Cheukting/mathqa huggingface dataset:
Question (physics): if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 5 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 26 / 143 , d ) 3 / 20 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 5 * 2 = 10 hours ; in 1 hour 15 journeymen can finish 1 / 10 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 10 = 3 / 20 of the job . answer : d ."
Answer: d
Question (other): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 3 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 ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 3 ) = ( 7 / 16 ) * v 1 ( v 1 - 3 ) / v 1 = 3 / 4 3 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 3 = 12 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 12 = 7 litres . answer : a"
Answer: a
Question (gain): rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 1500 . then his monthly salary is
Options: a ) rs . 6000 , b ) rs . 7500 , c ) rs . 8000 , d ) rs . 10,000 , e ) none
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 1500 ⇔ 20 / 100 x = 1500 ⇔ x = 1500 × 5 = 7500 . answer b"
Answer: b
Question (gain): what percentage of numbers from 1 to 95 have squares that end in the digit 0 ?
Options: a ) 1 , b ) 14 , c ) 9.47 , d ) 21 , e ) 22
Rationale: clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 95 are 10 , 20,30 , 40,50 , 60,70 , 80,90 . number of such numbers = 14 . required percentage = ( 9 / 95 * 100 ) = 9.47 % answer : c
Answer: c
Question (other): what is the square root of 400 , divided by 2 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 10
Rationale: "square root is a number times itself square root of 400 = 20 , 20 / 2 = 10 ( e ) 1"
Answer: e
Question (general): for a recipe for triple berry pie calls for cups of strawberries , raspberries , and blueberries in a ratio of 1 : 2 : 3 . how many total cups of fruit will you need to make the pie ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the ratio 1 : 2 : 3 represents 1 cup strawberries : 2 cups raspberries : 3 cups blueberries . 1 + 2 + 3 = 6 6 cups will be used for the pie . the answer is e
Answer: e
Question (probability): in how many ways can 21 books on english and 19 books on hindi be placed in a row on a shelf so that two books on hindi may not be together ?
Options: a ) 1540 , b ) 2314 , c ) 5420 , d ) 1240 , e ) 4512
Rationale: "we must place all these books as under : xexex … . xex there are 21 books on english , 19 books on hindi 19 places out of 22 can be chosen 22 c 19 = 22 c 3 = 1540 ways ans : a"
Answer: a
Question (physics): two trains 121 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.15 , e ) 7.12
Rationale: "t = ( 121 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.15 answer : d"
Answer: d
Question (gain): the number which exceeds 16 % of it by 63 is :
Options: a ) 75 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 63 x - 16 / 100 x = 63 x - 4 / 25 x = 63 21 / 25 x = 63 x = ( 63 x 25 / 21 ) = 75 answer a"
Answer: a
Question (general): the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 133 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 58 * 46 = 2668 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2668 – 2552 = 116 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 116 2 x = 266 x = 133 runs answer d"
Answer: d
Question (general): the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?
Options: a ) rs . 4007 , b ) rs . 4000 , c ) rs . 4028 , d ) rs . 4050 , e ) rs . 4032
Rationale: "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 * 2 ) = 10100 - - - ( i ) q + r = ( 6250 * 2 ) = 12500 - - - ( ii ) p + r = ( 5200 * 2 ) = 10400 - - - ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 = p + q + r = 16500 - - - ( iv ) subtracting ( ii ) from ( iv ) , we get , p = 4000 . p ' s monthly income = rs . 4000 . answer : b"
Answer: b
Question (general): how many integers between 324,700 and 387,600 have tens digit 1 and units digit 3 ?
Options: a ) 438 , b ) 629 , c ) 780 , d ) 879 , e ) 924
Rationale: "the integers are : 324,713 324,813 etc . . . 387,513 the number of integers is 3876 - 3247 = 629 the answer is b ."
Answer: b
Question (general): the salary of a , b , c , d , e is rs . 10000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8400 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 10000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8400 correct option : b"
Answer: b
Question (general): if ( 1 – 1.25 ) n = 3 , then n =
Options: a ) − 400 , b ) − 140 , c ) − 4 , d ) 4 , e ) - 12
Rationale: ( 1 – 1.25 ) n = 3 simplify to get : - 0.25 n = 3 rewrite as ( - 1 / 4 ) n = 3 multiply both sides by - 4 to get : n = - 12 answer : e
Answer: e
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 300 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2000 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 300 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 300 x = ( 10 x 4 x 300 ) / ( 6 ) x = 2000 . answer : c"
Answer: c
Question (geometry): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theboundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park is ?
