Cheukting/mathqa huggingface dataset:
Question (physics): mary can do a piece of work in 11 days . rosy is 10 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "ratio of times taken by mary and rosy = 110 : 100 = 11 : 10 suppose rosy takes x days to do the work . 11 : 10 : : 11 : x = > x = 10 days . hence , rosy takes 10 days to complete the work . answer : a"
Answer: a
Question (general): in a certain game of dice , the player ’ s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 24 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 1 / 216 , b ) 1 / 221 , c ) 1 / 212 , d ) 1 / 84 , e ) 1 / 42
Rationale: "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and jim will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : a ."
Answer: a
Question (other): 24 oz of juice p and 25 oz of juice v are mixed to make smothies m and y . the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie m ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d
Answer: d
Question (geometry): a volume of 10940 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 2735 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10940 l can be kept in ( 10940 / 4 ) hemispheres ans . 2735 answer : d"
Answer: d
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 80 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 87 , b ) 279 , c ) 80 , d ) 278 , e ) 379
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 / ( 80 - 40 ) = 1 hours so , the two trains meet at 11 a . m . the two trains meet 1 * 80 = 80 km away from mumbai . answer : c"
Answer: c
Question (general): 0 , 1 , 4 , 15 , 64 , ____
Options: a ) 225 , b ) 325 , c ) 125 , d ) 145 , e ) none
Rationale: "0 , 1,4 , 15,64 . . . . . 0 * 1 + 1 = 1 1 * 2 + 2 = 4 4 * 3 + 3 = 15 15 * 4 + 4 = 64 64 * 5 + 5 = 325 answer : b"
Answer: b
Question (general): virginia , adrienne , and dennis have taught history for a combined total of 93 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 40 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 93 = > 3 d = 93 + 27 = 120 = > d = 40 answer c"
Answer: c
Question (gain): if the simple interest on a certain sum of money for 5 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4 % , b ) 7 % , c ) 6 % , d ) 4 % , e ) 3 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 5 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 5 ) = 20 / 5 = 4 % answer : option d"
Answer: d
Question (general): how many six - digit numbers that do not contain the digits 5 or 8 are there ?
Options: a ) 483224 , b ) 156444 , c ) 229376 , d ) 816416 , e ) 316544
Rationale: "we can have 7 digits ( 1 , 2,3 , 4,6 , 7,9 ) for the first place ( hundred thousand ' s place ) . and similarly 8 digits for ten thousands , thousands , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 4,6 , 7,9 ) so in total 7 * 8 * 8 * 8 * 8 * 8 = 229376 hence c"
Answer: c
Question (general): simplify : 200 x 200 - 150 x 150
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 17500 , e ) none of them
Rationale: "( 200 ) ^ 2 - ( 150 ) ^ 2 = ( 200 + 150 ) ( 200 - 150 ) = 350 x 50 = 17500 . answer is d"
Answer: d
Question (general): a batsman in his 17 th innings makes a score of 80 and their by increasing his average by 3 . what is his average after the 17 thinnings ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "16 x + 80 = 17 ( x + 3 ) x = 27 + 3 = 30 answer : c"
Answer: c
Question (general): a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 90 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 5 % , b ) 4 % , c ) 3 % , d ) 2 % , e ) 1 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.9 ( 1.1 x ) = 0.99 x . the difference is 1 % . the answer is e ."
Answer: e
Question (general): a pharmaceutical company received $ 3 million in royalties on the first $ 30 million in sales of and then $ 9 million in royalties on the next $ 120 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 30 million in sales to the next $ 120 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 25 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 120 ) / ( 3 / 30 ) = 3 / 4 = 75 % it means that 9 / 120 represents only 75 % . therefore a decrease of 25 % . answer c"
Answer: c
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 126 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.85 , e ) 2.1
Rationale: "speed = 126 * 5 / 18 = 35 m / sec time taken = 100 / 35 = 2.85 sec . answer : d"
Answer: d
Question (physics): youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 8 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 12 , d ) 15 , e ) 20
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 480 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 480 - - - - > 40 x = 480 - - > x = 12 . option c"
Answer: c
Question (other): there are two names given johnson and jones . if one letter is picked from both simultaneously at random , then find the probability that the letter is same ?
