 8,000 , b ) s . 9,000 , c ) s . 20,000 , d ) s . 10,000 , e ) s . 50,000
Rationale: [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 700 x = 8000 answer a
Answer: a
Question (general): the average weight of 8 persons increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 89 kg , e ) 25 kg
Rationale: total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . answer : d
Answer: d
Question (general): in a village of 100 households , 85 have at least one dvd player , 90 have at least one cell phone , and 55 have at least one mp 3 player . if x and y are respectively the greatest and lowest possible number of households that have all 3 of these devices , x – y is :
Options: a ) 65 , b ) 55 , c ) 45 , d ) 35 , e ) 25
Rationale: am i missing something here ? ? ? it seems straightforward . . . . . . the obvious maximum that have all 3 is 55 , because you are limited by the smallest number . the minimum is simply the sum of the max of each people who dont have the product , so : 100 - 90 = 10 do n ' t have cell 100 - 85 = 15 do n ' t have dvd and 100 - 55 = 45 do n ' t have mp 3 so a total of 10 + 15 + 45 = 70 combined who might not have some combination of the 3 products . so subtract that from 100 , to give you the minimum of the people who could have all 3 and you get 100 - 70 = 30 . 55 - 30 = 25 e
Answer: e
Question (other): of the diplomats attending a summit conference , 14 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 180
Rationale: { total } = { french } + { russian } - { both } + { neither } { total } = 14 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 180 . answer : e .
Answer: e
Question (gain): in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 80 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 3200 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 80 * 100 = 2.5 % . we are told that 2.5 % approximates the percent of tagged fish in the pond . since there are 80 tagged fish , then we have 0.025 x = 80 - - > x = 3,200 . answer : d ."
Answer: d
Question (gain): the cost price of an article is 25 % of the marked price . calculate the gain percent after allowing a discount of 50 % .
Options: a ) 25 % , b ) 50 % , c ) 100 % , d ) 150 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 25 . s . p = rs . 50 . â ˆ ´ gain % = [ 25 / 25 * 100 ] % = 100.0 % . answer c"
Answer: c
Question (general): the total marks obtained by a student in mathematics and physics is 40 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 30
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 40 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 40 + 20 ) / 2 = 30 . answer : e"
Answer: e
Question (geometry): anup manages to draw 7 circles of equal radii with their centres on the diagonal of a square such that two extreme circles touch two sides of the square and each middle circle touches two circles on either side . find the ratio of radius of the circles to the side of the square .
Options: a ) 1 : ( 2 + 6 ^ ( 1 / 2 ) )
b ) 1 : ( 4 + 7 ^ ( 1 / 3 ) )
c ) ( 2 + 7 ^ ( 1 / 2 ) ) : 1
d ) ( 2 + 7 ^ ( 1 / 2 ) ) : 2
e ) none of these
Rationale: diagonal of square = ( 2 * r ) * 7 + ( 2 ^ ( 1 / 2 ) * r - r ) * 2 diagonal has 7 squares diameters length + little distance between extreme squares to the end point [ form a square of side r from center of extreme circle to the extreme end to find distance ] distance = 2 ^ ( 1 / 2 ) * r - r d = a * 2 ^ ( 1 / 2 ) a = 2 ^ ( 1 / 2 ) * [ 6 * r + 2 ^ ( 1 / 2 ) * r ] r / a = 1 : [ 2 + 6 * 2 ^ ( 1 / 2 ) ] answer is none of the above answer : e
Answer: e
Question (physics): a light flashes every 20 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 180 , e ) 750
Rationale: "1 flash = 20 sec for 1 min = 3 flashes so for 1 hour = 3 * 60 = 180 flashes . answer : d"
Answer: d
Question (other): the cost of 3 pens and 5 pencils is rs . 240 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 720 , c ) rs . 300 , d ) rs . 150 , e ) none of these
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 240 15 x + 5 x = rs . 240 x = 240 / 20 = 12 : . cost of 1 pen = 5 x = 5 x 12 = 60 : . cost of 12 pens , i . e . ( one dozen ) = 60 x 12 = rs . 720 answer : option b"
Answer: b
