regisss/math_qa huggingface dataset:
Problem: the average of 6 integers is 63 , and none of these integers is greater than 100 . if the average of 3 of the integers is 65 , what is the least possible value of one of the other two integers ?
Options: a ) 45 , b ) 62 , c ) 75 , d ) 83 , e ) 90
Rationale: when it comes to averages , we know thataverage value = ( sum of n values ) / n we can rewrite this into a useful formula : sum of n values = ( average value ) ( n ) the average of five integers is 63 so , the sum of all 5 integers = ( 63 ) ( 6 ) = 378 the average of three of the integers is 65 so , the sum of the 3 integers = ( 65 ) ( 3 ) = 195 so , the sum of the 2 remaining integers = 378 - 195 = 183 if the sum of the 2 remaining integers = 183 , and we want to minimize one value , we must maximize the other value . 100 is the maximum value so let 1 integer = 100 , which means the other must equal 83 answer : d
Answer: d
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ?
Options: a ) 3 hours , b ) 2.4 hours , c ) 1.4 hours , d ) 1 hour , e ) none of these
Rationale: "explanation : let the duration of the flight be x hours . then 600 / x − 600 / x + 1 / 2 = 200 600 / x − 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x − 3 = 0 = > ( 2 x + 3 ) ( x − 1 ) = 0 neglecting the negative value for x we get x = 1 option d"
Answer: d
Problem: what is the tens digit of 7 ^ 1415 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1415 = 4 * 353 + 3 the ten ' s digit will be 4 . answer e"
Answer: e
Problem: the ratio of 2 numbers is 3 : 4 and their h . c . f . is 4 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 48 , d ) 36 , e ) 60
Rationale: "let the numbers be 3 x and 4 x their h . c . f . = 4 so the numbers are 3 * 4 , 4 * 4 = 12,16 l . c . m . = 48 answer is c"
Answer: c
Problem: a 140 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 ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 40
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 140 = 40 answer : e"
Answer: e
Problem: the sum of 3 consecutive numbers is definitely :
Options: a ) positive , b ) divisible by 2 . , c ) divisible by 3 , d ) divisible by 4 . , e ) divisible by 5
Rationale: "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : c"
Answer: c
Problem: a tree is 12 m tall and casts an an 8 m long shadow . at the same time , a flag pole caste a 100 m long shadow . how long is the flag pole ?
Options: a ) 150 m , b ) 200 m , c ) 125 m , d ) 115 m , e ) none
Rationale: answer ∵ 8 m shadow means original height = 12 m ∴ 1 m shadow means original height = 12 / 8 m ∴ 100 m shadow means original height = ( 12 / 8 ) x 100 m = ( 6 / 4 ) x 100 = 6 x 25 = 150 m correct option : a
Answer: a
Problem: in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62
Rationale: "diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a"
Answer: a
Problem: if x is equal to the sum of the integers from 20 to 30 , inclusive , and y is the number of even integers from 20 to 30 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 361 , d ) 461 , e ) 561
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 20 + ( 11 - 1 ) * 1 } = 11 * 25 = 275 = x number of even number = ( 30 - 20 ) / 2 + 1 = 6 = y x + y = 275 + 6 = 281 b"
Answer: b
Problem: the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 36 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 36 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 36 x = 0.06 the answer is b ."
Answer: b
Problem: there are 60 slots around a circle , numbered 1 to 60 . a man starts fromthe first slot and jumps to the 5 th slot . from there he jumps to the 9 th slot andso on . in which slot will he land in his 2200 th jump ?
