Cheukting/mathqa huggingface dataset:
Question (gain): in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 3000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 23000 , b ) 22000 , c ) 20000 , d ) 25000 , e ) 30000
Rationale: "winner - looser 55 % - 45 % if 3000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 3,000 people compose 10 % of all voters , which means that the total number of votes is 30,000 . answer : e ."
Answer: e
Question (general): a departmental store has 9 managers and 18 associates . the 9 managers have an average salary of $ 1300 . the 18 associates have an average salary of $ 12000 . what is the average salary for the departmental store ?
Options: a ) $ 3556.25 , b ) $ 3988.89 , c ) $ 3836.56 , d ) $ 3745.56 , e ) $ 3428.56
Rationale: number of managers is 9 their average salary is $ 1300 number of associates is 18 their average salary is $ 12,000 total salary of managers is 9 * 1300 = $ 11700 total salary of associates is 18 * 12,000 = $ 96,000 total salary for the departmental store is 96,000 + 11700 = 107700 average salary for the departmental store is 107700 / 9 + 18 = 3988.89 answer is b
Answer: b
Question (other): how many different positive integers are factors of 256 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 16 , e ) 18
Rationale: "16 × 16 = 4 ^ 2 × 4 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d"
Answer: d
Question (other): find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 ?
Options: a ) 240 / 1576 , b ) 240 / 1542 , c ) 240 / 1547 , d ) 240 / 1528 , e ) 240 / 1529
Rationale: "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c"
Answer: c
Question (general): a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 70 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 36 % , e ) 50 %
Rationale: say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 70 % more ie . , 170 recliners hence her sales tields 170 * 80 = $ 13600 increase in sales = 13600 - 10000 = $ 3600 so % increase = 3600 * 100 / 10000 = 36 % d is the answer
Answer: d
Question (general): the least number , which when divided by 12 , 31 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 16748 , d ) 548 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 31 , 20 , 54 ) + 8 = 16740 + 8 = 16748 . answer : c"
Answer: c
Question (general): timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey . if he made no stops during the trip and his average speed for the entire journey was 40 mph , for what fraction of the total time did he drive at 50 mph ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 3 / 4 , e ) 3 / 5
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire journey was 40 mph , then he drove at 50 mph for a longer duration of time . 10 30 10 - - 40 - - - - - - 50 this shows that you can divide the entire journey into 4 equal parts . thus , 3 / 4 part he drove at 50 mph and 1 / 4 part he drove at 10 mph . answer : d
Answer: d
Question (physics): a certain car uses 12 gallons of gasoline in traveling 420 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "420 / 10 = 42 the difference is 42 - 35 = 7 . answer d"
Answer: d
Question (general): in august , a cricket team that played 120 matches won 26 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 65 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 31.2 + x by solving we get x = 65 answer : c"
Answer: c
Question (general): the average weight of a , b and c is 65 kg . if the average weight of a and b be 60 kg and that of b and c be 70 kg , then the weight of a is :
Options: a ) 55 kg , b ) 65 kg , c ) 75 kg , d ) 45 kg , e ) 63 kg
Rationale: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 65 x 3 ) = 195 â € ¦ . ( i ) a + b = ( 60 x 2 ) = 120 â € ¦ . ( ii ) b + c = ( 70 x 2 ) = 140 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 260 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 65 . substituting b in ( ii ) a + 65 = 120 a = 55 a â € ™ s weight = 55 kg . answer a"
Answer: a
Question (physics): a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1
Rationale: "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 = > 4 days answer a"
Answer: a
Question (general): if a ^ 2 + b ^ 2 = 15 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2
Options: a ) 10 , b ) 20 , c ) 60 , d ) 30 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 15 - 20 = - 5 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 15 + 20 = 35 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 35 - 5 = 30 d"
Answer: d
Question (general): a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 105 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 27 , c ) 25 , d ) 15 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 105 × 9 / 35 = 3 × 9 = 27 answer is b ."
