Cheukting/mathqa huggingface dataset:
Question (geometry): the least perfect square , which is divisible by each of 21 , 36 and 66 is
Options: a ) 213414 , b ) 213424 , c ) 213434 , d ) 213444 , e ) none of these
Rationale: "explanation : l . c . m . of 21 , 36 , 66 = 2772 now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444 option d"
Answer: d
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 40 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.4 c ( 40 % profit ) x = 1.4 / . 8 * c x = 7 / 4 c original selling price is 1.75 c which is 75 % profit answer e"
Answer: e
Question (probability): in a throw of dice what is the probability of getting number greater than 5
Options: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 9
Rationale: "number greater than 5 is 6 , so only 1 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 1 / 6 b )"
Answer: b
Question (general): in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 4 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 147
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 4 % so total man = 150 * . 96 = 144 women will be = 175 - 144 = 31 so population after two years = [ 135 ^ 2 + 31 ^ 2 ] ^ . 5 = 147.30 = 147 so population after two year = 147 answer : e"
Answer: e
Question (general): if | x + 132 | = 32 what is the sum of all the values of x .
Options: a ) - 264 , b ) 200 , c ) - 64 , d ) 0 , e ) - 328
Rationale: there will be two cases x + 132 = 32 and x + 132 = - 32 solve for x = > x = 32 - 132 = > x = - 100 or x = - 32 - 132 = > x = - 164 the sum of both values will be - 164 + - 100 = - 264 answer is a
Answer: a
Question (other): of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 19 boys and 41 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 19 boys . so 19 - 6 - 6 = 7 boys must be neither happy nor sad . answer ( b )"
Answer: b
Question (gain): a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 64 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 48 , b ) 52 , c ) 54 , d ) 58 , e ) 56
Rationale: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 64 or 1 / 7 t + 1 t = 64 therefore t = 64 * 7 / 8 = 56 e"
Answer: e
Question (geometry): if the radius of a circle that centers at the origin is 5 , how many points q on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : q = c"
Answer: c
Question (geometry): the ratio of the radius of two circles is 1 : 5 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 2 : 9 , c ) 1 : 25 , d ) 3 : 7 , e ) 3 : 4
Rationale: "r 1 : r 2 = 1 : 5 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 1 : 25 answer : c"
Answer: c
Question (general): the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 98 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) a ) 318 , 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 * 98 + 6 * 65 - 11 * 60 = 318 answer is a
Answer: a
Question (gain): a man bought 40 shares of rs . 60 at 8 discount , the rate of dividend being 1212 % the rate of interest obtained is
Options: a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.42 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 8 = rs . 52 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 52 ) interest obtained = 40 × 7.5 × 100 / 40 × 52 = 14.42 % answer : option d"
Answer: d
Question (geometry): the area of a triangle is 615 m 2 . if one of its sides is 123 metre , find the length of the perpendicular dropped on that side from opposite vertex .
Options: a ) 15 metres
b ) 12 metres
c ) 10 metres
d ) 9 metres
e ) none of these
Rationale: in a triangle , area = 1 ⁄ 2 × length of perpendicular × base or 615 = 1 ⁄ 2 × length of perpendicular × 123 ∴ length of perpendicular = 615 × 2 / 123 = 10 m answer c
Answer: c
Question (gain): in an election between the two candidates , the candidates who gets 60 % of votes polled is wined by 280 votes majority . what is the total number of votes polled ?
Options: a ) 1400 , b ) 1500 , c ) 1600 , d ) 1700 , e ) 1800
Rationale: note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a
Answer: a
Question (general): solve the equation for x : 6 x - 47 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 6
Rationale: "e 6 9 x + x = 13 + 47 10 x = 60 = > x = 6"
Answer: e
Question (general): what is the remainder if 7 ^ 12 is divided by 100 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 7 ^ 16 can be written as ( 7 ^ 4 ) ^ 3 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 3 by 100 , the reminder is 1 ^ 3 = 1 answer : a
Answer: a
Question (general): calculate the average of all the numbers between 10 and 86 which are divisible by 9 .
