regisss/math_qa huggingface dataset:
Problem: mr . jones gave 40 % of the money he had to his wife . he also gave 20 % of the remaining amount to his 3 sons . and half of the amount now left was spent on miscellaneous items and the remaining amount of rs . 12000 was deposited in the bank . how much money did mr . jones have initially ?
Options: a ) 40000 , b ) 45000 , c ) 50000 , d ) 62000 , e ) none of these
Rationale: explanation : let the initial amount be x , amount given to his wife = ( 40 / 100 ) x = 2 x / 5 balance = ( x - ( 2 x / 5 ) ) = 3 x / 5 amount given to his wife = ( 20 / 100 ) * ( 3 x / 5 ) = 3 x / 25 balance = 3 x / 5 - 3 x / 25 = 12 x / 25 amountt spent on miscellaneous items = ( 1 / 2 ) * ( 12 x / 25 ) = 6 x / 25 which is equal to 12000 hence , = > 6 x / 25 = 12000 = > x = 50000 answer : c
Answer: c
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 170 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 170 + p c + m = 170 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 170 / 2 = 85 . answer : d"
Answer: d
Problem: find the compound interest on rs . 10000 at 12 % rate of interest for 1 year , compounded half - yearly
Options: a ) rs . 1036 , b ) rs . 1236 , c ) rs . 1186 , d ) rs . 1206 , e ) rs . 1226
Rationale: "amount with ci = 10000 [ 1 + ( 12 / 2 * 100 ) ] 2 = rs . 11236 therefore , ci = 11236 – 10000 = rs . 1236 answer : b"
Answer: b
Problem: 25 onions on a scale weigh 5.12 kg . when 3 onions are removed from the scale , the average weight of the 22 onions is 200 grams . what is the average weight ( in grams ) of the 3 onions which were removed ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 260 , e ) 280
Rationale: 22 * 200 = 4400 . the other 3 onions weigh a total of 720 grams . the average weight is 720 / 3 = 240 grams . the answer is c .
Answer: c
Problem: a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 220 , b ) s . 120 , c ) s . 320 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 360 and 240 . difference in profit share = 360 - 240 = 120 answer : b"
Answer: b
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 5 inches wide on each side , the total area would have been ( m + 144 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 10 ) ( y + 10 ) = m and so ( 2 ) xy + 10 x + 10 y + 100 = m + 144 let ' s subtract equation ( 1 ) from equation ( 2 ) . 8 x + 8 y + 96 = 144 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b
Problem: 3 candidates contested an election and received 1000 , 2000 and 4000 votes respectively . what percentage of the total votes did the winning candidate got ?
Options: a ) 30 % , b ) 50 % , c ) 57 % , d ) 62 % , e ) 75 %
Rationale: total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c
Answer: c
Problem: the area of a triangle will be when a = 3 m , b = 5 m , c = 10 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1
Rationale: s = ( 3 + 5 + 10 ) / 2 = 9 answer : d
Answer: d
Problem: what is the sum of all 5 digit numbers which can be formed with the digits 0 , 1,2 , 3,4 without repetation ?
Options: a ) 2599980 , b ) 235500 , c ) 923580 , d ) 765432 , e ) 765434
Rationale: "10 ( 11111 ) * 4 ! - 10 ( 1111 ) 3 ! = 2599980 answer : a"
Answer: a
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 64 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 64 ( x - y ) - - > x + y = 64 . answer : d ."
Answer: d
Problem: 20 litres of mixture contains 40 % alcohol and the rest water . if 8 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 26.32 % , b ) 35.14 % , c ) 28.57 % , d ) 25 % , e ) 31.14 %
Rationale: "alcohol in the 20 litres of mix . = 40 % of 20 litres = ( 40 * 20 / 100 ) = 8 litres water in it = 20 - 8 = 12 litres new quantity of mix . = 20 + 8 = 28 litres quantity of alcohol in it = 8 litres percentage of alcohol in new mix . = 8 * 100 / 28 = 50 / 3 = 28.57 % answer is c"
Answer: c
Problem: jane makes toy bears . when she works with an assistant , she makes 90 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 120 % d"
Answer: d
Problem: 12.036 divided by 0.04 gives :
Options: a ) 30.09 , b ) 300.9 , c ) 30.06 , d ) 100.9 , e ) 300.6
Rationale: "= 12.036 / 0.04 = 1203.6 / 4 = 300.9 answer is b ."