Options: a ) 1
b ) 5
c ) 41
d ) 45
e ) 46
Rationale: every 15 th jump , he comes back to 1 st position so , 2200 / 15 = remainder 10 hence 10 th position is 41 st slot answer : c
Answer: c
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 6 hrs , e ) 5 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 6 ) = 1 / 6 the cistern will be filled in 6 / 1 hrs i . e . , 6 hrs . answer : d"
Answer: d
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: if x ^ 2 + 1 / x ^ 2 = 9 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 72 , c ) 79 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 9 andsquareboth sides : ( x ² + 1 / x ² ) ² = 81 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 81 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 81 simplify : x ⁴ + 1 / x ⁴ = 79 answer : c"
Answer: c
Problem: a certain no . when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c"
Answer: c
Problem: a , b and c started a partnership business by investing rs . 24000 , rs . 32000 , rs . 36000 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 ) 92000 , e ) 50000
Rationale: "a : b : c = 24000 : 32000 : 36000 = 6 : 8 : 9 let total profit = p then p ã — 9 / 23 = 36000 p = ( 36000 ã — 23 ) / 9 = 92000 answer is d ."
Answer: d
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 60 / kg . how much did a kg of coffee cost in june ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 60 = > x = 60 e"
Answer: e
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 300 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 700 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 300 meters , thus second time she runs 2 * 300 = 600 meters . since second time ( when they run full circumference ) brenda runs 600 meters and sally runs 150 meters , thus the circumference is 600 + 150 = 750 meters . answer : d ."
Answer: d
Problem: a person travels equal distances with speeds of 8 km / hr , 9 km / hr and 10 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 7 km , d ) 5 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 8 + x / 9 + x / 10 = 47 / 60 x / 3 = 47 / 60 = > x = 2.33 . total distance = 3 * 2.33 = 6.99 km . answer : c"
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 127.05 , what is value of j ?
Options: a ) 300 , b ) 320 , c ) 370 , d ) 400 , e ) 450
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 127.05 here 127 is the quotient . given that remainder = 16 so , 127.05 = 127 + 16 / j so , j = 320 answer : b"
Answer: b
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 5 years will be
Options: a ) 22 : 17 , b ) 9 : 11 , c ) 5 : 4 , d ) 4 : 5 , e ) 8 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 5 ) : ( 12 + 5 ) = 22 : 17 answer : a"
Answer: a
Problem: there is an antique clock exhibition . so many clock are piled up with distinct numbers tagged with them . the person managing it hangs different clocks numbers periodically on the main wall . at 9 : 20 am , he hung the clock number 200 ; at 11 : 00 am , he hung the clock number 30 ; at 4 : 00 pm , he hung the clock number 240 . which numbered clock will he hang on the wall when the time is 7 : 30 pm ?
Options: a ) 313 , b ) 314 , c ) 315 , d ) 316 , e ) 317
Rationale: solution : he will hang clock number 315 at 7 : 30 pm . the person has been hanging the clock number which corresponds with the angle between the hour hand and the minute hand of the clock at that time . answer c
Answer: c
Problem: the mean of 30 values was 150 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) none of the above
Rationale: "corrected mean = 150 × 30 − 135 + 165 / 30 = 4500 − 135 + 165 / 30 = 4530 / 30 = 151 answer a"
Answer: a
Problem: machine a and machine b are each used to manufacture 550 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 5.5 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 550 qt = 500 for a : ( t + 10 ) ( q ) = 550 qt + 10 q = 550 500 + 10 q = 550 q = 5 so a can produce 5 / hour . then b can produce = 5 ( 1.1 ) = 5.5 / hour . a"
Answer: a
Problem: a batch of cookies was divided amomg 4 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 5 / 8
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 4 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 4 ) = 5 / 12 x = 5 / 8 answer : e"
Answer: e
Problem: there are , in a certain league , 8 teams , and each team face another team for a total of 12 times . how many games are played in the season ?
Options: a ) 150 , b ) 121 , c ) 144 , d ) 180 , e ) 1200
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 144 option c ."
Answer: c
Problem: a man spends rs . 1700 per month on an average for the first 3 months , rs 1550 for next 4 months and rs . 1800 per month for the last 5 months and saves rs . 5200 a year . what is his average monthly income ?
Options: a ) 2025 , b ) 2125 , c ) 2225 , d ) 2325 , e ) 2425
Rationale: explanation : total expenditure for the first 3 months = 3 ã — 1700 = 5100 total expenditure for 4 months = 4 ã — 1550 = 6200 total expenditure for 5 months = 5 ã — 1800 = 9000 total expenditure and saving ( which is income for one year ) = 5100 + 6200 + 9000 + 5200 = rs . 25500 so , average monthly income = 25500 / 12 = rs . 2125 answer b
Answer: b
Problem: 25 x 10 + 25 x 11 = ?
