regisss/math_qa huggingface dataset:
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 11 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 123.20
Rationale: "correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.11 ( $ 1120 ) = $ 123.20 . the correct answer is e ."
Answer: e
Problem: how much is 60 % of 40 is greater than 4 / 5 of 30 ?
Options: a ) 8 , b ) 3 , c ) 7 , d ) 0 , e ) 1
Rationale: "( 60 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 24 - 24 = 0 answer : d"
Answer: d
Problem: a train speeds past a pole in 22 seconds and a platform 140 m long in 33 seconds . its length is ?
Options: a ) 280 , b ) 260 , c ) 300 , d ) 290 , e ) 270
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 22 = > y = x / 22 x + 140 / 33 = x / 22 x = 280 m . answer : a"
Answer: a
Problem: find the greatest number which on dividing 6215 and 7373 , leaves a reminder of 23 and 29 respectively
Options: a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 144
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 6215 - 23 ) and ( 7373 - 29 ) = hcf ( 6192 , 7344 ) = 144 option e"
Answer: e
Problem: an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are blue ?
Options: a ) 20 / 969 , b ) 20 / 875 , c ) 21 / 876 , d ) 3 / 512 , e ) 2 / 9
Rationale: "sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 3 blue balls were drawn from bag = 6 c 3 = 20 probability = 20 / 969 ans - a"
Answer: a
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 8 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 8 = 40 km imo , correct answer is ` ` c . ' '"
Answer: c
Problem: the sum of ages of 5 children born at the intervals of 2 years each is 55 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 7 , c ) 6 , d ) 9 , e ) 8
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 55 - 20 = 35 x = 7 . age of the youngest child = x = 7 years . answer : b"
Answer: b
Problem: what is the probability of getting a sum 9 from two throws of dice .
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these
Rationale: "explanation : total number of cases = 6 * 6 = 36 favoured cases = [ ( 3,6 ) , ( 4,5 ) , ( 6,3 ) , ( 5,4 ) ] = 4 so probability = 4 / 36 = 1 / 9 option b"
Answer: b
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 5 full , while jug y is 4 / 7 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 20 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 5 ) = l cx = 5 l liters cx is capacity of x cy x ( 4 / 7 ) = l cy = 7 l / 4 liters cy is capacity of y now , y is 7 l / 4 - l empty = 3 l / 4 empty so , we can put only 3 l / 4 water in jug y from jug x jug x ' s remaining water = l - 3 l / 4 = l / 4 fraction of x which contains water = water / cx = ( l / 4 ) / 5 l = 1 / 20 answer will be d"
Answer: d
Problem: two goods trains each 820 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 27.32 , c ) 76.6 , d ) 78.72 , e ) 21
Rationale: relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 820 + 820 = 1640 m . required time = 1640 * 6 / 125 = 78.72 sec . answer : d
Answer: d
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours c will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) c = 5 . , d ) c = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double c = 6 hrs . . so closest to that option is 5 ."
Answer: c
Problem: indu gave bindu rs . 1875 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 2 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "1875 = d ( 100 / 4 ) 2 d = 3 answer : d"
Answer: d
Problem: how many integers are between 7 and 57 / 4 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "57 / 4 = 14 . xx we are not concerned about the exact value of 57 / 4 as we just need the integers . since the values are small , we can write down the integers . the different integers between 7 and 57 / 4 would be 7 , 8 , 9 , 10 , 11 , 12 , 13,14 total number of integers = 8 option d"
Answer: d
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 9 : 32 , b ) 9 : 30 , c ) 32 : 9 , d ) 19 : 32 , e ) 18 : 30
Rationale: "water : soap = 3 : 4 soap : salt = 15 : 20 = > for 15 soap , salt = 20 = > for 4 soap , salt = ( 20 / 15 ) * 4 = 80 / 15 = 16 / 3 so , water : soap : salt = 3 : 4 : 16 / 3 = 9 : 12 : 16 after open container , water : soap : salt = 4.5 : 12 : 16 so , water : salt = 4.5 : 16 = 9 : 32 answer : a"
Answer: a
Problem: 3 / 5 * [ ( 2 / 3 + 3 / 8 ) / 2 ] - 1 / 16 =
Options: a ) 1 / 4 , b ) 19 / 16 , c ) 15 / 16 , d ) 9 / 13 , e ) 0
Rationale: we need to simplify the expression using pemdas . parentheses exponents multiplication anddivision addition andsubtraction the calculation of an equation or expression must be carried out in the following order : 1 ) operations within parentheses ( or absolute value bars or radicals ) 2 ) exponents 3 ) multiplication and division from left to right 4 ) addition and subtraction from left to right the answer is a .