Answer: b
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 5 % chemical x and 95 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 24 % , b ) 26 % , c ) 28 % , d ) 30 % , e ) 32 %
Rationale: "the amount of chemical x in the solution is 20 + 0.05 ( 80 ) = 24 liters . 24 liters / 100 liters = 24 % the answer is a ."
Answer: a
Problem: the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 4.4 miles in the sixth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 35 , b ) 40 , c ) 48 , d ) 51 , e ) 54
Rationale: "( 4.4 miles / 8 minutes ) * 60 minutes / hour = 33 mph let x be the original speed . x - 5 ( 3 ) = 33 x = 48 mph the answer is c ."
Answer: c
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score r for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a ."
Answer: a
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 240 meter length ?
Options: a ) 65 seconds , b ) 46 seconds , c ) 40 seconds , d ) 97 seconds , e ) 48 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 240 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : e"
Answer: e
Problem: in one year , the population , of a village increased by 10 % and in the next year , it decreased by 10 % . if at the end of 2 nd year , the population was 7920 , what was it in the beginning ?
Options: a ) 8008 , b ) 8000 , c ) 8022 , d ) 8021 , e ) 8022
Rationale: "x * 110 / 100 * 90 / 100 = 7920 x * 0.99 = 7920 x = 7920 / 0.99 = > 8000 answer : b"
Answer: b
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 35 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 864 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 135 % of $ 640 = $ 864 d"
Answer: d
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3720 , r will receive
Options: a ) 720 , b ) 700 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3720 * ( 6 / 31 ) = 120 * 6 = 720 . answer : option a"
Answer: a
Problem: it costs $ 2 for the first 15 minutes to use the bumper cars at a fair ground . after the first 15 minutes it costs $ 6 per hour . if a certain customer uses the bumper cars for 3 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 22 , b ) $ 3 , c ) $ 15 , d ) $ 21 , e ) $ 30
Rationale: 3 hrs 25 min = 205 min first 15 min - - - - - - > $ 2 time left is 190 min . . . now , 60 min costs $ 6 1 min costs $ 6 / 60 190 min costs $ 6 / 60 * 190 = > $ 19 so , total cost will be $ 19 + $ 2 = > $ 21 the answer will be ( d ) $ 21
Answer: d
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 30 paise per sq . metre
Options: a ) s 255 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 30 = 25500 p in rs = 25500 / 100 = rs 255 answer : a"
Answer: a
Problem: john and andrew can finish the work 9 days if they work together . they worked together for 6 days and then andrew left . john finished the remaining work in another 6 days . in how many days john alone can finish the work ?
Options: a ) 30 days , b ) 60 days , c ) 18 days , d ) 80 days , e ) 90 days
Rationale: amount of work done by john and andrew in 1 day = 1 / 9 amount of work done by john and andrew in 6 days = 6 ã — ( 1 / 9 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 6 days amount of work john can do in 1 day = ( 1 / 3 ) / 6 = 1 / 18 = > john can complete the work in 18 days answer : c
Answer: c
Problem: of the 14,210 employees of the anvil factory , 3 / 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 , 14.3 % . 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 . a"
Answer: a
Problem: what percent is 400 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 10 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 400 / 1000 ã — 100 = 40000 / 1000 = 40 % answer is b"
Answer: b
Problem: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 160 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 184 , b ) 367 , c ) 269 , d ) 177 , e ) 191
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 160 x + ( x - 160 ) = 208 2 x = 368 x = 184 runs answer : a"
Answer: a
Problem: the total age of a and b is 14 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 14 + b + c = > a ? c = 14 + b ? b = 14 = > c is younger than a by 14 years answer : option d"
Answer: d
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 22,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 3500 net price of the car in 02 = 18700 + 3500 = $ 22200 correct option : c"
Answer: c
Problem: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m , what is its area ?