Options: a ) 163600 m , b ) 178600 m , c ) 153600 m , d ) 163600 m , e ) 173600 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Question (gain): reema took a loan of rs 1500 with simple interest for as many years as the rate of interest . if she paid rs . 735 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: explanation : let rate = r % then time = r years . = > 1500 ∗ r ∗ r / 100 = 735 = > r 2 = 49 = > r = 7 % option c
Answer: c
Question (physics): a can do a piece of work in 5 days and b can do it in 7 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 11 , c ) 7 / 12 , d ) 9 / 12 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 7 ( a + b ) ’ s one day work = 1 / 5 + 1 / 7 = 12 / 35 = > time = 35 / 12 = 2 9 / 12 days answer : option d"
Answer: d
Question (general): find the value of m 72519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Question (gain): sandy buys an old scooter for $ 800 and spends $ 200 on its repairs . if sandy sells the scooter for $ 1200 , what is the gain percent ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 25 %
Rationale: selling price / total cost = 1200 / 1000 = 1.2 the gain percent is 20 % . the answer is c .
Answer: c
Question (physics): a certain bacteria colony doubles in size every day for 21 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 20 , d ) 15 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 21 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 20 times . answer : c . similar questions to practice : hope it helps ."
Answer: c
Question (other): a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 6000 , b ) 9000 , c ) 9500 , d ) 12000 , e ) none
Rationale: "sol . let b ’ s capital be rs . x . then , 3500 * 12 / 7 x = 2 / 3 ⇔ 14 x = 126000 ⇔ x = 9000 . answer b"
Answer: b
Question (other): how many consecutive zeros are there at the end of 100 ! ( 100 factorial ) ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: number of zeros will be 24 reason 100 / 5 = 20 20 / 5 = 4 so the total number of 5 will be 20 + 4 = 24 answer : d
Answer: d
Question (other): the ratio of spinsters to cats is 2 to 7 . if there are 55 more cats than spinsters , how many spinsters are there ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 55 x = 11 and the number of spinsters is 2 ( 11 ) = 22 . the answer is c ."
Answer: c
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 4000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 500 , d ) s . 800 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 4000 ) = rs . 500 answer = c"
Answer: c
Question (general): a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 20 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 64 , b ) 130 , c ) 140 , d ) 160 , e ) 120
Rationale: "white : yellow = x : ( x + 20 ) = 8 : 13 - - > 13 x = 8 x + 160 - - > x = 32 . the total # of balls originally x + x = 32 + 32 = 64 . answer : a ."
Answer: a
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 10000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 17 % , b ) 19 % , c ) 24.8 % , d ) 14 % , e ) 16 %
Rationale: "total cp = rs . 42000 + rs . 10000 = rs . 52000 and sp = rs . 64900 profit ( % ) = ( 64900 - 52000 ) / 52000 * 100 = 24.8 % answer : c"
Answer: c
Question (general): find the average of all numbers between 5 and 45 which are divisible by 6
Options: a ) 26 , b ) 24 , c ) 28 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 6 + 12 + 18 + 24 + 30 + 36 + 42 / 6 ) = 168 / 6 = 28 option c"
Answer: c
Question (physics): a group of men decided to do a work in 40 days , but 5 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 60 , b ) 15 , c ) 40 , d ) 10 , e ) 25
Rationale: "original number of men = 5 * 60 / ( 60 - 40 ) = 15 answer is b"
Answer: b
Question (physics): if an object travels at nine feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 1800 , e ) 32400
Rationale: "speed = 9 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 9 = 32400 answer e"
Answer: e
Question (general): the youngest of 4 children has siblings who are 3 , 6 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 30 , what is the age of the youngest sibling ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "x + ( x + 3 ) + ( x + 6 ) + ( x + 7 ) = 120 4 x + 16 = 120 4 x = 104 x = 26 the answer is e ."
Answer: e
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 126 grams of water ?
Options: a ) 110 , b ) 112 , c ) 114 , d ) 116 , e ) 118
Rationale: "( 16 / 18 ) * 126 = 112 grams the answer is b ."
Answer: b
Question (general): in what ratio p : q should the mixture p of milk and water in the ratio of 6 : 1 be mixed with another mixture q of milk and water in the ratio 3 : 4 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 3 : 4
Rationale: "( 6 / 7 ) * p + ( 3 / 7 ) * q = ( 1 / 7 ) * p + ( 4 / 7 ) * q 5 p = q p / q = 1 / 5 the answer is c ."