Answer: a
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 100 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 76 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 100 * 3 = 300 miles . therefore , total distance covered = 80 + 300 = 380 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 380 / 5 = 76 miles per hour . choice e"
Answer: e
Problem: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 93 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 15 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 93 % water and 7 % of non - water , so now 1 pound of non - water composes 7 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.07 = 15 pounds . answer : b ."
Answer: b
Problem: the cost of the paint is rs . 50 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 20 feet each side
Options: a ) rs . 962 , b ) rs . 6000 , c ) rs . 546 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 20 ^ 2 = 2400 sq . ft quantity of paint required = ( 2400 / 20 ) = 120 kg cost of painting = 50 x 120 = rs . 6000 answer : b"
Answer: b
Problem: a man can row downstream at 25 kmph and upstream at 15 kmph . find the time to reach a destination point at a distance of 50 km along the downstream .
Options: a ) 4 hrs . , b ) 1 hrs . , c ) 3 hrs . , d ) 2 hrs . , e ) 2 1 / 2 hrs .
Rationale: "let the speed of the man in downstream = 25 kmph . distance to be covered along the stream = 50 kmph = > time taken = d / s = 50 / 25 = 2 hrs . answer : d"
Answer: d
Problem: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 160 meter length ?
Options: a ) 11 seconds , b ) 41.6 seconds , c ) 40 seconds , d ) 88 seconds , e ) 19 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 160 = 520 meter time = distance / speed = 520 * ( 2 / 25 ) = 41.6 seconds answer : b"
Answer: b
Problem: the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2016 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2016 14 x ^ 2 = 2016 x ^ 2 = 144 x = 12 answer is b"
Answer: b
Problem: a certain airline ' s fleet consisted of 90 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let x be the number of years . 4 x > 90 - 3 x 7 x > 90 x > 12 + 6 / 7 the answer is c ."
Answer: c
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 78 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 16.66 % , c ) 30 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 18 / 60 ) * 100 = ( 3 / 10 ) * 100 = 30 % . c"
Answer: c
Problem: what is the perimeter of a square field whose diagonal is 8 â ˆ š 2 ?
Options: a ) 64 m , b ) 32 m , c ) 30 m , d ) 16 m , e ) 18 m
Rationale: "explanation : a â ˆ š 2 = b â ˆ š 2 - > a = 8 4 a = 32 m answer is b"
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 37 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 250 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : a"
Answer: a
Problem: find the simple interest on $ 1000 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 1000 * 3 * 10 / 100 = $ 300 answer is b"
Answer: b
Problem: two pipes a and b can separately fill a cistern in 60 minutes and 75 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 50 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 110 min , d ) 120 min , e ) 130 min
Rationale: "1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 third pipe can empty in 100 minutes answer : b"
Answer: b
Problem: of the 20,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e
Answer: e
Problem: if jimmy drinks 8 ounces of water each time for 8 times a day . how much gallons of water he would have to prepare ahead to drink for 5 days ? ( 1 ounce = 0.0078125 gallon )
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: 8 ounces * 8 times / day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon . 5 days need 0.5 * 5 = 2.5 gallons . correct option : 2.5 answer : d
Answer: d
Problem: 100 people are attending a newspaper conference . 45 of them are writers and more than 36 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 26 , b ) 24 , c ) 18 , d ) 20 , e ) 22
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 45 + { editors } - x + 2 x - - > x = 55 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 37 , thus x = { both } = 55 - 37 = 18 . answer : c ."
