Cheukting/mathqa huggingface dataset:
Question (other): if 0.75 of a number is equal to 0.025 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 1 : 30 , d ) 20 : 3 , e ) 30 : 7
Rationale: "0.75 a = 0.025 b - > a / b = 0.025 / 0.75 = 25 / 750 = 1 / 30 : . a : b = 1 : 30 answer : c"
Answer: c
Question (gain): a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 60 minutes and a model y computer can complete the same task in 30 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ?
Options: a ) 18 , b ) 16 , c ) 15 , d ) 17 , e ) 20
Rationale: "let ' s say 1 work is processing 60 gb of data . model x : 1 gb per min model y : 2 gb per min working together , 1 x and 1 y = 3 gb per min so , 20 times as many computers would work at 60 gb per min . so no . of x = 20 answer is e"
Answer: e
Question (physics): a certain number of men can do a work in 40 days . if there were 5 men less it could be finished in 10 days more . how many men are there ?
Options: a ) 15 men , b ) 25 men , c ) 18 men , d ) 12 men , e ) 14 men
Rationale: "explanation : x * 40 = ( x - 5 ) * 50 5 x - 4 x = 25 x = 25 men answer : option b"
Answer: b
Question (general): mike earns $ 12 per hour and phil earns $ 6 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 50 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 12 is 6 let it be x % less , then = 12 ( 1 - x / 100 ) = 6 1 - x / 100 = 6 / 12 x = 100 / 2 x = 50 % ans a"
Answer: a
Question (physics): a can do a job in 45 days and b can do it in 30 days . a and b working together will finish four times the amount of work in - - - - - - - days ?
Options: a ) 30 days , b ) 45 days , c ) 80 days , d ) 72 1 / 2 days , e ) 72 days
Rationale: "1 / 45 + 1 / 30 = 5 / 90 = 1 / 18 18 / 1 = 18 * 4 = 72 days answer : e"
Answer: e
Question (general): a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 982 in total compensation , how many total hours did he work that week ?
Options: a ) 57 , b ) 51 , c ) 59 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 982 - 560 = 422 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 422 / 24.5 = 17.2 = 17 approx . total hrs = 40 + 17 = 57 answer a"
Answer: a
Question (general): the least number which when divided by 3 , 4 , 5 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 167 , b ) 243 , c ) 252 , d ) 336 , e ) none of these
Rationale: "explanation : l . c . m of 3 , 4 , 5 , 8 = 120 therefore required number is of the form 120 k + 3 . least value of k for which ( 120 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 120 x 2 + 3 ) = 243 answer : b"
Answer: b
Question (general): 70 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 71 , c ) 27 , d ) 61 , e ) 81
Rationale: "explanation : 70 + 5 * 12 / ( 180 / 3 ) = 70 + 5 * 12 / ( 60 ) = 70 + ( 5 * 12 ) / 60 = 70 + 1 = 71 . answer : b"
Answer: b
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 4 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 16
Rationale: "a / 8 = 4 * 4 = > a = 4 * 4 * 8 x * 2 x = 4 * 4 * 8 x = 8 = > 2 x = 16 answer : e"
Answer: e
Question (physics): 14 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 27.5 days , b ) 15.5 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days
Rationale: "14 * 25 = 20 * x = > x = 17.5 days answer : c"
Answer: c
Question (physics): a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 50 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 276 , b ) 271 , c ) 200 , d ) 278 , e ) 268
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 50 - 40 ) = 4 hours so , the two trains meet at 2 p . m . the two trains meet 4 * 50 = 200 km away from mumbai . answer : c"
Answer: c
Question (general): reduce 368 / 598 to the lowest terms
Options: a ) 30 / 25 , b ) 28 / 13 , c ) 28 / 29 , d ) 8 / 13 , e ) none of these
Rationale: explanation : we can do it easily by in two steps step 1 : we get the hcf of 368 and 598 which is 46 step 2 : divide both by 46 , we will get the answer 8 / 13 answer : option d
Answer: d
Question (gain): a , b and c started a partnership business by investing rs . 5000 , rs . 8000 , rs . 9000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 88000 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 5000 : 8000 : 9000 = 5 : 8 : 9 let total profit = p then p ã — 9 / 22 = 36000 p = ( 36000 ã — 22 ) / 9 = 88000 answer is c ."