Options: a ) 725 , b ) 720 , c ) 600 , d ) 525 , e ) none of them
Rationale: "= 25 x ( 10 + 11 ) ( by distributive law ) = 25 x 21 = 525 answer is d"
Answer: d
Problem: the average of 25 results is 45 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 740 , b ) 750 , c ) 690 , d ) 780 , e ) 708
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 45 or , x = 708 . answer : option e"
Answer: e
Problem: the sale price sarees listed for rs . 400 after successive discount is 20 % and 15 % is ?
Options: a ) 297 , b ) 272 , c ) 342 , d ) 762 , e ) 269
Rationale: "400 * ( 80 / 100 ) * ( 85 / 100 ) = 272 answer : b"
Answer: b
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability q that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: the required probability q = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer .
Answer: d
Problem: in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.60 per kg , so that the mixture be worth rs 3.25 a kg ?
Options: a ) 3 / 5 , b ) 3 / 2 , c ) 5 / 3 , d ) 5 / 7 , e ) 7 / 3
Rationale: "c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.60 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.6 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.35 ) / ( 0.15 ) = 7 / 3 e"
Answer: e
Problem: of the families in city x in 1994 , 40 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 30 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?
Options: a ) 50 % , b ) 52 % , c ) 56 % , d ) 70 % , e ) 74 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 40 * 130 / 100 = 52 number of families in 1998 = 104 the percentage = 52 / 104 * 100 = 50 % . answer : a"
Answer: a
Problem: one - third less than 35 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 45
Rationale: lots of ways to tackle this . 35 % of 180 = 63 1 / 3 of 63 = 21 so , 1 / 3 less than 63 is equal to 63 - 21 = 42 answer : d
Answer: d
Problem: country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 420 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 214 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1080 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 420 mill / 2 month i . e . $ 210 mill / month difference / month = 210 - 120 = 90 difference / year = $ 90 mill * 12 = $ 1080 mill answer : e"
Answer: e
Problem: a company produces 65000 bottles of water everyday . if a case can hold 13 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 13 number of cases required to hold 65000 bottles = 65000 / 13 = 5000 cases . so the answer is c = 5000"
Answer: c
Problem: what will be the fraction of 5 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 5 * 1 / 100 = 1 / 20 . option a"
Answer: a
Problem: operation # is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 4 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Problem: calculate the area of a triangle , if the sides are 13 cm , 12 cm and 5 cm , what is its area ?
Options: a ) 36 cm 2
b ) 35 cm 2
c ) 30 cm 2
d ) 32 cm 2
e ) 31 cm 2
Rationale: the triangle with sides 13 cm , 12 cm and 5 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 12 * 5 = 30 cm 2 answer : c
Answer: c
Problem: 1 , 3,5 , 7,9 , . . 50 find term of sequnce for this .
Options: a ) 1356 , b ) 1557 , c ) 1688 , d ) 1700 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Problem: if a ^ 2 + b ^ 2 = 177 and ab = 54 then find the value of a + b / a - b ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 117 + 2 * 24 = 225 a + b = 15 ( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 117 - 2 * 54 a - b = 3 a + b / a - b = 15 / 3 = 5 answer is c ."
Answer: c
Problem: a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 210 pounds of the mixture ?
Options: a ) 150 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 210 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 210 = 150 pounds answer ( a )"
Answer: a
Problem: the simple interest on a sum of money will be rs . 1200 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 2400 , e ) 1732
Rationale: "p - - - 10 - - - - 1200 p - - - 5 - - - - - 600 3 p - - - 5 - - - - - 1800 - - - - - - = > 2400 answer : d"
Answer: d
Problem: pipe p can drain the liquid from a tank in 4 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 3 / 4 , d ) 17 / 29 , e ) 3 / 8
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 4 / 4 ) rq ] = 4 / 4 = 1 also , rp = rr / ( 2 / 3 ) = > 1 = rr / ( 2 / 3 ) = > rr = 2 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 1 + 2 / 3 = 8 / 3 = 1 / ( 3 / 8 ) thus running simultaneously , pipe q will drain 3 / 8 of the liquid . thus answer = e ."
