Cheukting/mathqa huggingface dataset:
Question (gain): jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 50,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 25,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 50,000 i . e . rs . 25,000 answer : c"
Answer: c
Question (general): the difference between the place values of 7 and 3 in the prime number 527435 is
Options: a ) 4 , b ) 5 , c ) 45 , d ) 6970 , e ) none
Rationale: "solution ( place value of 7 ) - ( place value of 3 ) = ( 7000 - 30 ) = 6970 . answer d"
Answer: d
Question (other): in a certain school , the ratio of boys to girls is 5 to 13 . if there are 160 more girls than boys , how many boys are there ?
Options: a ) 100 , b ) 36 , c ) 45 , d ) 72 , e ) 117
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 160 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 160 . so 1 part corresponds to 160 / 8 = 20 and so 5 parts correspond to 5 * 10 = 100 . a"
Answer: a
Question (physics): ajay can walk 4 km in 1 hour . in how many hours he can walk 40 km ?
Options: a ) 5 hrs , b ) 10 hrs , c ) 15 hrs , d ) 20 hrs , e ) 30 hrs
Rationale: "1 hour he walk 4 km he walk 40 km in = 40 / 4 * 1 = 10 hours answer is b"
Answer: b
Question (general): ramesh has solved 108 questions in an examination . if he got only ‘ 0 ’ marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer .
Options: a ) 78 , b ) 79 , c ) 80 , d ) 81 , e ) 82
Rationale: if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d
Answer: d
Question (geometry): what is the measure of the angle x made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c"
Answer: c
Question (gain): after decreasing 15 % in the price of an article costs rs . 915 . find the actual cost of an article ?
Options: a ) 915 , b ) 1000 , c ) 1076 , d ) 1067 , e ) 1760
Rationale: "cp * ( 85 / 100 ) = 915 cp = 10.76 * 100 = > cp = 1076 answer : c"
Answer: c
Question (physics): dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 12 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "dan can complete 1 / 15 of the job per hour . in 12 hours , dan completes 12 ( 1 / 15 ) = 4 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 1 / 5 / 1 / 10 = 2 hours . the answer is a ."
Answer: a
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 17 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 26 ° , d ) 36 ° , e ) 52 °
Rationale: here all percentage when summed we need to get 100 % . as per data 17 + 24 + 15 + 29 + 8 = 93 % . so remaining 7 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 7 % will be 26 degrees . . imo option c .
Answer: c
Question (gain): find the c . i . on a sum of rs . 1600 for 9 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 3388 , b ) 2778 , c ) 2522 , d ) 2988 , e ) 2771
Rationale: "a = 1600 ( 21 / 20 ) 3 = 2522 answer : c"
Answer: c
Question (gain): if the cost price of 20 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 20 % loss , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 50 % loss
Rationale: "explanation : 20 cp = 25 sp cost price cp = 25 selling price sp = 20 formula = ( sp - cp ) / cp * 100 = ( 20 - 25 ) / 25 * 100 = 20 % loss answer : option a"
Answer: a
Question (gain): peter invests a sum of money and gets back an amount of $ 830 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 664 , c ) 698 , d ) 758 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 830 = 24 interest earned for 3 years = 24 * 3 = 72 amount invested = 830 - 72 = 758 answer : d"
Answer: d
Question (general): the simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months . how much amount was borrowed ?
Options: a ) 15000 , b ) 25000 , c ) 7500 , d ) 14500 , e ) none of these
Rationale: let the amount be x . from the question , x × 14 × 6 / 1200 − x × 8 × 8 / 1200 = 250 ∴ x = 15000 answer a
Answer: a
Question (general): how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 57 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 5
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 5 . so , one more solution , where a = b is not possible . so , answer will be e ."
Answer: e
Question (gain): if $ 120 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 340 , e ) $ 450
Rationale: "120 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 120 + 120 * ( r / 100 ) * ( 3 ) = 240 = > r = 100 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 450 answer is e ."