Answer: c
Problem: two trains , a and b , started simultaneously from opposite ends of a 120 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 120 - mile trip in 6 hours ; train b , traveling at a constant rate , completed the 120 - mile trip in 4 hours . how many miles had train a traveled when it met train b ?
Options: a ) 28 , b ) 36 , c ) 48 , d ) 50 , e ) 54
Rationale: "as the ratio of the rates of a and b is 4 to 6 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 4 / ( 4 + 6 ) = 4 / 10 of 120 miles : 120 * 4 / 10 = 48 miles . answer : c ."
Answer: c
Problem: if a speaks the truth 55 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.29 , b ) 0.33 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 55 / 100 = 0.55 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.55 × 0.6 = 0.33 answer : b"
Answer: b
Problem: the closest approximation of ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . answer : c"
Answer: c
Problem: to complete a work a and b takes 8 days , b and c takes 12 days , a , b and c takes 6 days . how much time a and c will take
Options: a ) 24 days , b ) 16 days , c ) 12 days , d ) 8 days , e ) none of these
Rationale: explanation : a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + b + c 1 day work = 1 / 6 we can get a work by ( a + b + c ) - ( b + c ) and c by ( a + b + c ) - ( a + b ) so a 1 day work = 1 / 6 − 1 / 12 = 1 / 12 similarly c 1 day work = 1 / 6 − 1 / 8 = 4 − 3 / 24 = 1 / 24 so a and c 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 so a and c can together do this work in 8 days option d
Answer: d
Problem: 16 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 8 , e ) 7
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 16 = 7 answer : e"
Answer: e
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 34 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 34 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 30 / 10 = 3 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 3 = 12 + 4 = 16 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 16 / 4 = 4 hrs . . . answer b"
Answer: b
Problem: if log 2 x - 5 log x + 6 = 0 , then what would the value / values of x be ?
Options: a ) 5.3296 , b ) 6.3296 , c ) 7.3296 , d ) 8.3296 , e ) 9.3296
Rationale: log ( 2 x ) - 5 log ( x ) + 6 = 0 ( given ) log ( 2 x ) - log ( x ^ 5 ) = - 6 log ( 2 x / x ^ 5 ) = - 6 [ since log ( a ) - log ( b ) = log ( a / b ) ] apply anti log 2 / ( x ^ 4 ) = e ^ - 6 2 / ( x ^ 4 ) = 2.4788 * 10 ^ - 3 x ^ 4 = 806.85 x = 5.3296 answer : a
Answer: a
Problem: the salary of a person was reduced by 25 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 33.33 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: "let the original salary be $ 100 new salary = $ 75 increase on 75 = 25 increase on 100 = [ ( 25 / 75 ) 100 ] % = 33.33 % answer is b"
Answer: b
Problem: if a light flashes every 6 seconds , how many times will it flash in 1 / 3 of an hour ?
Options: a ) 101 , b ) 201 , c ) 301 , d ) 401 , e ) 501
Rationale: "in 1 / 3 of an hour there are 20 * 60 = 1200 seconds the number of 6 - second intervals = 1200 / 6 = 200 after the first flash , there will be 200 more flashes for a total of 201 . the answer is b ."
Answer: b
Problem: if ( x + 1 ) ( x + 3 ) = x ^ 2 + x , what is a possible value of x ?
Options: a ) 2 , b ) 3 , c ) - 1 / 3 , d ) - 3 , e ) - 1
Rationale: rearranging the given expression : ( x + 1 ) ( x + 3 ) = x ^ 2 + x i . e . x ^ 2 + 4 x + 3 = x ^ 2 + x i . e . 3 x = - 3 i . e . x = - 3 / 3 = - 1 answer : option e had it been a difficult expression to solve further , then we could have used options to check which one satisfies the expression after solving it as further as possible .