Options: a ) 24 / 35 , b ) 17 / 35 , c ) 8 / 25 , d ) 6 / 35 , e ) 1 / 25
Rationale: this question can also be solved by using ' brute force ' - you just have to ' map out ' the possibilities . the namejohnsonhas 7 letters and the namejoneshas 5 letters , so there are ( 7 ) ( 5 ) = 35 possible pairings of letters that can occur . of those 35 , the pairings that include the same letter both times are : j and j 1 st o and o 1 st n and n s and s 2 nd o and o 2 nd n and n total : 6 so the probability that the two randomly selected letters will match is 6 / 35 . d
Answer: d
Question (general): the expression ( 11.98 × 11.98 + 11.98 × x + 0.02 × 0.02 ) will be a perfect square for x equal to
Options: a ) 0.02 , b ) 0.2 , c ) 0.04 , d ) 0.4 , e ) 4
Rationale: "solution given expression = ( 11.98 ) 2 + ( 0.02 ) 2 + 11.98 × x . for the given express to be a perfect square , we must have 11.98 × x = 2 × 11.98 × 0.02 or x = 0.04 . answer c"
Answer: c
Question (general): when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 101.50 , what was the total value of the item ?
Options: a ) $ 1,850 , b ) $ 2,450 , c ) $ 2,750 , d ) $ 3,150 , e ) $ 3,450
Rationale: "let x be the value in excess of $ 1,000 . 0.07 x = 101.5 x = $ 1,450 the total value was $ 1,450 + $ 1,000 = $ 2,450 . the answer is b ."
Answer: b
Question (physics): a and b go around a circular track of length 300 m on a cycle at speeds of 18 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 60 sec , d ) 665 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 300 / ( 90 * 5 / 18 ) , 300 / ( 54 * 5 / 18 ) } = lcm ( 12 , 20 ) = 60 sec . answer : c"
Answer: c
Question (general): the unit digit in the product 1457 * 7863 * 4575 * 9719 is ?
Options: a ) 5 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 7 * 3 * 5 * 9 = 5 answer is a"
Answer: a
Question (gain): tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 72000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 34000 , e ) 40000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 72000 = 40000 e"
Answer: e
Question (general): the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) .
Options: a ) 178.89 cm , b ) 178.29 cm , c ) 178.79 cm , d ) 177.89 cm , e ) 178.69 cm
Rationale: calculated average height of 35 boys = 180 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm = 180 * 35 cm - 166 cm + 106 cm / 35 = 180 cm - 60 / 35 cm = 180 cm - 1.71 cm = 178.29 cm . answer : b
Answer: b
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 70 sq . cm . find the length of the rectangle .
Options: a ) 12 cm , b ) 14 cm , c ) 16 cm , d ) 18 cm , e ) 20 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 70 = > 5 x - 25 = 70 = > x = 18 . length of the rectangle = 18 cm . answer : option d"
Answer: d
Question (general): a + 2 b = 6 , ab = 4 2 / a + 1 / b = ?
Options: a ) 3 / 2 , b ) 5 / 2 , c ) 7 / 2 , d ) 9 / 2 , e ) 11 / 2
Rationale: 2 / 2 + 1 / 2 = 1 + 1 / 2 = 3 / 2 answer : a
Answer: a
Question (general): a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 20 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 25 % , e ) 26 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.2 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 20 % income the savings increased by 100 % . or s = . 2 i or s = 20 % of income c is the answer"
Answer: c
Question (general): a fair 2 sided coin is flipped 6 times . what is the probability that tails will be the result at least twice , but not more than 5 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 7 / 8 , d ) 57 / 64 , e ) 15 / 16
Rationale: it would be easier to calculate the probability of opposite event and subtract it from 1 . opposite event : 0 tail , 1 tail , 6 tails . probability of getting no tails : 1 / 2 ^ 6 = 1 / 64 probability of getting 1 tail : 6 c 1 ∗ 1 / 2 ^ 6 = 6 / 64 , we must multiply by 6 c 1 or by 6 as tail can occur for any flip from 6 , hence in 6 ways ; probability of getting 6 tails : 1 / 2 ^ 6 = 1 / 6 ^ 4 p = 1 − ( 1 / 64 + 6 / 64 + 1 / 64 ) = 56 / 64 = 7 / 8 answer : c .