Answer: b
Question (physics): mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 80 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 35 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 80 , t = t d = 80 t since they went the same distance : 50 t + 50 / 4 = 80 t 30 t = 50 / 4 = 50 / 120 * 60 = 25 min t = 25 min d
Answer: d
Question (general): in a recent head - to - head run - off election , 18,000 absentee ballets were cast . 3 / 7 of the absentee ballets were thrown out and 2 / 9 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "4 / 7 * 7 / 9 ( total absentee votes ) = 4 / 9 ( total votes ) = 4 / 9 * 18000 = 8000 answer is d"
Answer: d
Question (other): how many multiples of 2 are there between 10 and 100 ( both are inclusive ) ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 46 , e ) 3
Rationale: the answer is ( 100 - 10 ) / 2 + 1 = 46 answer is d
Answer: d
Question (gain): if 25 % of a number exceeds 8 % of it by 11.9 , then find the number ?
Options: a ) 76 , b ) 70 , c ) 55 , d ) 65 , e ) 22
Rationale: "use the elimination method to find the correct option . of all the options only 70 fits 25 % of 70 = 17.5 8 % of 70 = 5.6 17.5 - 5.6 = 11.9 required number is 70 . answer : b"
Answer: b
Question (general): in a 20 litre mixture ratio of milk and water is 3 : 1 . how much milk should added so that mixture ratio become 4 : 1 ?
Options: a ) 3 , b ) 2 , c ) 8 , d ) 6 , e ) 5
Rationale: amount of milk = 20 × 3 / 4 = 15 litre and water = 5 litre let x litre milk to be added then 15 + x / 5 = 4 / 1 = 15 + x = 20 , x = 5 answer e
Answer: e
Question (gain): the price of an item is discounted 5 percent on day 1 of a sale . on day 2 , the item is discounted another 5.00001 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 80 % , b ) 82.5 % , c ) 83 % , d ) 84 % , e ) 85.5 %
Rationale: "let initial price be 100 price in day 1 after 5 % discount = 95 price in day 2 after 5 % discount = 90.25 price in day 3 after 10 % discount = 81.23 so , price in day 3 as percentage of the sale price on day 1 will be = 81.23 / 95 * 100 = > 85.5 % answer will definitely be ( e )"
Answer: e
Question (physics): a 14 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 4
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 14 = 4 answer : e"
Answer: e
Question (geometry): what is the smallest positive perfect square that is divisible by 9 , 15 , and 25 ?
Options: a ) 100 , b ) 225 , c ) 900 , d ) 1,600 , e ) 4,900
Rationale: "the number needs to be divisible by 3 ^ 2 , 3 * 5 , and 5 ^ 2 . the smallest such perfect square is 3 ^ 2 * 5 ^ 2 = 225 the answer is b ."
Answer: b
Question (general): a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 18.1 , c ) 17.5 , d ) 18.7 , e ) 19.1
Rationale: a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.50 + $ 15.6 = $ 18.1 . answer : b .
Answer: b
Question (physics): water is poured into a tank so that the tank is being filled at the rate of 5 cubic feet per hour . if the empty rectangular tank is 10 feet long , 6 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ?
Options: a ) 40
b ) 45
c ) 50
d ) 55
e ) 60
Rationale: the volume the tank is : length * width * depth = 10 * 6 * 5 = 300 cubic feet . 300 cubic feet / 5 cubic feet per hour = 60 hours . it will take 60 hours to fill the tank . the answer is e .
Answer: e
Question (physics): a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 69 km downstream .
Options: a ) 3.6 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 13 km / hr speed of the stream = 6 km / hr speed downstream = ( 13 + 6 ) = 19 km / hr time taken to travel 69 km downstream = 69 â  „ 19 = 17 â  „ 4 = 3.6 hours answer is a"
Answer: a
Question (probability): a string of 50 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.05 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.05 , b ) ( 0.05 ) ^ 50 , c ) 1 - ( 0.96 ) ^ 50 , d ) 1 - ( 0.95 ) ^ 50 , e ) ( 0.95 ) ^ 50
Rationale: the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 50 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.05 = 0.95 the the probability that none of the 50 light bulbs fails is 0.95 ^ 50 . hence , the probability that at least one light bulb fails is 1 - 0.95 ^ 50 . answer : d . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 50 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.05 = 5 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) .