Answer: e
Problem: a company recently conducted a survey and found that 20,000 of its customers live in rural areas . if the number of customers who live in urban areas is 100 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 40,000 , b ) 45,000 , c ) 50,000 , d ) 55,000 , e ) 60,000
Rationale: "the number of customers in urban areas is 20,000 + 1 * 20,000 = 40,000 . the answer is a ."
Answer: a
Problem: as a treat for her two children , a mother runs to the freezer in which she has 3 cherry ice pops , 4 orange ice pops , and 4 lemon ice pops . she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one being jealous of the other and getting even more upset . what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?
Options: a ) 3 / 5 , b ) 5 / 7 , c ) 8 / 11 , d ) 11 / 15 , e ) 13 / 20
Rationale: p ( 2 cherry ) = 3 / 11 * 2 / 10 = 6 / 110 p ( 2 orange ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 lemon ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 of the same flavor ) = 30 / 110 p ( 2 different flavors ) = 1 - 30 / 110 = 80 / 110 = 8 / 11 the answer is c .
Answer: c
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 70 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 60
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 70 = > v = 60 ( option e ) ."
Answer: e
Problem: a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 10 metres apart , how many poles will be needed ?
Options: a ) 28 , b ) 56 , c ) 57 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 10 ] = 28 m answer a"
Answer: a
Problem: if in a race of 80 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 16 m , b ) 18 m , c ) 15 m , d ) 14 m , e ) 11 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 80 * 5 ) / 25 = 16 m hence , a beats b by 16 m . answer : a"
Answer: a
Problem: when two dice are rolled , what is the probability that the sum of the two numbers is 6 ?
Options: a ) 1 / 9 , b ) 5 / 36 , c ) 1 / 3 , d ) 2 / 36 , e ) none of the above
Rationale: we have 5 outcomes that satisfy the question : 1 - 5 2 - 4 3 - 3 4 - 2 5 - 1 the probability is ( 1 / 6 * 1 / 6 ) * 5 = 5 / 36 . i think the answer is b
Answer: b
Problem: two trains start from a & b and travel towards each other at speed of 50 kmph and 60 kmph resp . at the time of the meeting the second train has traveled 100 km more than the first . the distance between them .
Options: a ) 800 km , b ) 900 km , c ) 1000 km , d ) 1100 km , e ) 1200 km
Rationale: let the distance traveled by the first train be x km then distance covered by the second train is x + 100 km x / 50 = x + 100 / 60 x = 500 so the distance between a & b is x + x + 100 = 1100 km answer is d .
Answer: d
Problem: a dog takes 5 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 16 : 7 , b ) 15 : 7 , c ) 20 : 7 , d ) 7 : 15 , e ) 14 : 7
Rationale: explanation : dog : hare = ( 5 * 3 ) leaps of hare : 7 leaps of hare = 15 : 7 answer : b
Answer: b
Problem: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value a of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] a = z - x = x + 9 - x = 9 ans : d"
Answer: d
Problem: 0.1 + ( 0.1 ) ^ 2 + ( 0.1 ) ^ 3 =
Options: a ) 0.1 , b ) 0.111 , c ) 0.1211 , d ) 0.2341 , e ) 0.3
Rationale: "explanation : 0.1 + ( 0.1 ) ^ 2 + ( 0.1 ) ^ 3 = 0.1 + 0.01 + 0.001 = 0.111 answer : option b"
Answer: b
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 48 sec
Rationale: "train length = 360 m platform length = 140 m time = ? length = speed * time total length = 360 + 140 = 500 m speed = 45 km / hr = 45 * ( 5 / 18 ) ( m / sec ) = 12.5 m / sec time = length / speed = 500 / 12.5 = 40 sec answer : d"
Answer: d
Problem: convert the 17 / 36 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 1.3 , d ) 1.1 , e ) 1.2
Rationale: "17 / 36 m / s = 17 / 36 * 18 / 5 = 17 / 10 = 1.7 kmph . answer : a"
Answer: a
Problem: two guys a and b leave point a and point b simultaneously and travel towards point b and point a on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will b take to cover the entire journey between point b and point a ?