Options: a ) 49.5 , b ) 41.5 , c ) 45.5 , d ) 40.5 , e ) 47.5
Rationale: "explanation : numbers divisible by 9 are 18,27 , 36,45 , 54,63 , 72,81 , average = ( 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 , ) / 8 = 396 / 8 = 49.5 answer : a"
Answer: a
Question (physics): what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 203 , b ) 211 , c ) 219 , d ) 227 , e ) 235
Rationale: speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 156 = 219 meters the answer is c .
Answer: c
Question (general): zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 6 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 6 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 6 3 x - 2 ( 6 - x ) = 25 3 x - 12 + 2 x = 25 5 x = 37 x = 7.4 or between 7 and 8 . ( ans b )"
Answer: b
Question (general): the average of first 17 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 18 , d ) 20 , e ) 24
Rationale: "sum of 17 even numbers = 17 * 18 = 306 average = 306 / 17 = 18 answer : c"
Answer: c
Question (general): the average of all odd numbers up to 200 is
Options: a ) 50 , b ) 100 , c ) 120 , d ) 75 , e ) 80
Rationale: "the numbers are 1,3 , 5,7 , - - - - - - - - , 197,199 average = ( 199 - 1 ) / 2 + 1 = 100 answer is b"
Answer: b
Question (physics): a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 11 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 11 + 10 = 21 . the answer is c ."
Answer: c
Question (other): the ratio between the presents of the a and b is 2 : 3 . if b is 5 years older than a , what will be the ratio of the ages of a and b after 5 years ?
Options: a ) 3 : 4 , b ) 1 : 2 , c ) 2 : 3 , d ) 5 : 6 , e ) 1 : 3
Rationale: "let a and b ages will be 2 x and 3 x 3 x - 2 x = 5 x = 5 required ratio = 2 x + 5 : 3 x + 5 = 15 : 20 = 3 : 4 answer is a"
Answer: a
Question (gain): a man gains 40 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 180 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 140 / 100 ) x = 7 x / 5 new s . p . = 2 ( 7 x / 5 ) = 14 x / 5 profit = 14 x / 5 - x = 9 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 9 x / 5 ) * ( 1 / x ) * 100 = 180 % option b"
Answer: b
Question (general): if x * y = xy – 2 ( x + y ) for all integers x and y , then 1 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 4 , d ) 4 , e ) 1
Rationale: "1 * ( - 3 ) = 1 * ( - 3 ) - 2 ( 1 + ( - 3 ) ) = - 3 + 4 = 1 option ( e )"
Answer: e
Question (gain): on increasing the price of t . v . sets by 40 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 12 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 140 × 80 ) = rs . 11200 increase % = 1200 / 10000 × 100 = 12 % answer : d"
Answer: d
Question (general): 0.002 x 0.5 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.01 , d ) 0.1 , e ) none of these
Rationale: "explanation : 2 x 5 = 10 . sum of decimal places = 4 0.002 x 0.5 = 0.001 answer - b"
Answer: b
Question (gain): a 10 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 125 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 10 , investment = rs . ( 100 / 8 x 10 ) = rs . 125 ∴ market value of rs . 100 stock = rs . 125 answer b"
Answer: b
Question (gain): a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 300 . find the sum ?
Options: a ) 7000 , b ) 2500 , c ) 2778 , d ) 2800 , e ) 2791
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 300 = > 36 x / 100 - 24 x / 100 = 300 = > 12 x / 100 = 300 = > x = 2500 . answer : b"
Answer: b
Question (general): at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 4 / 5 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 47 / 200 , b ) 31 / 200 , c ) 17 / 100 , d ) 11 / 100 , e ) 7 / 50
Rationale: "males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 5 * 2 / 5 = 2 / 25 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 25 = 31 / 200 the answer is b ."
Answer: b
Question (general): how many quarters are equal to 4 dollars ?