Answer: c
Question (general): 5 n + 2 > 12 and 7 n - 5 < 37 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 6
Rationale: "5 n > 10 - - > n > 2 7 n < 42 - - > n < 6 2 < n < 6 answer : e"
Answer: e
Question (gain): a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 5 / 100 x 12000 ) = rs . 600 . answer b"
Answer: b
Question (geometry): two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 49 . find the ratio of their corresponding heights .
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 4 / 7 , e ) 2 / 3
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 16 / 49 - - > height / height = 4 / 7 . answer : d ."
Answer: d
Question (gain): two numbers are respectively 50 % and 100 % more than a third number . the percentage that is first of the second is ?
Options: a ) 65 % , b ) 83 % , c ) 27 % , d ) 42 % , e ) 75 %
Rationale: "i ii iii 150 200 100 200 - - - - - - - - - - 150 100 - - - - - - - - - - - ? = > 75 % answer : e"
Answer: e
Question (physics): if an object travels 300 feet in 5 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 39 , b ) 38 , c ) 40 , d ) 41 , e ) 34
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 300 feet in 5 sec then it travels 300 / 5 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 60 feet in 1 hour = 216000 feet in 1 hr = 216000 / 5280 miles in 1 hour = 21600 / 528 miles / hr ~ 41 miles / hr answer - d"
Answer: d
Question (gain): rs . 875 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 875 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1061 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 875 ) = rs . 81 rate = ( 100 x 81 / 875 x 3 ) = 108 / 35 % new rate = ( 108 / 35 + 4 ) % = 248 / 35 % new s . i . = rs . ( 875 x 248 / 35 x 3 / 100 ) rs . 186 . ∴ new amount = rs . ( 875 + 186 ) = rs . 1061 . answer c"
Answer: c
Question (general): 0.003 * ? * 0.0003 = 0.00000027
Options: a ) 9 , b ) 3 , c ) 0.3 , d ) 0.03 , e ) none of these
Rationale: "explanation : 0.003 * ? * 0.0003 = 0.00000027 3 / 1000 * ? * 3 / 10000 = 3 / 1000 * 3 / 1000 * 3 / 100 ? = 3 / 10 = 0.3 answer is c"
Answer: c
Question (physics): a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3400 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 2040 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 136 so , a ’ s amount = 120 × 15 = rs . 2040 . answer : option c"
Answer: c
Question (general): what will be the reminder when ( 19 ^ 19 + 19 ) is divided by 20 ?
Options: a ) 18 , b ) 40 , c ) 21 , d ) 43 , e ) 28
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 19 ^ 19 + 1 ) will be divisible by ( 19 + 1 ) ; ( 19 ^ 19 + 1 ) + 18 when divided by 20 will give 18 as remainder . correct option : a"
Answer: a
Question (gain): a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 12 % . their gross income from sales for one month increases by what percent ?
Options: a ) 0.4 % , b ) 0.8 % , c ) 2 % , d ) 4 % , e ) 8 %
Rationale: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.12 x = 1.008 * ( p * x ) , an increase of 0.8 % . the answer is b ."
Answer: b
Question (general): a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 102 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 102 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 40 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 102 ) / ( 3 / 20 ) = 30 / 54 = 58,5 % it means that 9 / 108 represents only 58,5 % . therefore a decrease of 45 % . answer c"
Answer: c
Question (geometry): the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 55 , then how long is the base of isosceles triangle ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the base of the isosceles triangle is 55 - 20 - 20 = 15 units the answer is c ."