Options: a ) 2520
b ) 2510
c ) 2525
d ) 2025
e ) 2020
Rationale: l - b = 23 . . . ( 1 ) perimeter = 206 2 ( l = b ) = 206 l + b = 103 . . . ( 2 ) ( 1 ) + ( 2 ) 2 l = 23 + 103 = 126 l = 126 / 2 = 63 metre substituting the value of l in ( 1 ) , we get 63 - b = 23 b = 63 - 23 = 40 metre area = lb = 63 ã — 40 = 2520 m 2 answer : a
Answer: a
Problem: a boat having a length 5 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 5 x 2 x 0.01 ) m 3 = 0.10 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.10 x 1000 ) kg = 100 kg . answer : a"
Answer: a
Problem: if 100 cats kill 100 mice in 100 days , then 4 cats would kill 4 mice in how many days ?
Options: a ) 1 day , b ) 4 days , c ) 40 days , d ) 100 days , e ) 50 days
Rationale: as 100 cats kill 100 mice in 100 days 1 cats kill 1 mouse in 100 days then 4 cats kill 4 mice in 100 days answer : d
Answer: d
Problem: what is the unit digit in 7105 ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "unit digit in 7105 = unit digit in [ ( 74 ) 26 * 7 ] but , unit digit in ( 74 ) 26 = 1 unit digit in 7105 = ( 1 * 7 ) = 7 answer : c"
Answer: c
Problem: of the 55 cars on a car lot , 40 have air - conditioning , 25 have power windows , and 12 have both air - conditioning and power windows . how many of the cars on the lot have neither air - conditioning nor power windows ?
Options: a ) 15 , b ) 8 , c ) 10 , d ) 2 , e ) 18
Rationale: total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d
Answer: d
Problem: what is the remainder when 49 ^ 74 - 5 ^ 74 is divided by 24 ?
Options: a ) 2 , b ) 1 , c ) 0 , d ) 3 , e ) none of these
Rationale: "easiest way for me : 49 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : c"
Answer: c
Problem: a sum of 13,400 amounts to 14,400 in 2 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 4 % , e ) 8 %
Rationale: "d 4 % s . i . = ( 14400 - 13400 ) = 1000 . rate = ( 100 x 1000 ) / ( 13400 x 2 ) % = 4 %"
Answer: d
Problem: a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 420 less than the sum lent . what was the sum lent ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "p - 420 = ( p * 5 * 8 ) / 100 p = 700 the answer is c ."
Answer: c
Problem: 30 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 20 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 30 : : 18 : x [ please pay attention , we have written 27 : 30 rather than 30 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 30 \ times 18 } { 27 } } x = 20 so 20 days will be required to get work done by 27 men . answer : a"
Answer: a
Problem: if n is a positive integer and n ^ 2 is divisible by 200 , then what is the largest positive integer that must divide n ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 36 , e ) 50
Rationale: 200 = 2 ^ 3 * 5 ^ 2 if 200 divides n ^ 2 , then n must be divisible by 2 ^ 2 * 5 = 20 the answer is c .
Answer: c
Problem: john paid a sum of money for purchasing 20 pens , which he recovered in full when he sold 10 of them . what was his percentage of profit or loss per pen ?
Options: a ) 100 % , b ) 150 % , c ) 90 % , d ) 80 % , e ) 95 %
Rationale: a 100 % if the sum he paid whilst purchasing 20 pens = a , then the cost price of each pen = a / 20 . since the amount he got whilst selling 10 pens is also = a then the selling price of each pen = a / 10 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 10 - a / 20 = a / 20 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 20 ) / ( a / 20 ) x 100 = 100 %
Answer: a
Problem: if x is a positive number and 1 / 3 the square root of x is equal to 3 x , then x =
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 81 , d ) 1 , e ) 81
Rationale: "1 / 3 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 9 x or x = 81 x ^ 2 - > divide by x 1 = 81 x x = 1 / 81 c ."