Options: a ) 16 , b ) 8 , c ) 12 , d ) 9 , e ) 7
Rationale: "4 * 4 = 16 quarters answer : a"
Answer: a
Question (general): 1391 x 1391 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1934881
Rationale: "1391 x 1391 = ( 1391 ) 2 = ( 1400 - 9 ) 2 = ( 1400 ) 2 + ( 9 ) 2 - ( 2 x 1400 x 9 ) = 1960000 + 81 - 25200 = 1960081 - 25200 = 1934881 . answer : e"
Answer: e
Question (physics): danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 33 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 16.5 minutes , b ) 33 minutes , c ) 49.5 minutes , d ) 66 minutes , e ) 99 minutes
Rationale: "danny ' s time is 33 minutes . the time to reach halfway is 16.5 minutes . steve ' s time is 66 minutes . the time to reach halfway is 33 minutes . the time difference is 33 - 16.5 = 16.5 minutes the answer is a ."
Answer: a
Question (gain): the compound interest on $ 30,000 at 7 % p . a is $ . 4347 . find out the period ( in years ) ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "amount = 30,000 + 4347 = 34347 . . . . . . . . . now by using compound interest formula we get , 30,000 * ( 107 / 100 ) ^ n = 34347 = = = = > n = 2 years ans - c"
Answer: c
Question (general): a fair 2 sided coin is flipped 4 times . what is the probability that tails will be the result at least twice , but not more than 4 times ?
Options: a ) 1 / 8 , b ) 2 / 3 , c ) 5 / 8 , d ) 4 / 7 , e ) 3 / 7
Rationale: "at least twice , but not more than 4 timesmeans exactly 2 times , 3 times , 4 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 4 c 2 / 2 ^ 4 + 4 c 3 / 2 ^ 4 = 10 / 16 = 5 / 8 option : c"
Answer: c
Question (general): i have only 1 $ and 2 $ note . i want to give 95 $ to john . how many maximum number of 1 $ note i need ?
Options: a ) 53 , b ) 35 , c ) 47 , d ) 95 , e ) 62
Rationale: "to give 95 $ we need of 95 1 $ notes so ans is d"
Answer: d
Question (general): how many multiples of 6 are less than 5000 , and also multiples of 8 ?
Options: a ) 104 , b ) 208 , c ) 625 , d ) 832 , e ) 833
Rationale: "lcm of 6 & 8 = 24 tried dividing 5000 by 24 got quotient 208.33 ' so b is answer"
Answer: b
Question (physics): audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 5 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 6 , c ) 15 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 5 breaks = . 3 / 5 = . 06 hrs = 6 m so answer is b ) 10 mins"
Answer: b
Question (geometry): find the sum of divisors of 544 which are perfect squares .
Options: a ) 32 , b ) 64 , c ) 42 , d ) 21 , e ) none of these
Rationale: "544 = 25 + 171 = ( 2 ) 0 + ( 2 ) 1 + ( 2 ) 2 + ( 2 ) 3 + ( 2 ) 4 + ( 2 ) 5 x ( 17 ) 0 + ( 17 ) 1 . here 20 = 1 = 11 a perfect square , 22 and 24 = 16 = 44 are perfect squares , hence , 1 + 4 + 16 = 21 . correct answer is : d"
Answer: d
Question (gain): a glass was filled with 10 ounces of water , and 0.03 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.006 % , b ) 0.06 % , c ) 0.6 % , d ) 6 % , e ) 60 %
Rationale: "we are given that 0.03 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20 . this gives us : 0.03 x 20 = 0.6 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.6 / 10 ) x 100 % ( 6 / 100 ) x 100 % = 6 % answer d"
Answer: d
Question (physics): a cistern is normally filled in 6 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 24 , d ) 99 , e ) 11
Rationale: 1 / 6 - 1 / x = 1 / 8 x = 24 answer : c
Answer: c
Question (physics): a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 50 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 50 percent 150 min . answer : b
Answer: b
Question (geometry): the diagonals of a rhombus are 10 cm and 12 cm . find its area ?