Answer: c
Question (gain): one fourth of one third of two fifth of a number is 10 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 120 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 10 then x = 10 * 30 = 300 40 % of 300 = 120 answer : option c"
Answer: c
Question (general): in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 52 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 22
Rationale: "you should notice that 52 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 22 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . e"
Answer: e
Question (general): find the average of first 8 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 22.5 , e ) 21
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 ) / 8 = 22.5 answer is d"
Answer: d
Question (general): a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 16 heads and 45 legs . how many cats does the ship host ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 8 , e ) 7
Rationale: "a ' s + co + ca + cats = 16 . sa ' s + 1 + 1 + cats = 16 or sa ' s + cats = 14 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 45 sa ' s * 2 + cats * 4 = 42 or sa ' s + cats * 2 = 21 or 14 - cats + cat * 2 = 21 then cats = 7 e"
Answer: e
Question (geometry): how many 1 x 1 x 1 cubes can you fit in a 15 x 16 x 13 box ?
Options: a ) 3,200
b ) 3,150
c ) 3,448
d ) 3,120
e ) 2,980
Rationale: the answer is d ) 3,120 . a 1 x 1 x 1 cube has an area of 1 . the 15 x 16 x 13 box has an area of 3,120 . if you divide 3,120 by 1 , you get 3,120 . therefore the answer is d .
Answer: d
Question (physics): the lcm of two numbers is 2310 and hcf is 83 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 913 , b ) 825 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 83 / 210 = 11 * 83 = 913 answer : a"
Answer: a
Question (physics): nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days , they completed 1 / 3 part of work . than how many more employees should nhai hire to finish it in time working 10 hours a day ?
Options: a ) 55 , b ) 60 , c ) 70 , d ) 50 , e ) 65
Rationale: explanation : the given problem can be written in a tabular form like below : - men days hour work planned 100 50 8 1 actual 100 25 8 1 / 3 remaining ? 25 10 2 / 3 we can apply chain rule now . total men required to complete the remaining work = 100 × ( 25 / 25 ) × ( 8 / 10 ) × ( 2 / 3 ) / ( 1 / 3 ) = 160 . so additional men required = 160 - 100 = 60 . answer is b
Answer: b
Question (physics): a man is walking at a speed of 6 km per hour . after every km he takes rest for 6 minutes . how much time will he take to cover a distance of 12 km .
Options: a ) 3 hr , b ) 5 hr 42 min , c ) 4 hrs . 10 min , d ) 3 hr . 6 min , e ) none of these
Rationale: "explanation : for 12 km he takes 11 times rest . 11 x 6 = 66 minutes rest = 1 hr 6 min for 12 km , 2 hr is required + rest = 2 + 1 hr 6 m = 3 hr . 6 min answer : option d"
Answer: d
Question (general): what least number must be subtracted from 9671 so that the remaining number is divisible by 2 ?
Options: a ) 3 , b ) 1 , c ) 16 , d ) 11 , e ) 15
Rationale: "on dividing 9671 by 2 , we get remainder = 1 . required number be subtracted = 1 answer : b"
Answer: b
Question (general): find the value of ( 200 + 200 / 90 ) × 90
Options: a ) 18500 , b ) 18200 , c ) 17500 , d ) 16500 , e ) 13500
Rationale: "( 18000 + 200 ) / 90 * 90 = 18200 answer : b"
Answer: b
Question (geometry): mr . loyd wants to fence his square shaped land of 130 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 52
Rationale: "if each side is 120 feet . . then total perimeter is 130 * 4 = 520 poles every 10 feet hence no of poles = 520 / 10 = 52 answer : e"
Answer: e
Question (general): a beekeeper has 600000 bees living in 4 beehives . among these beehives , the sizes of the beehives are proportional to the numbers of bees living in them . no beehive has less than 80 % the number of bees of any other beehive . what is the maximum possible number of bees that the greatest beehive could have ?
Options: a ) 20,000 , b ) 176470 , c ) 10000 , d ) 13000 , e ) 56600
Rationale: x be the # of bees in the hive with the max # of bees . let other hives have same # of bees . so , x + 3 * ( 0.8 ) * x = 600,000 = > 3.4 x = 600,000 = > x = 176470 . b is the answer .
Answer: b
Question (physics): if 36 men can do a piece of work in 25 hours , in how many hours will 10 men do it ?