Options: a ) 65 , b ) 90 , c ) 70 , d ) 75 , e ) 80
Rationale: let x per minute be the speed of a and y per minute be the speed of b . after meeting at a point , a travels for 32 mins and b travels for 50 mins . so distance covered by each of them post point of crossing a = 32 x and b = 50 y the distance covered by a and b before they cross each would be distance covered by b and a post crossing respectively . therefore distance covered by b before he meets a = 32 x time taken by b cover 32 x distance = 32 x / y mins therefore total time taken by b = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of a and b = x + y therefore time taken before a and b meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by b reach destination after meeting a = 50 mins total travel time for b = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins b
Answer: b
Problem: in what time will a train 140 m long cross an electric pole , it its speed be 190 km / hr ?
Options: a ) 2.6 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 190 * 5 / 18 = 53 m / sec time taken = 140 / 53 = 2.6 sec . answer : a"
Answer: a
Problem: if 63 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 24 % , b ) 27 % , c ) 30 % , d ) 33 % , e ) 36 %
Rationale: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 17 % = 33 % . the answer is d ."
Answer: d
Problem: the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 26.25 , what is the perimeter of the garden , in feet ?
Options: a ) 28 , b ) 36 , c ) 40 , d ) 42 , e ) 64
Rationale: "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 26.25 ( p ^ 2 ) / 16 = 2 p + 26.25 p ^ 2 = 32 p + 420 p ^ 2 - 32 p - 420 = 0 p ^ 2 - 42 p + 10 p - 420 = 0 p ( p - 42 ) + 10 ( p + 42 ) = 0 ( p - 42 ) ( p + 10 ) = 0 p = 42 or - 10 discarding negative value , p = 42 answer is d"
Answer: d
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 95 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the average daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 95 - 55 = 40 n = 8 the answer is c ."
Answer: c
Problem: how many seconds will a 300 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 sec , b ) 30 sec , c ) 86 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 300 * 3 / 50 = 18 sec . answer : e"
Answer: e
Problem: by investing in 1623 % stock at 64 , one earns rs . 1600 . the investment made is
Options: a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 6144 , e ) s . 6760
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1600 , investment needed = 64 × 3 × 1600 / 50 = 6144 answer : option d"
Answer: d
Problem: abcd is a parallelogram . bd = 2 . the angles of triangle bcd are all equal . what is the perimeter of the parallelogram ?
Options: a ) 12
b ) 9 √ 3
c ) 9
d ) 8
e ) 3 √ 3
Rationale: so , bc = bd = cd = ba = ad = 2 the parallelogram has 4 equal sides bc = cd = ba = ad = 2 so the perimeter of the parallelogram will be 2 * 4 = 8 hence answer will be ( d ) 2
Answer: d
Problem: the number 42 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 10 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 42 : 1 , 4 , 9 , 16 , 25 , 36 . now , 42 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 42 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 42 equals to 1 + 16 + 25 = 1 ^ 2 + 4 ^ 2 + 5 ^ 2 = 42 - - > 1 + 5 + 4 = 10 . answer : b ."
Answer: b
Problem: if the price of petrol increases by 40 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 28.6 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 40 ) i . e 140 . now , his consumption should be reduced to : - = ( 140 − 100 ) / 140 ∗ 100 . hence , the consumption should be reduced to 28.6 % . answer : d"
Answer: d
Problem: how many factors does 36 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 2 ^ 4 3 ^ 4 total factors = ( 4 + 1 ) ( 4 + 1 ) = 25 . answer is d ."