Answer: d
Question (gain): a sum was put at simple interest at a certain rate for 7 years had it been put at 2 % higher rate , it would have fetched 140 more . find the sum .
Options: a ) 500 , b ) 750 , c ) 1000 , d ) 1250 , e ) 1500
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 140 = p × 7 x 2 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 140 × 100 / 7 × 2 = 1000 answer 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 8 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 8 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 = 8 3 x - 2 ( 8 - x ) = 25 3 x - 16 + 2 x = 25 5 x = 41 x = 8.2 or between 8 and 9 . 9 ans c )"
Answer: c
Question (general): a positive 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 ?
Options: a ) 7 / 3 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "sq rt ( 7 x / 3 ) = x = > 7 x / 3 = x ^ 2 = > x = 7 / 3 ans - a"
Answer: a
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 23 , b ) 19 , c ) 42 , d ) 20 , e ) 21
Rationale: "let the total number of workers be x . then , 8000 x = ( 18000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 84000 = x = 42 . answer : c"
Answer: c
Question (general): a company charges a fixed rental of rs . 350 per month . it allows 200 calls free per month . each call is charge at rs . 1.4 when the number of calls exceed 200 per month and it charges rs . 1.6 when the number of calls exceeds 400 per month and so on . a customer made 150 calls in february and 250 calls in march . by how much percent each call is cheaper in march than each call in february .
Options: a ) 28 % , b ) 25 % , c ) 18.5 % , d ) 16 % , e ) none of these
Rationale: solution : charge per call in february = 350 / 150 = 7 / 3 = 2.33 charge per call in march = [ 350 + ( 50 * 1.4 ) ] / 250 = 420 / 250 = 42 / 25 = 1.68 % cheaper call rate in march = [ ( 2.33 - 1.68 ) / 2.33 ] * 100 = 28 % . answer : option a
Answer: a
Question (general): 3 * 12 + 3 * 13 + 3 * 16 + 11 = ?
Options: a ) 122 , b ) 126 , c ) 134 , d ) 148 , e ) 151
Rationale: 3 * 12 + 3 * 13 + 3 * 16 + 11 = 36 + 39 + 48 + 11 = 134 the answer is c .
Answer: c
Question (general): a certain roller coaster has 7 cars , and a passenger is equally likely to ride in any 1 of the 7 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 7 times , what is the probability that the passenger will ride in each of the 7 cars ?
Options: a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 720 / 16807 , e ) 1
Rationale: "if he is to ride 6 times and since he can choose any of the 6 cars each time , total number of ways is = 7 * 7 * 7 * 7 * 7 * 7 = 117649 now the number of ways if he is to choose a different car each time is = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 so the probability is = 5040 / 117649 = 720 / 16807 answer : d"
Answer: d
Question (physics): what is the greatest of 3 consecutive integers whose sum is 18 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 18 ; = > 3 n = 15 ; = > n = 5 the greatest of the three numbers is therefore 5 + 2 = 7 answer : b"
Answer: b
Question (gain): a man can row his boat with the stream at 16 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 3 kmph , c ) 6 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 16 us = 4 s = ? s = ( 16 - 4 ) / 2 = 6 kmph answer : c"
Answer: c
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 6.0 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 1,800
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 6 $ then total value is 300 * 6.0 = 1800 . imo option e is correct answer . ."
Answer: e
Question (other): a certain quantity of 45 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 45 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 20 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 10 % . therefore , 10 out of 20 is 1 / 2 and c is the answer ."
Answer: c
Question (general): there are 16 bees in the hive , then 8 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 24 , e ) 25
Rationale: 16 + 8 = 24 . answer is d .