Question (gain): the regular price per can of a certain brand of soda is $ 0.55 . if the regular price per can is discounted 25 percent when the soda is purchased in 24 - can cases , what is the price of 70 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 24.48 , e ) $ 28.87
Rationale: "the discounted price of one can of soda is ( 0.75 ) ( $ 0.55 ) , or $ 0.4125 therefore , the price of 70 cans of soda at the discounted price would be ( 70 ) ( $ 0.4125 ) = 28.875 answer : e"
Answer: e
Question (other): the ratio between the number of sheep and the number of horses at the stewart farm is 2 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 60
Rationale: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 2 x = 2 * 8 = 16 . hence b"
Answer: b
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3600 , b ) 2988 , c ) 2789 , d ) 2887 , e ) 1297
Rationale: "manager ' s monthly salary rs . ( 1600 * 21 - 1500 * 20 ) = rs . 3600 . answer : a"
Answer: a
Question (general): a call center has two teams . each member of team a was able to process 6 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 6 calls , so total calls for team a = 30 fraction for team b = 40 / ( 40 + 30 ) = 4 / 7 = answer = c"
Answer: c
Question (gain): after decreasing 24 % in the price of an article costs rs . 1064 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1200 , d ) 6151 , e ) 1400
Rationale: "cp * ( 76 / 100 ) = 1064 cp = 14 * 100 = > cp = 1400 answer : e"
Answer: e
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5120 , c ) 6420 , d ) 8960 , e ) none
Rationale: "explanation clearly , l = ( 48 – 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer b"
Answer: b
Question (general): 300 × ? + ( 12 + 4 ) × 1 / 8 = 602
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 5 , d ) d ) 2 , e ) e ) 8
Rationale: explanation : = > 300 × ? + ( 12 + 4 ) × 1 / 8 = 602 = > 300 × ? = 602 - ( 12 + 4 ) × 1 / 8 = > 300 × ? = 602 - 2 = 600 = > ? = 600 / 300 = 2 answer : option d
Answer: d
Question (general): if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 36 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 6
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 36 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 37 incorrect c . 2 / 2 = 2 / 3 + 2 / 38 incorrect d . 2 / 3 = 2 / 4 + 2 / 39 incorrect e . 2 / 4 = 2 / 5 + 2 / 40 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Question (physics): girl and boy together can complete a piece of work in 35 days while girl alone can complete the same work in 60 days . boy alone will be able to complete the same working in :
Options: a ) 72 , b ) 75 , c ) 84 , d ) 88 , e ) 90
Rationale: subtraction of fraction ab − cd = ad − cbbd girl and boy finish one work with company = 35 days ( girl + boy ) ′ s one day ’ s work = 135 girl alone finish the same work = 60 days girl ′ s one day ’ s work = 160 b ′ s one day ’ s work = ( a + b ) ′ s one day ’ s work - a ′ s one day ’ s work 135 − 160 = 184 hence b alone can complete the work in 84 days
Answer: b
Question (gain): what is 15 percent of 34
Options: a ) 5.1 , b ) 4.1 , c ) 3.1 , d ) 2.1 , e ) none of these
Rationale: "explanation : it will be 15 % of 34 = ( 15 / 100 ) * 34 = 5.10 answer : option a"
Answer: a
Question (gain): rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
Options: a ) 2288 , b ) 27669 , c ) 1766 , d ) 1000 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 140 x = 1000 answer : d"
Answer: d
Question (general): the difference between the local value and the face value of 7 in the numeral 32675149 is ?
Options: a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of these
Rationale: "( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 d )"
Answer: d
Question (general): the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 42 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 42 , it is 26 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 42 is already 26 more than 16 and hence we only have 29 - 26 = 3 extra to distribute between r and s . since s must be greater than r , r can be 16 + 1 = 17 and s can be 16 + 2 = 18 . so r is 17 . answer ( a )
Answer: a
Question (geometry): a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 231 trial and error : 20 * 10 = 200 ( too low ) 21 * 11 = 231 the length is 21 meters . the answer is a ."