Answer: d
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.8 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.8 * 2 ) + ( 3.85 * 2 ) ] = 8.4 . required average = ( 8.4 / 2 ) = 4.2 . a"
Answer: a
Problem: 14 times a number gives 210 . the number is
Options: a ) 11 , b ) 12 , c ) 15 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 14 × n = 210 ⇒ n = 15 correct option : c"
Answer: c
Problem: the average of 7 numbers is 24 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) 110 , b ) 122 , c ) 120 , d ) 125 , e ) 145
Rationale: "explanation : average of new numbers = 24 * 5 = 120 answer : option c"
Answer: c
Problem: a cycle is bought for rs . 900 and sold for rs . 1080 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 25 % , d ) 40 % , e ) 28 %
Rationale: "900 - - - - 180 100 - - - - ? = > 20 % answer : b"
Answer: b
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 5 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 40
Rationale: "explanation : t = 15 / 45 * 60 = 20 answer : option c"
Answer: c
Problem: if rs . 544 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 384 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 544 * 2 / 17 = rs . 64 b ' s share = 544 * 3 / 17 = rs . 96 c ' s share = 544 * 12 / 17 = rs . 384 . answer : d"
Answer: d
Problem: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: we will have a negative product only if 1 , 2 , 3 , or 4 are selected from set t . p ( negative product ) = 4 / 8 = 1 / 2 the answer is d .
Answer: d
Problem: a 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 500 , b ) 350 , c ) 828 , d ) 277 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 489 = 50 / 3 3 x + 900 = 2400 = > x = 500 m . answer : a"
Answer: a
Problem: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years . find the average age of the women ?
Options: a ) 87 , b ) 98 , c ) 30 , d ) 29 , e ) 37
Rationale: "20 + 22 + 8 * 2 = 58 / 2 = 29 answer : d"
Answer: d
Problem: a tank contains 7,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 4.77 % , b ) 5.77 % , c ) 6.77 % , d ) 7.77 % , e ) 8.77 %
Rationale: "we start with 7,000 gallons of a solution that is 5 % sodium chloride by volume . this means that there are 0.05 x 7,000 = 350 gallons of sodium chloride . when 2,500 gallons of water evaporate we are left with 4,500 gallons of solution . from here we can determine what percent of the 4,500 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 350 / 4,500 ) x 100 = ? 0.077 x 100 = ? = 7.7 % answer is d ."
Answer: d
Problem: if 20 % of x is 15 less than 15 % of 1500 , then x is ?
Options: a ) 872 , b ) 738 , c ) 837 , d ) 840 , e ) 1050
Rationale: "20 % of x = x / 5 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 5 = 225 - 15 = > x / 5 = 210 = > x = 1050 . answer : e"
Answer: e
Problem: a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the difference of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 9 , c ) 28 , d ) 26 , e ) 21
Rationale: "x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 6 / 5 = > 5 x = 3 x + 12 = > x = 6 = > y = 5 / 2 * 6 = 15 so x - y = 9 the answer is b"
Answer: b
Problem: the average of numbers 0.34204 , 0.34203 , 0.34202 and 0.34201 is ?
Options: a ) 0.34202 , b ) 0.34204 , c ) 0.342022 , d ) 0.342025 , e ) none
Rationale: "answer average = ( 0.34204 + 0.34203 + 0.34202 + 0.34201 ) / 4 = 1.3681 / 4 = 0.342025 correct option : d"
Answer: d
Problem: what is the total number of integers between 10 and 100 ( exclusive ) that are divisible by 7 ?