Answer: d
Question (general): let raj be 3 years older than ravi and hema be two years younger than ravi . raj is 3 times as old as rahul who is hema ’ s brother . the ratio of the ages of hema and her brother is 3 : 2 . find by how much percentage raj ’ s age is more than hema ’ s when raj will be 20 years old .
Options: a ) 33.33 , b ) 27.33 , c ) 28.38 , d ) 29.37 , e ) 28.31
Rationale: answer : 33.33
Answer: a
Question (gain): the salaries of a and b together amount to $ 6000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 4500 , e ) $ 5200
Rationale: "let a ' s salary is x b ' s salary = 6000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 6000 - x ) x = $ 4500 answer is d"
Answer: d
Question (general): gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 50 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 70
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 50 . thus , 3434 ( 90 + x ) = 50 + x or 270 + 3 x = 200 + 4 x or x = 70 answer : e"
Answer: e
Question (geometry): the diagonal of a rectangle is cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
Options: a ) 18
b ) 77
c ) 625
d ) 276
e ) 191
Rationale: explanation : ( or ) { \ color { black } l ^ { 2 } + b ^ { 2 } = 41 } also , { \ color { black } ( l + b ) ^ { 2 } = l ^ { 2 } + b ^ { 2 } + 2 lb } = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . answer : a ) 18
Answer: a
Question (gain): an empty fuel tank with a capacity of 214 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 106
Rationale: say there are a gallons of fuel a in the tank , then there would be 214 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 214 - a gallons of fuel b is 0.16 ( 214 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 214 - a ) = 30 - - > a = 106 . answer : e .
Answer: e
Question (other): if 27.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 638 , b ) 330 , c ) 550 , d ) 430 , e ) 880
Rationale: "students enrolled in biology are 27.5 % and therefore not enrolled are 72.5 % . so of 880 is 880 * . 225 = 638 answer is a 638"
Answer: a
Question (other): the ratio of local and international calls made by amy this week is 5 to 2 . if the ratio changes to 5 to 3 after amy makes 3 more international calls , how many local calls did amy make this week ?
Options: a ) 3 , b ) 5 , c ) 10 , d ) 15 , e ) 21
Rationale: the ratio of local and international calls made by amy this week is 5 to 2 let the current ratio be 5 x / 2 x the ratio changes to 5 to 3 after amy makes three more international calls 5 x / ( 2 x + 3 ) = 5 / 3 solving we get x = 3 initial ratio 15 : 6 ( 5 : 2 ) final ratio 15 : ( 6 + 3 ) = 15 : 9 = 5 : 3 so total number of local calls = 15 answer : d
Answer: d
Question (gain): on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is :
Options: a ) 10 % , b ) 10.5 % , c ) 12 % , d ) none of these , e ) can not be determined
Rationale: "solution difference in c . i . and s . i . for 2 years = rs . ( 696.30 - 660 ) = rs . 36.30 . s . i . for one year = rs . 330 . ∴ s . i . on rs . 330 for 1 year = rs . 36.30 . ∴ rate ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer d"
Answer: d
Question (geometry): what is the ratio between perimeters of two squares one having 4 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 4 : 1 , e ) 3 : 3
Rationale: "d = 4 d d = d a √ 2 = 4 d a √ 2 = d a = 4 d / √ 2 a = d / √ 2 = > 4 : 1 answer : d"
Answer: d
Question (physics): what is the distance covered by a train if it travels with a speed of 150 kmh for 8 hours ?
Options: a ) 1000 km , b ) 700 km , c ) 800 km , d ) 1400 km , e ) 1200 km
Rationale: "distance = time x speed distance = 150 x 8 = 1200 answer : e"
Answer: e
Question (general): following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 12 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 16 . , d ) 14 . , e ) 14.5
Rationale: "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 12 / 1.5 = 8 total price = 8 + 8 = 16 c is the answer"
Answer: c
Question (gain): of the 120 passengers on flight 750 , 55 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 58
Rationale: number of passengers on flight = 120 number of female passengers = . 5 * 120 = 66 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 66 - 8 = 58 answer e
Answer: e