Answer: c
Problem: find the smallest number of 6 digits exactly divisible by 25 , 3545 and 15 .
Options: a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665
Rationale: smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b .
Answer: b
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 21 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 3 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 21 s = ( 27 x + 17 y ) / ( x + y ) = 21 = ( 27 x + 17 y ) / = 21 ( x + y ) = 6 x = 4 y = x / y = 4 / 6 = 2 / 3 i . e 2 : 3 answer : c"
Answer: c
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %
Rationale: ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a
Answer: a
Problem: if two - third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be .
Options: a ) 90 seconds , b ) 70 seconds , c ) 60 seconds , d ) 9 minutes , e ) 120 seconds
Rationale: "2 / 3 filled in 6 mint 1 / 3 filled in 3 mint thn 2 / 3 + 1 / 3 = 6 + 3 = 9 minutes answer : d"
Answer: d
Problem: a batsman makes a score of 76 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 36 , b ) 28 , c ) 42 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 76 = 17 x or x = ( 76 – 48 ) = 28 . answer b"
Answer: b
Problem: find the remainder of the division ( 2 ^ 14 ) / 7 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "find the pattern of the remainders after each power : ( 2 ^ 1 ) / 7 remainder 2 ( 2 ^ 2 ) / 7 remainder 4 ( 2 ^ 3 ) / 7 remainder 1 - - > this is where the cycle ends ( 2 ^ 4 ) / 7 remainder 2 - - > this is where the cycle begins again ( 2 ^ 5 ) / 7 remainder 4 continuing the pattern to ( 2 ^ 14 ) / 7 gives us a remainder of 4 final answer : d ) 4"
Answer: d
Problem: a can do a job in 18 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 12 ½ days , e ) none of these
Rationale: "1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 11 ¼ * 2 = 22 ½ days answer : b"
Answer: b
Problem: barbata invests $ 2600 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1300 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2600 + 0.05 * 2600 + x + 0.08 x = 2600 + x + 0.06 ( 2600 + x ) 0.05 * 2600 + 0.08 x = 0.06 x + 0.06 * 2600 0.02 x = 2600 ( 0.06 - 0.05 ) x = 2600 * 0.01 / 0.02 = 1300 ans : ` ` c ' '"
Answer: c
Problem: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses w at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) w = 256 , d ) w = 384 , e ) w = 480
Rationale: "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Problem: if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 501 , e ) 613
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 40 + ( 11 - 1 ) * 1 } = 11 * 45 = 495 = x number of even number = ( 50 - 40 ) / 2 + 1 = 6 = y x + y = 495 + 6 = 501 d"
Answer: d
Problem: a man swims downstream 28 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 6.5 , b ) 8.6 , c ) 7.5 , d ) 9.2 , e ) 5.5
Rationale: "28 - - - 4 ds = 7 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : e"
Answer: e
Problem: alice and bob drive at constant speeds toward each other on a highway . alice drives at a constant speed of 30 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if alice is 100 km away from bob at 7 am , and also 100 km away from bob at 11 am , then how fast is bob driving ( in kilometers per hour ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: alice and bob complete 200 km / 4 hours = 50 km / hour bob ' s speed is 50 - 30 = 20 km / hour the answer is a .
Answer: a
Problem: the calendar of the year 2040 can be used again in the year ?
Options: a ) 2063 , b ) 2061 , c ) 2111 , d ) 2191 , e ) 2068
Rationale: "explanation : given year 2040 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2040 + 28 = 2068 answer : e"
Answer: e
Problem: how many integers from 1 to 100 exist such that each is divisible by 5 and also has 5 as a digit ?