Answer: e
Problem: a number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 4 = ( n / 4 ) - 4 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 8 â ‡ ’ ( 5 n - 4 n ) / 20 = 8 â ˆ ´ n = 160 option : a"
Answer: a
Problem: a , b , c together can earn $ 600 per day . while a and c together earn $ 400 and b and c together can earn $ 300 . the daily earnings of c ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 250 , d ) $ 300 , e ) $ 500
Rationale: b ' s daily earnings = 600 - 400 = $ 200 a ' s daily earnings = 600 - 300 = $ 300 c ' s daily earnings = 600 - 200 - 300 = $ 100 answer is a
Answer: a
Problem: a can do a piece of work in 3 days of 5 hours each and b alone can do it in 5 days of 3 hours each . how long will they take it to do working together 3 / 4 hours a day ?
Options: a ) 6 days , b ) 5 days , c ) 10 days , d ) 9 days , e ) 8 days
Rationale: a ' s work per hour = 1 / 15 b ' s work per hour = 1 / 15 a & b ' s work per hour together = ( 1 / 15 ) + ( 1 / 15 ) = 2 / 15 so a & b together complete the work in 15 / 2 hours . . . if they work 2 1 / 2 = 5 / 2 hours a day , it will take ( 15 / 2 ) / ( 3 / 4 ) days = 10 days . . . answer : c
Answer: c
Problem: if the price of a certain bond on may 1 st was 3 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 114.28 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 3 / 4 * 12 = 9 ; the price on july 1 st = 8 * 1.5 = 12 . the average price of the bond on may 1 st and july 1 st = ( 9 + 12 ) / 2 = 10.5 . the price of the bond on june 1 st ( 12 ) is 24 / 21 times ( 114.28 % ) the average price of the bond on may 1 st and july 1 st . answer : b .
Answer: b
Problem: a 300 m long train crosses a platform in 40 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 367 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 40 = 50 / 3 3 x + 900 = 2000 = > x = 367 m . answer : d"
Answer: d
Problem: the average age of a class of 25 students is 26 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 52 , d ) 62 , e ) 73
Rationale: "total age of all students = 25 ã — 26 total age of all students + age of the teacher = 26 ã — 27 age of the teacher = 27 ã — 26 â ˆ ’ 25 ã — 26 = 26 ( 27 â ˆ ’ 25 ) = 26 ã — 2 = 52 answer is c ."
Answer: c
Problem: the difference between two numbers is 1356 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 340
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 smaller number = 270 answer : b"
Answer: b
Problem: on a test , the boys in the class averaged 90 points and the girls in the class averaged 96 points . if the overall class average was 94 points , what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5
Rationale: ( 96 g + 90 b ) / ( g + b ) = 94 96 g + 90 b = 94 ( g + b ) 2 g = 4 b b / g = 1 / 2 the answer is a .
Answer: a
Problem: 9 - 3 ÷ 1 / 3 + 3 = ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: 9 - 3 1 / 3 + 3 = 9 - 3 ÷ 1 / 3 + 3 = 9 - ( 3 x 3 ) + 3 = 9 - 9 + 3 = 3 correct answer : b
Answer: b
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 5 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 5 n = > 35 q + 10 = > remainder = > 10 for some integer q alternatively = > n = 2 > 5 n = > 10 = > 10 divided by 7 will leave a remainder 3 hence c"
Answer: c
Problem: in the coordinate plane , points ( x , 2 ) and ( 8 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 8 , b ) 6 , c ) 5 , d ) 3 , e ) 2
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 2 ) = ( 4 , 2 ) and ( 8 , y ) = ( 8,4 ) - - > x + y = 4 + 4 = 8 . answer : a"
Answer: a