Answer: c
Question (general): a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find b ' s share .
Options: a ) rs . 2592 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 9 / 30 ) ã — 8640 ] = rs . 2592 answer : option a"
Answer: a
Question (physics): a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4 litres a minute . when the tank is full , the inlet is opened and due to the leak the tank is empty in 8 hours . the capacity of the tank ( in litres ) is
Options: a ) 5780 litres , b ) 5770 litres , c ) 5760 litres , d ) 5750 litres , e ) 5740 litres
Rationale: "explanation : work done by the inlet in 1 hour = 1 / 6 − 1 / 8 = 1 / 24 work done by inlet in 1 min = 1 / 24 ∗ 1 / 60 = 1 / 1440 = > volume of 1 / 1440 part = 4 liters volume of whole = ( 1440 * 4 ) litres = 5760 litres . option c"
Answer: c
Question (general): how many digits will be there to the right of the decimal point in the product of 95 and . 02554 ?
Options: a ) 6 , b ) 7 , c ) 4 , d ) 5 , e ) 8
Rationale: product of 95 and . 02554 is 2.4263 . therefore number of digits to right of decimal point is 4 answer is c .
Answer: c
Question (general): the average of first 9 odd numbers is ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "sum of 9 odd no . = 90 average = 81 / 9 = 9 answer : e"
Answer: e
Question (general): dacid obtained 86 , 85 , 92 , 87 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 89 , d ) 26 , e ) 75
Rationale: "average = ( 86 + 85 + 92 + 87 + 95 ) / 5 = 445 / 5 = 89 . answer : c"
Answer: c
Question (physics): david and andrew can finish the work 12 days if they work together . they worked together for 8 days and then andrew left . david finished the remaining work in another 8 days . in how many days david alone can finish the work ?
Options: a ) 30 days , b ) 60 days , c ) 70 days , d ) 80 days , e ) 24 days
Rationale: amount of work done by david and andrew in 1 day = 1 / 12 amount of work done by david and andrew in 8 days = 8 ã — ( 1 / 12 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 david completes 1 / 3 work in 8 days amount of work david can do in 1 day = ( 1 / 3 ) / 8 = 1 / 24 = > david can complete the work in 24 days answer : e
Answer: e
Question (other): a firm is comprised of partners and associates in a ratio of 2 : 63 . if 45 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 9 of the increase in 45 associates . the ratio changed from 18 : 567 to 18 : 612 . thus the number of partners is 18 . the answer is d ."
Answer: d
Question (gain): a , b and c started a partnership business by investing rs . 27000 , rs . 72000 , rs . 81000 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 ) 80000 , d ) 90000 , e ) 50000
Rationale: a : b : c = 27000 : 72000 : 81000 = 3 : 8 : 9 let total profit = p then p × 9 / 20 = 36000 p = ( 36000 × 20 ) / 9 = 80000 answer is c .
Answer: c
Question (general): a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30,000 , c receives :
Options: a ) s . 7,000 , b ) s . 7,200 , c ) s . 7,400 , d ) s . 7,700 , e ) s . 7,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 30000 x 12 / 50 ) = rs . 7,200 . b"
Answer: b
Question (gain): a pair of articles was bought for $ 50 at a discount of 20 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 31.25 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 80 % of x = 25 x = 25 * 100 / 80 = $ 31.25 answer is b"
Answer: b
Question (gain): what percentage of numbers from 1 to 60 have 1 or 9 in the unit ' s digit ?
Options: a ) 12 , b ) 14.11 , c ) 18.33 , d ) 20 , e ) 21
Rationale: "clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 60 are 1 , 9 , 11 , 19 , 21 , 29 , 31 , 39 , 41 , 49 , 51 , 59 number of such number = 11 answer : c"
Answer: c
Question (gain): shop offered 32 % offer for every shirt , smith bought a shirt at rs . 650 . and what was the shop ' s original selling price ?
Options: a ) 955 , b ) 550 , c ) 600 , d ) 700 , e ) 750
Rationale: "sp * ( 68 / 100 ) = 650 sp = 9.55 * 100 = > cp = 955 answer : a"
Answer: a
Question (gain): each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 96 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 25 , c ) 92 , d ) 96 , e ) 98
Rationale: out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 96 % water and 4 % of non - water , so now 1 pound of non - water composes 4 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.04 = 25 pounds . answer : b .