Options: a ) 22 , b ) 38 , c ) 60 , d ) 88 , e ) 90
Rationale: explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 10 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 10 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 10 } = 90 hence , 10 men can do it in 90 hours . answer : e ) 90
Answer: e
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 10 percent on food , and 40 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 10 , others = 40 tax on clothing = 2 tax on others = 3.2 percentage = 5.2 / 100 = 5.2 % answer : d"
Answer: d
Question (general): if the average ( arithmetic mean ) of 4 x - 5 , 8 x - 6 , and 9 x + 5 is 279 , what is the value of x ?
Options: a ) 18 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: "am of 4 x - 5 , 8 x - 6 , and 9 x + 5 = 4 x - 5 + 8 x - 6 + 9 x + 5 / 3 = 31 x / 3 given that 31 x / 3 = 279 x = 837 / 31 = 27 x = 27 answer is c"
Answer: c
Question (general): a retailer bought a hat at wholesale and marked it up 70 % to its initial price of $ 34 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.7 x = 34 and x = 34 / 1.7 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 6 more . the answer is c .
Answer: c
Question (general): an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 90 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 15 / 16 . e"
Answer: e
Question (gain): a fruit seller had some oranges . he sells 30 % oranges and still has 420 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 600 , c ) 220 , d ) 400 , e ) none of these
Rationale: "explanation : he sells 30 % of oranges and still there are 420 oranges remaining = > 70 % of oranges = 420 ⇒ ( 70 × total oranges ) / 100 = 420 ⇒ total oranges / 100 = 6 ⇒ total oranges = 6 × 100 = 600 answer : option b"
Answer: b
Question (gain): 70 is subtracted from 30 % of a number , the result is 20 . find the number ?
Options: a ) 150 , b ) 997 , c ) 266 , d ) 300 , e ) 271
Rationale: ( 30 / 100 ) * x – 70 = 20 3 x = 900 x = 300 answer : d
Answer: d
Question (gain): sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 0.5 % more . she would get how much ?
Options: a ) 9320 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 0.5 ) / 100 = 120 9200 - - - - - - - - 9320 answer : a"
Answer: a
Question (general): the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 88 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 88 + 6 * 65 - 11 * 60 = 258 answer is a"
Answer: a
Question (geometry): what is the area of a square field whose sides have a length of 13 meters ?
Options: a ) 225 sq m , b ) 169 sq m , c ) 128 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "13 * 13 = 169 sq m the answer is b ."
Answer: b
Question (gain): what is the cp of rs 100 stock at 6 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 94.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 6 + 1 / 5 94.2 thus the cp is rs 94.2 . answer : c"
Answer: c
Question (geometry): the edges of cuboid are 4 cm ; 5 cm and 6 cm . find its surface area ?
Options: a ) 228
b ) 148
c ) 992
d ) 772
e ) 222
Rationale: 2 ( 4 * 5 + 5 * 6 + 4 * 6 ) = 148 answer : b
Answer: b
Question (physics): x does a work in 15 days . y does the same work in 30 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 30 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 30 ) = 1 / 10 both together will finish the work in 10 days . correct option is a"
Answer: a
Question (physics): two trains of equal lengths take 10 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 ) 13 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 12 + 6 = 18 m / sec . required time = ( 120 + 120 ) / 18 = 13 sec . answer : b"
Answer: b
Question (general): set a contains all the even numbers between 4 and 50 inclusive . set b contains all the even numbers between 104 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2400 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 4 , 6 . . . 50 set b contains 104 , 106 . . . 150 number of terms in each set = 24 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 24 = 2400 answer a"
Answer: a
Question (general): for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 8.2 – 8.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 8.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 8.2 – 8.2 * = 8.2 - 6 = 2.2 answer : d ."
Answer: d
Question (general): ( 1000 ) 7 ÷ ( 10 ) 20 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 20 = ( 10 ) 21 / ( 10 ) 20 = 10 ( 1 ) = 10 option a"
Answer: a
Question (general): a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number v is
Options: a ) 74 , b ) v = 75 , c ) v = 175 , d ) v = 680 , e ) 690
Rationale: i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb
Answer: b