Options: a ) 10 , b ) 12 , c ) 11 , d ) 20 , e ) 25
Rationale: "5 , 15,25 , 35,40 , 50,55 , 65,75 , 85,95 so there are total 11 such type of numbers . answer : c"
Answer: c
Problem: in what time will a train 100 metres long cross an electic pole , if its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) none
Rationale: "sol . speed = [ 144 x 5 / 18 ] m / sec = 40 m / sec . time taken = ( 100 / 40 ) sec = 2.5 sec . answer a"
Answer: a
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 120 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 25 2 x + 3 x = 600 x = 120 km answer is d"
Answer: d
Problem: from a group of 4 boys and 4 girls , 4 children are to be randomly selected . what is the probability that 2 boys and 2 girls will be selected ?
Options: a ) 12 / 29 , b ) 14 / 31 , c ) 16 / 33 , d ) 18 / 35 , e ) 20 / 37
Rationale: "the total number of ways to choose 4 children from 8 is 8 c 4 = 70 the number of ways to choose 2 boys and 2 girls is 4 c 2 * 4 c 2 = 6 * 6 = 36 p ( 2 boys and 2 girls ) = 36 / 70 = 18 / 35 the answer is d ."
Answer: d
Problem: a wooden box of dimensions 8 m x 3 m x 6 m is to carry rectangularboxes of dimensions 8 cm x 3 cm x 2 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 3000000 , e ) none of these
Rationale: explanation : number = ( 800 * 300 * 600 ) / 8 * 3 * 2 = 3000000 answer : d
Answer: d
Problem: a can do a work in 8 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 8 b rate = 1 / 24 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 24 ) = 1 / 6 a & b finish the work in 6 days correct option is e"
Answer: e
Problem: what is the remainder when 50 ! is divided by 16 ^ 8 ? ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "16 raise to 8 = 2 raise to 32 , now highest power of 2 divisible by 50 ! is 25 + 12 + 6 + 3 + 1 = 47 since 2 raise to 47 is divisible , 2 raise to 32 also will be divisible answer : a"
Answer: a
Problem: two goods trains each 1250 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 ) 278 , c ) 48 , d ) 27 , e ) 120
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 1250 + 1250 = 2500 m . required time = 2500 * 6 / 125 = 120 sec . answer : e"
Answer: e
Problem: if the cost price of 140 pencils is equal to the selling price of 100 pencils , the gain percent is
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "let c . p . of each pencil be re . 1 . then , c . p . of 100 pencils = rs . 100 ; s . p . of 100 pencils = rs . 140 . gain % = 40 / 100 * 100 = 40 % answer : e"
Answer: e
Problem: mother , her daughter and her grand child weighs 140 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 44 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 140 kg daughter + child = 60 kg mother = 140 - 60 = 80 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 80 = 16 kg so now daughter = 140 - ( mother + child ) = 140 - ( 80 + 16 ) = 44 kg answer : a"
Answer: a
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 5 : 2 . the first number is :
Options: a ) a ) 3 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 5 : 2 x = 1 = > 3 x = 3 answer : a"
Answer: a
Problem: a mixture of sand and cement contains , 3 parts of sand and 5 parts of cement . how much of the mixture must be substituted with sand to make the mixture half sand and half cement ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 1 / 8
Rationale: we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c .