Answer: a
Question (gain): a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 20 , c ) 90 , d ) 80 , e ) 11
Rationale: "600 - - - - 180 100 - - - - ? = > 80 % answer : d"
Answer: d
Question (general): how many integers are between 3 and 86 / 7 , inclusive ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "86 / 7 = 12 . xx we are not concerned about the exact value of 86 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 3 and 86 / 7 would be 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 total number of integers = 10 option c if we need to find the number of integers between two numbers n and m , where m > n the number of integers = m - n + 1 in the given question , the number of integers = 12 - 3 + 1 = 10 answer : c"
Answer: c
Question (physics): a man goes downstream at 15 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 3.5 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 15 - 8 ) kmph = 3.5 kmph . correct option : b"
Answer: b
Question (general): if 12 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 9.00 , e ) $ 20.00
Rationale: d for me 11 people with 1 $ each - > maximum = 9
Answer: d
Question (geometry): the diagonals of a rhombus are 12 cm and 20 cm . find its area ?
Options: a ) 329 , b ) 288 , c ) 120 , d ) 238 , e ) 31
Rationale: "1 / 2 * 12 * 20 = 120 answer : c"
Answer: c
Question (gain): the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 76,875 , how much profit did the business make ?
Options: a ) $ 98,000 , b ) $ 106,000 , c ) $ 112,000 , d ) $ 118,000 , e ) $ 123,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 76,875 p = $ 123,000 the answer is e ."
Answer: e
Question (physics): a and b can do a piece of work in 40 days and 40 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 / 40 + 1 / 40 ] = 10 [ 1 + 1 / 40 ] = 1 / 2 a complete remaining work in 1 / 2 * 40 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 20 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 5 , e ) 12.5
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 20 run rate needed = 250 / 20 = 12.5 answer : option e"
Answer: e
Question (gain): a car dealership has 40 cars on the lot , 30 % of which are silver . if the dealership receives a new shipment of 80 cars , 40 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 35 % , b ) 37.5 % , c ) 45 % , d ) 47.5 % , e ) 50 %
Rationale: "number of silver cars before shipment = 30 % of 40 = 12 number of silver cars after shipment = 60 % of 80 = 48 total number of silver cars out of 120 = 48 + 12 = 60 , which is 50 % e is my answer ."
Answer: e
Question (physics): a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 12 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 1.25 , b ) 1.75 , c ) 2.25 , d ) 2.75 , e ) 3.25
Rationale: "time = 6 / 4 + 6 / 8 = 18 / 8 = 2.25 hours the answer is c ."
Answer: c
Question (general): the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 5 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 54
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 5 th year = 50 , 6 th year = 50 - 5 = 45 . the correct answer is c ."
Answer: c
Question (other): in what ratio must rice of rs . 32 per kg be mixed with rice of rs . 42 per kg so that cost of mixture is rs . 20 per kg ?
Options: a ) 13 : 6 , b ) 13 : 5 , c ) 11 : 6 , d ) 11 : 5 , e ) 12 : 5
Rationale: "( 20 - 42 ) / ( 32 - 20 ) = 22 / 12 = 11 : 6 answer : c"
Answer: c
Question (probability): in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 5 , d ) 1 / 7 , e ) 3 / 5
Rationale: "total draws = prizes + blanks = 10 + 25 = 35 probability of getting a prize = 10 / 35 = 2 / 7 correct option is b"
Answer: b
Question (general): if the number is divided by 3 , it reduced by 48 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 72 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 48 = > 2 x / 3 = 48 = > x = 72 answer : option d"
Answer: d
Question (geometry): an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 80 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 480 cm
Rationale: "we have 80 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues . so we have 80 , 40,20 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 80 / 1 - ( 1 / 2 ) = 160 equilateral triangle perimeter is 3 a = 3 * 160 = 480 . so option e ."
Answer: e
Question (general): if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 , then n =
Options: a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 25
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 = > 4 x 2 ^ 2 n = 4 ^ 26 = 2 ^ 52 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 52 = > 2 ^ ( 2 n + 2 ) = 2 ^ 52 = > 2 n + 2 = 52 = > n = 25 so . answer will be e"
Answer: e
Question (general): if a - b = 5 and a 2 + b 2 = 34 , find the value of ab .
Options: a ) a ) 4.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 34 - 25 = 9 ab = 4.5 . answer : a"
Answer: a
Question (gain): john makes $ 60 a week from his job . he earns a raise and now makes $ 110 a week . what is the % increase ?
Options: a ) 16 % , b ) 83.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 50 / 60 ) * 100 = ( 5 / 6 ) * 100 = 83.33 % . b"
Answer: b
Question (physics): a certain number of workers can do a work in 35 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 35 - 10 ) / 10 = 25 answer is a"
Answer: a