Answer: e
Question (gain): redo ’ s manufacturing costs for sets of horseshoes include a $ 10,500 initial outlay , and $ 30 per set . they can sell the sets $ 60 . if profit is revenue from sales minus manufacturing costs , and the company producessells 1000 sets of horseshoes , what was their profit ?
Options: a ) $ 19500 , b ) $ 15500 , c ) $ 29500 , d ) $ 39500 , e ) $ 1500
Rationale: "total manufacturing cost = 10500 + 1000 * 30 = 40500 total selling cost = 1000 * 60 = 60000 profit = 60000 - 40500 = 19500 answer : a"
Answer: a
Question (general): a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 9 : 6 : 5 , respectively , by weight . if 40 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4
Rationale: we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 9 x + 6 x + 5 x = 40 20 x = 40 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 5 ) ( 2 ) = 10 pounds of apples = ( 9 ) ( 2 ) = 18 thus we know that there are 18 – 10 = 8 more pounds of apples than grapes . answer is c .
Answer: c
Question (gain): the population of a town increases 20 % and 25 % respectively in two consecutive years . after the growth the present population of the town is 1500 . then what is the population of the town 2 years ago ?
Options: a ) a ) 1000 , b ) b ) 1100 , c ) c ) 1200 , d ) d ) 1300 , e ) e ) 1400
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1500 * 100 / 120 * 100 / 125 = 1000 answer : option a"
Answer: a
Question (general): when a random experiment is conducted , the probability that event a occurs is 1 / 4 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 14 / 65 , b ) 27 / 128 , c ) 33 / 140 , d ) 37 / 165 , e ) 41 / 187
Rationale: "one case is : 1 / 4 * 1 / 4 * 3 / 4 * 3 / 4 = 9 / 256 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 9 / 256 ) = 27 / 128 the answer is b ."
Answer: b
Question (general): what is the thousandths digit in the decimal equivalent of 64 / 5000 ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 6
Rationale: "64 / 5000 = 64 / ( 5 * 10 ^ 3 ) = ( 64 / 5 ) * 10 ^ - 3 = 12.8 * 10 ^ - 3 = . 0128 thousandths digit = 2 answer a"
Answer: a
Question (general): find the average of all the numbers between 6 and 34 which are divisible by 5 .
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 32
Rationale: "solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 5 = 20 . answer b"
Answer: b
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.32 , b ) 0.44 , c ) 32 , d ) 44 , e ) 55
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 24 = 32 cents . answer : c ."
Answer: c
Question (physics): a train running at the speed of 162 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 405 meter , e ) 265 meter
Rationale: "speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time ( 45 ) * 9 = 405 meter answer : d"
Answer: d
Question (general): a student has to obtain 30 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?
Options: a ) 750 , b ) 600 , c ) 650 , d ) 550 , e ) 500
Rationale: "let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b"
Answer: b
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 5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 7200 , d ) 2870 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 5 = 7200 . answer : c"
Answer: c
Question (general): we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 560 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 50 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b ."
Answer: b
Question (general): among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 10 % of listco ' s sales staff . listco employs 72 level - 1 employees , 20 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 46 , b ) 48 , c ) 56 , d ) 32 , e ) 58
Rationale: "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 72 and that c and l 1 = 0.10 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.1 x = 20 , therefore the grand total is 200 . now we know that l 2 is 200 - 72 = 128 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 52 = 48 . thus b is the correct answer choice"
Answer: b
Question (gain): the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1498 respectively . what is the rate of interest ?
Options: a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %
Rationale: "1498 - 1400 = 98 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 98 ) / ( 1400 ) = 7 % the answer is c ."