Options: a ) 10 , b ) 13 , c ) 15 , d ) 12 , e ) 11
Rationale: "14 , 21 , 28 , . . . , 91,98 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 98 - 14 ) / ( 7 ) + 1 = 12 + 1 = 13 answer is b"
Answer: b
Problem: if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 52 , c ) 69 , d ) 78 , e ) 84
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 70 = 350 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 350 i . e . 5 a = 340 i . e . a = 68 i . e . largest e = 68 + 10 = 78 answer : option d"
Answer: d
Problem: a rectangular photograph is surrounded by a border that is 3 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 6 inches wide on each side , the total area would have been ( m + 178 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) 20
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 6 ) ( b + 6 ) = m - - - - ( 2 ) and ( l + 12 ) ( b + 12 ) = m + 178 - - - - - - - - - > ( l + 12 ) ( b + 12 ) - 178 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 6 ) ( b + 6 ) = ( l + 12 ) ( b + 12 ) - 178 lb + 6 l + 6 b + 36 = lb + 12 l + 12 b + 144 - 168 simplify 6 l + 6 b = 60 - - - - - - > 2 ( l + b ) = 20 ( check eq ( 1 ) ) answer is e"
Answer: e
Problem: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length e of a cube whose surface area is equal to 6 z ?
Options: a ) e = 16 , b ) e = 8 √ 2 , c ) e = 8 , d ) e = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 1 : 2 . the first number is :
Options: a ) a ) 27 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 9 = > 3 x = 27 answer : a"
Answer: a
Problem: what number times ( 1 ⁄ 6 ) ^ 2 will give the value of 6 ^ 3 ?
Options: a ) 6 , b ) 36 , c ) 216 , d ) 1296 , e ) 7776
Rationale: "x * ( 1 / 6 ) ^ 2 = 6 ^ 3 x = 6 ^ 2 * 6 ^ 3 = 6 ^ 5 = 7776 the answer is e ."
Answer: e
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 18 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 32 , b ) 52 , c ) 62 , d ) 42 , e ) 48
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 18 ) = ( 7 / 16 ) * v 1 ( v 1 - 18 ) / v 1 = 3 / 4 18 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 18 = 72 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 72 = 42 litres . answer : d"
Answer: d
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 560 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,000 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 560 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 24000 answer : b"
Answer: b
Problem: a can do a piece of work in 16 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 12
Rationale: "8 / 16 + 6 / x = 1 x = 12 days answer : e"
Answer: e
Problem: what is the normal price of an article sold at $ 72 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 92 , b ) $ 96 , c ) $ 100 , d ) $ 104 , e ) $ 108
Rationale: 0.8 * 0.9 * cost price = $ 72 cost price = $ 100 the answer is c .
Answer: c
Problem: during a certain two - week period , 76 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 16 a , b ) 19 a , c ) 17 a , d ) 18 a , e ) 20 a
Rationale: "total movies = 100 . comedies = 76 . action + drama = 24 . since there were 5 times as many dramas as action movies , then action + 5 * action = 24 - - > action = a = 4 . comedies = 76 = 19 a . answer : b ."
Answer: b
Problem: of the 200 stamps in a collection , 80 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 60 , b ) 90 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 60 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 60 + 30 ) = 90 the answer is b ."
Answer: b
Problem: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets ?
Options: a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 3 * 6 = 18 days to produce 3 w widgets . answer : c"
Answer: c
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 3 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 180 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 3 ) * 270 = 90 gallons total paint used = 180 gallons . option b"
Answer: b
Problem: the cost of 2 chairs and 3 tables is rs . 1400 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 200
Rationale: "explanation : 2 c + 3 t = 1400 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 200 = > t - c = 200 answer : e"
Answer: e
Problem: if a truck is traveling at a constant rate of 108 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 20 , b ) 24 , c ) 30 , d ) 36 , e ) 48
Rationale: speed = 108 km / hr = > 108,000 m / hr in one minute = > 108000 / 60 = 1800 meters in one sec = > 1800 / 60 = 30 meters time = total distance need to be covered / avg . speed = > 600 / 30 = 20 and hence the answer : a
Answer: a
Problem: if x + y = 4 and x 2 y 3 + y 2 x 3 = 36 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "xy = 3 as x + y = 4 x 2 y 3 + y 2 x 3 = 36 x 2 y 2 ( y + x ) = 36 substituting x + y x 2 y 2 = 4 xy = 4 answer : d"
Answer: d
Problem: what is the least number that should be added to 1054 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1054 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."
Answer: d