Answer: c
Problem: the sum of ages of 5 children born 3 years different each is 65 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . x + 12 = 7 + 12 = 19 b"
Answer: b
Problem: a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 24.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 20.00
Rationale: let the cost price of book = x selling price of book = 24 $ markup % = 20 ( 120 / 100 ) x = 24 = > x = 20 answer e
Answer: e
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 10 percent , but profits were 15 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 135 % , d ) 124.2 % , e ) 138 %
Rationale: "the profit 0 f 2009 in terms of 2008 = 0.9 * 15 / 10 * 100 = 135 % c"
Answer: c
Problem: find the simple interest on $ 10000 at 6 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 600 , d ) $ 710 , e ) $ 1000
Rationale: "p = $ 10000 r = 6 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 6 * 1 / 100 = $ 600 answer is c"
Answer: c
Problem: a mixture contains milk and water in the ratio 5 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 5 : 3 . the quantity of milk in the original mixture is ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "milk : water = 5 : 2 5 x : 2 x + 10 = 5 : 3 3 [ 5 x ] = 5 [ 2 x + 10 ] 15 x = 10 x + 50 15 x - 10 x = 50 x = 10 the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 x = 70 short cut method : milk : water = 5 : 2 after adding 10 liters of water milk : water = 5 : 3 milk is same but water increse 10 liters then the water ratio is increse 1 parts 1 part - - - - - > 10 liters the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 parts - - - - - > 70 liters ( answer is = 70 ) short cut method - 2 : for only milk problems milk : water 5 : 2 5 : 3 milk ratio same but water ratio 1 part incress per 10 liters 1 part of ratio - - - - - - - > 10 liters 7 part of ratio - - - - - - - > 70 liters c )"
Answer: c
Problem: of the 3,600 employees of company x , 12 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 40 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 %
Answer: a
Problem: a man two flats for $ 675958 each . on one he gains 13 % while on the other he loses 13 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.69 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 13 / 10 ) ^ 2 = 120 / 71 = 1.69 % answer is a"
Answer: a
Problem: what is the greatest of 3 consecutive integers whose sum is 30 ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "30 / 3 = 10 the three numbers are 9 , 10 , and 11 . the answer is d ."
Answer: d
Problem: students of 3 different classes appeared in common examination . pass average of 10 students of first class was 45 % , pass average of 15 students of second class was 60 % and pass average of 25 students of third class was 80 % then what will be the pass average of all students of 3 classes ?
Options: a ) 74 % , b ) 75 % , c ) 67 % , d ) 72 % , e ) none
Rationale: solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c
Answer: c
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Rationale: "the triangle with sides 20 cm , 12 cm and 16 cm is right angled , where the hypotenuse is 20 cm . area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Answer: d
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 2 , b ) 28 , c ) 25 , d ) 99 , e ) 12
Rationale: "d = 100 + 150 = 250 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 25 sec . answer : c"
Answer: c
Problem: 34.94 + 240.016 + 23.98 = ?
Options: a ) 298.936 , b ) 298.694 , c ) 289.496 , d ) 289.469 , e ) 298.964
Rationale: 34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a .
Answer: a
Problem: meera purchased two 3 items from a shop . total price for 3 items is rs . 2000 / - she have given rs . 3000 / - what is the balance amount meera got ?
Options: a ) 650 , b ) 1000 , c ) 1500 , d ) 800 , e ) 750
Rationale: total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b
Answer: b
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 86 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: "correct average = 35 x 72 + ( 86 - 36 ) / 35 ≈ 72 + 1.43 = 73.43 answer d"
Answer: d
Problem: what is the smallest integer e greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?
Options: a ) 21 , b ) 41 , c ) e = 121 , d ) 241 , e ) 481
Rationale: or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c
Answer: c
Problem: a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 30 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 40 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 28 % , b ) 82 % , c ) 24.33 % , d ) 29.109 % , e ) 78 %
Rationale: "anyways , one can infer that he ' steals ' 30 % from suppliers and then charges 40 % extra to customers so basically 1.3 * 1.4 = 1.82 given that 1 is start point , we get 21 % more hence answer is b"
Answer: b
Problem: in 60 litres mixture milk and water are in the ratio 3 : 1 . after adding how many liters of water its ratio will become 3 : 2
Options: a ) 1 , b ) 15 , c ) 7 , d ) 5 , e ) 12
Rationale: "milk quantity = 3 / 4 * 60 = 45 water quantity = 60 - 45 = 15 new ratio of m : w = 45 : 15 + x = 3 : 2 45 + 3 x = 90 x = 15 answer is b"
Answer: b
Problem: how many numbers from 2 to 13 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 6
Rationale: "2 / 2 = 1 and 13 / 2 = 6 6 - 1 = 5 5 + 1 = 6 numbers . answer : e"
Answer: e
Problem: in a class of 37 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 37 - 29 = 8 play neither answer is b"
Answer: b
Problem: a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 86 km downstream .