Options: a ) 158 , b ) 60 , c ) 150 , d ) 123 , e ) 117
Rationale: "1 / 2 * 10 * 12 = 60 answer : b"
Answer: b
Question (physics): a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm 3 , then the weight of the pipe is :
Options: a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) none
Rationale: "solution external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 × ( 42 ) - ( 32 ) × 21 ) cm 3 = ( 22 / 7 × 7 × 1 × 21 ) cm 3 = 462 cm 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"
Answer: b
Question (general): in the forestside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: given there are 50 students in the forestside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .
Answer: a
Question (general): on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 b )"
Answer: b
Question (physics): kathleen can paint a room in 4 hours , and anthony can paint an identical room in 5 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 40 / 9 , c ) 15 / 8 , d ) 9 / 4 , e ) 15 / 4
Rationale: "( 1 / 4 + 1 / 5 ) t = 2 t = 40 / 9 answer : b"
Answer: b
Question (general): if 0.75 : x : : 10 : 8 , then x is equal to :
Options: a ) a ) 0.6 , b ) b ) 0.8 , c ) c ) 0.85 , d ) d ) 0.5 , e ) e ) none
Rationale: "( x * 10 ) = ( 0.75 * 8 ) x = 6 / 10 x = 0.6 answer = a"
Answer: a
Question (general): there are 2 sections a and b in a class , consisting of 36 and 44 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?
Options: a ) 35.29 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 55.12 kg , e ) 29.78 kg
Rationale: total weight of 36 + 44 students = 36 * 44 + 44 * 35 = 2980 average weight of the class is = 2980 / 80 = 37.25 kg answer is b
Answer: b
Question (general): a box contains 100 pairs of shoes ( 200 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 199 , d ) 1 / 10 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 200 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 199 ( as after taking one at random there are 199 shoes left and only one is the pair of the first one ) = 1 / 199 answer : c ."
Answer: c
Question (general): the nasdaq index has decreased by 70 % since year 2000 . how much should the index increase in order to gain the same value as in year 2000 ?
Options: a ) 400 % , b ) 80 % , c ) 233 % , d ) 60 % , e ) none of the above
Rationale: let x be the index in the year 2000 . after the decrease it becomes 0.3 x now for 0.3 x to reach 1 x it has to raise by 0.7 x . the increase needs to be 0.7 x / 0.3 x * 100 = 233.3 % answer c
Answer: c
Question (physics): the sum of three consecutive numbers is 102 . the greatest among these three number is :
Options: a ) 26 , b ) 35 , c ) 29 , d ) 30 , e ) 31
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 102 3 x = 102 x = 33 greatest number , ( x + 2 ) = 35 . answer : b"
Answer: b
Question (general): a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 40 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 94 % , b ) 87.5 % , c ) 55 % , d ) 56.25 % , e ) 36 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 50 % impurities to the product . it means that he is selling $ 5 worth of product for $ 7.5 . so his profit is $ 7.5 - $ 4 = $ 3.5 and his profit percent is ( 3.5 / 4 ) * 100 = 87.5 % answer : - b"
Answer: b
Question (gain): if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 52 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 53.30 , b ) s . 53.22 , c ) s . 51.219 , d ) s . 53.18 , e ) s . 51.10
Rationale: explanation : sum = ( 52 * 100 ) / ( 2 * 5 ) = rs . 520 amount = [ 520 * ( 1 + 5 / 100 ) 2 ] = rs . 573.3 c . i . = ( 573.3 - 520 ) = rs . 53.30 . answer : a
Answer: a
Question (physics): 29 persons can repair a road in 16 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 12.88 , b ) 3.88 , c ) 13.88 , d ) 15 , e ) 18.8
Rationale: "let the required number of days be x more persons , less days ( indirect proportion ) more hours , less days ( indirect proportion ) hence we can write as ( persons ) 29 : 30 } : : x : 16 ( hours ) 5 : 6 29 * 5 * 16 = 30 * 6 * x x = 12.88 answer : a"
Answer: a