Answer: c
Question (physics): a man can row 9 kmph in still water . when the river is running at 3.1 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 2.21 , b ) 2.48 , c ) 9.24 , d ) 7.29 , e ) 7.94
Rationale: "m = 9 s = 3.1 ds = 12.1 us = 5.9 x / 12.1 + x / 5.9 = 1 x = 3.97 d = 3.97 * 2 = 7.94 answer : e"
Answer: e
Question (other): a man invests some money partly in 12 % stock at 105 and partly in 8 % stock at 88 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 31 : 44 , b ) 31 : 27 , c ) 16 : 15 , d ) 35 : 44 , e ) 35 : 27
Rationale: "n case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer : option d"
Answer: d
Question (physics): a man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 15 / 2 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 15 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 15 , d = 15 b - 15 c ; every 5 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 15 b - 15 c = 5 b + 5 c , - - > b = 2 c , - - > d = 15 b - 15 b / 2 = 15 b / 2 . interval = \ frac { d } { b } = \ frac { 15 / 2 b } { b } = 15 / 2 answer : e ( 15 / 2 minutes ) ."
Answer: e
Question (general): rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a
Answer: a
Question (general): a number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 7 / 3 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b"
Answer: b
Question (general): how many of the positive divisors of 240 are also multiples of 4 not including 240 ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 12
Rationale: "240 = 2 ^ 4 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 1 , and 1 . there are ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 240 . the answer is d ."
Answer: d
Question (general): one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?
Options: a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31
Rationale: connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d
Answer: d
Question (gain): in the manufacture of a certain product , 6 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.3 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "0.06 * 0.05 = 0.003 = 0.3 % the answer is b ."
Answer: b
Question (general): in a group of ducks and cows , the total number of legs are 26 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c"
Answer: c
Question (physics): a man walking at 3 / 4 th of the speed , reaches his office late by 2 hours . what is the usual time ?
Options: a ) 5 hours , b ) 3 hours , c ) 6 hours , d ) 12 hours , e ) 15 hours
Rationale: at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c
Answer: c
Question (general): given a + b = 1 , find the value of 2 a + 2 b . two solutions are presented below . only one is correct , even though both yield the correct answer .
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 1
Rationale: because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 × 1 = 2 . correct answer d
Answer: d
Question (gain): a sum fetched total simple interest of 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 8925 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 45 % of p = 4016.25 or , p = 8925 answer a"
Answer: a
Question (general): what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 5 if each digit can be used only once in each number ?
Options: a ) 2210 , b ) 2220 , c ) 2230 , d ) 2240 , e ) 2250
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 555 ) = 2220 the answer is b ."
Answer: b
Question (general): a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 25 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 9 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 25 % are male i . e 25 / 100 * 20 = 5 geese ( males ) and now we know out of the total 20 geese , 5 are male , then 15 have to be female . now the ratio part , male geese ratios = 5 / 30 = 1 / 6 . - a female geese ratios = 15 / 70 = 3 / 14 - b cross multiply equations a and b and you get = 9 / 7 . ans e"
Answer: e
Question (physics): the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is ?
Options: a ) 288 , b ) 277 , c ) 308 , d ) 988 , e ) 112
Rationale: "other number = ( 11 * 7700 ) / 275 = 308 . answer : c"
Answer: c
Question (physics): a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 7 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 7 = 21 the answer is b ."
Answer: b
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of four metre is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 4 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 4 + 4 = 30 meter answer is e ."
Answer: e
Question (general): each of the integers from 1 to 17 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: "out of the 17 integers : 9 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )"
Answer: d
Question (general): the averge score of a cricketer for 10 matches is 45 runs . if the average for the first 6 matches is 48 . then find the average for the last 4 matches ?
Options: a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36
Rationale: sum of last 4 matches = ( ( 10 × 45 ) – ( 6 × 48 ) = 162 average = 162 / 4 = 40.5 answer : d
Answer: d
Question (gain): a shopkeeper fixes the marked price of an item 40 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 23.85 % , b ) 22.85 % , c ) 21.85 % , d ) 20.85 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 140 required gain = 8 % , so selling price = rs 108 discount = 140 - 108 = 32 discount % = ( 32 / 140 ) * 100 = 22.85 % option b"
Answer: b