Options: a ) 4.1 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 15 km / hr speed of the stream = 6 km / hr speed downstream = ( 15 + 6 ) = 21 km / hr time taken to travel 86 km downstream = 86 â  „ 16 = 17 â  „ 4 = 4.1 hours answer is a"
Answer: a
Problem: on dividing a number by 357 , we get 38 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 38 = ( 17 * 21 * y ) + ( 17 * 2 ) + 4 = 17 * ( 21 y + 2 ) + 4 . required number = 4 . answer is a"
Answer: a
Problem: bhanu spends 30 % of his income on petrol on scooter 12 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 62 , b ) 140 , c ) 84 , d ) 60 , e ) 123
Rationale: given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 12 % ( 700 ) = rs . 84 answer : c
Answer: c
Problem: a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 370 - meter long platform ?
Options: a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 370 ) / 10 = 52 seconds the answer is d ."
Answer: d
Problem: a pump can fill a tank with water in 3 hours . because of a leak , it took 3 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 30 hr , d ) 14 hr , e ) 16 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 3 - 3 1 / 3 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : c"
Answer: c
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 13 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 13 x = 45 - - > 87 / 77 * x = 45 - - > x = 45 * 77 / 87 = 677 / 17 = ~ 40 . answer : c ."
Answer: c
Problem: in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ?
Options: a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let the universal set be x = { all students in the graduate physics course } , such that n ( x ) = 100 it will contain 2 mutually exclusive sets ; m ( all male students ) & f ( all female students ) , where n ( m ) = 70 , n ( f ) = 30 now 2 / 7 of all male students are married , implying their number = 20 . however the total number of married students = 30 , implying 10 married females . therefore 20 single females ; = 2 / 3 of total females . answer : d"
Answer: d
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio r of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio r of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Problem: if ( a - b - c + d = 18 ) and ( a + b - c - d = 4 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 49 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 4 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 4 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 14 ( 2 ) simplify - b + d = 7 b - d = - 7 ( b - d ) ^ 2 = ( - 7 ) ^ 2 = 49 my answer : a"
Answer: a
Problem: john purchased some shirts and trousers for $ 800 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: given that the total purchase of two items cost 800 . so the average purchase of one item will cost 800 / 2 = 400 . its given as total shirt cost 400 $ less . hence total shirt cost = 400 - 200 and total trouser cost = 400 + 200 5 shirts = 200 $ = = > one shirt = 40 $ one trouser = 40 + 20 = 60 $ total trousers = 600 / 60 = 10 . e
Answer: e
Problem: the average age of a class of 24 students is 23 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 ) 48 , d ) 52 , e ) 43
Rationale: "total age of all students = 24 ã — 23 total age of all students + age of the teacher = 25 ã — 24 age of the teacher = 25 ã — 24 â ˆ ’ 24 ã — 23 = 24 ( 25 â ˆ ’ 23 ) = 24 ã — 2 = 48 answer is c ."
Answer: c
Problem: 45 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 30 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 45 : : 18 : x [ please pay attention , we have written 27 : 45 rather than 45 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 45 \ times 18 } { 27 } } x = 30 so 30 days will be required to get work done by 27 men . answer : c"
Answer: c
Problem: 27 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 33 , b ) 66 , c ) 88 , d ) 100 , e ) 281
Rationale: "( 27 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 60 60 – 27 = 33 answer : a"
Answer: a
Problem: n and m are each 3 - digit integers . each of the numbers 2 , 3 , 4,5 , 6 , and 7 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 2 , 3 , 4 , 5 , 6 , 7 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 7 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 376 and 425 ( difference is 49 ) or try and make a pair with ( 5 * * and 6 * * ) . make the 5 * * number as large as possible and make the 6 * * number as small as possible . we get 574 and 623 ( difference is 49 ) b"
Answer: b
Problem: 54671 - 14456 - 35466 = ?
Options: a ) 2449 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 4749
Rationale: "e if we calculate we will get 4749"
Answer: e