Answer: b
Question (general): a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 150 pounds and the average weight of the others being 160 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 16
Rationale: "lets assume there are 2 x people . half of them have average weight of 150 and other half has 160 . maximum weight is = 2500 so 150 * x + 160 * x = 2500 = > 310 x = 2500 = > x is approximately equal to 8 . so total people is 2 * 8 = 16 answer e ."
Answer: e
Question (physics): two trains start from p and q respectively and travel towards each other at a speed of 50 km / hr and 40 km / hr respectively . by the time they meet , the first train has traveled 100 km more than the second . the distance between p and q is ?
Options: a ) 900 km , b ) 300 km , c ) 700 km , d ) 800 km , e ) 100 km
Rationale: a 900 km at the time of meeting , let the distance traveled by the second train be x km . then , distance covered by the first train is ( x + 100 ) km . x / 40 = ( x + 100 ) / 50 50 x = 40 x + 4000 = > x = 400 so , distance between p and q = ( x + x + 100 ) km = 900 km .
Answer: a
Question (general): if grapes are 92 % water and raisins are 20 % water , then how many kilograms did a quantity of raisins , which currently weighs 5 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 50 , b ) 54 , c ) 55 , d ) 56 , e ) 60
Rationale: "let x be the original weight . the weight of the grape pulp was 0.08 x . since the grape pulp is 80 % of the raisins , 0.08 x = 0.8 ( 5 ) . then x = 50 kg . the answer is a ."
Answer: a
Question (general): a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 70 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 90 , c ) 73 , d ) 82 , e ) 91
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 70 ( subtracting twice of incorrect from correct ) 3 x = 270 x = 90 answer : b"
Answer: b
Question (other): there are 8 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "the total number of ways to form a team of 4 is 8 c 4 = 70 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 6 c 2 = 15 . the number of ways to form an acceptable team is 70 - 15 = 55 . the answer is b ."
Answer: b
Question (gain): redo ’ s manufacturing costs for sets of horseshoes include a $ 10,000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 4500 , b ) $ 3500 , c ) $ 5500 , d ) $ 5000 , e ) $ 6300
Rationale: total manufacturing cost = 10000 + 500 * 20 = 20000 total selling cost = 500 * 50 = 25000 profit = 25000 - 20000 = 5000 answer : d
Answer: d
Question (physics): a 300 meter long train crosses a pla ƞ orm in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the pla ƞ orm .
Options: a ) 310 meter , b ) 335 meter , c ) 345 meter , d ) 350 meter , e ) none of these
Rationale: explanation : speed = distance / ɵ me = 300 / 18 = 50 / 3 m / sec let the length of the pla ƞ orm be x meters then distance = speed ∗ timex + 300 = 503 ∗ 39 = > 3 ( x + 300 ) = 1950 = > x = 350 meters answer : d
Answer: d
Question (general): what is the smallest positive integer x such that ( x + 1 ) ^ 2 is divisible by 28 , 98 , 242 , and 308 ?
Options: a ) 153 , b ) 308 , c ) 121 , d ) 96 , e ) 511
Rationale: "28 = 2 * 2 * 7 98 = 2 * 7 * 7 242 = 2 * 11 * 11 308 = 2 * 2 * 7 * 11 so ( x + 1 ) ^ 2 = 2 * 2 * 7 * 7 * 11 * 11 , which means ( x + 1 ) = 2 * 7 * 11 = 154 , which means x = 153 , which is option a"
Answer: a
Question (general): 18 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 153 , c ) 210 , d ) 220 , e ) 230
Rationale: "1 st person will shake hand with 17 people 2 nd person will shake hand with 16 people 3 rd person will shake hand with 15 people . . . . . . total no . of handshakes = 17 + . . . + 3 + 2 + 1 = 17 * ( 17 + 1 ) / 2 = 153 or , if there are n persons then no . of shakehands = nc 2 = 18 c 2 = 153 answer : b"
Answer: b
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 700 grams per kg , what is his percent ?
Options: a ) 42.8 % , b ) 25 % , c ) 55 % , d ) 28 % , e ) 55 %
Rationale: "700 - - - 300 100 - - - ? = > 42.8 % answer : a"
Answer: a