Answer: c
Question (physics): sum of two numbers prime to each other is 8 and their l . c . m . is 15 . what are the numbers ?
Options: a ) 3 and 5 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 10 , e ) 6 and 8
Rationale: "as two numbers are prime , only options satisfy ie option a and b and c but option d will not make the product of numbers i . e 15 answer : a"
Answer: a
Question (general): when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 120 , b ) $ 180 , c ) $ 310 , d ) $ 450 , e ) $ 640
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 × $ 0.4 = $ 180 the answer is b ."
Answer: b
Question (physics): the sector of a circle has radius of 21 cm and central angle 90 o . find its perimeter ?
Options: a ) 91.5 , b ) 75 , c ) 93 , d ) 94 , e ) 95
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 90 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 75 cm answer : option b"
Answer: b
Question (other): in what ratio should a variety of rice costing rs . 5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 1 / 2 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6
Rationale: let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5 ) = 1 / 2 answer : a
Answer: a
Question (general): 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 160 kg then find the average weight of all the 7 rounds ?
Options: a ) 91.4 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 160 / 7 = 91.4 kgs answer : a
Answer: a
Question (physics): bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 30 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 9 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 630 secs . his sis ' time = 576 secs . percent increase needed = ( 630 - 576 / 630 ) * 100 = 54 / 640 * 100 = 9 % . ans ( c ) ."
Answer: c
Question (general): sum of two numbers is 20 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 20 2 x – 3 y = 5 x = 13 y = 7 d )"
Answer: d
Question (physics): with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity e of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters .
Answer: d
Question (general): if p # q denotes the least common multiple of p and q , then t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Question (physics): how many seconds will it take for a car that is traveling at a constant rate of 90 miles per hour to travel a distance of 22 yards ? ( 1 mile = 1,160 yards )
Options: a ) 0.8 , b ) 0.5 , c ) 1.0 , d ) 1.1 , e ) 1.2
Rationale: speed = 90 miles / hr = 44 yard / s distance = 22 yards time = distance / speed = 22 / 44 = 0.5 sec ans - b
Answer: b
Question (physics): if 4 men and 1 boy working together , can do two times as much work per hour as a man and a boy together . find the ratio of the work done by a man and that of a boy for a given time ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 3 : 3 , d ) 1 : 2 , e ) 6 : 1
Rationale: 4 m + 1 b = 2 ( 1 m + 1 b ) 4 m + 1 b = 2 m + 2 b 2 m = 1 b the required ratio of work done by a man and a boy = 1 : 2 d
Answer: d
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 54 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.15 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : b"
Answer: b
Question (physics): two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 5 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.2 . , d ) 8 . , e ) 6.4
Rationale: w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 5 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 5 = 8 desks d is the correct answer .
Answer: d
Question (gain): a retailer buys 60 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 40 , b ) 65 , c ) 72 , d ) 78 , e ) 20
Rationale: let the market price of each pen be $ 1 then , cost price of 60 pens = $ 36 selling price of 60 pens = 99 % of $ 60 = $ 59.40 profit % = ( ( 23.40 * 100 ) / 36 ) % = 65 % answer b
Answer: b
Question (other): if 65 percent of a class answered the first question on a certain test correctly , 55 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 ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
Rationale: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 15 % = 40 % . the answer is b ."
Answer: b
Question (physics): a person starts walking at a speed of 5 km / hr through half the distance , rest of the distance he covers with aspeed 4 km / hr . total time of travel is 6 hours . what is the maximum distance he can cover ?
Options: a ) 20 km , b ) 40 km , c ) 60 km , d ) 80 km , e ) 26.6 km
Rationale: t = d / s , so 6 = x / 2 * 1 / 5 + x / 2 * 1 / 4 ( because half distance with 5 km / ph , and remaining half with 4 km / hr ) 6 = x ( 18 / 80 ) x = 26.6 km answer : e
Answer: e
Question (gain): the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 1 year ?
Options: a ) 12300 , b ) 12350 , c ) 12000 , d ) 12500 , e ) 12600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 120 / 100 = 12000 c"
Answer: c
Question (other): two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 95 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 50 , b ) 43 , c ) 45 , d ) 55 , e ) 60
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 93 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 / 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 95 - 45 = 50 option a"
Answer: a
Question (gain): what percent is 10 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 3 %
Rationale: "1 kg = 1000 gm 10 / 1000 × 100 = 1000 / 1000 = 1 % b )"
Answer: b
Question (general): 7 people went to a restaurant for dinner . 6 of them spent $ 11 each on their meals and the seventh person spent $ 6 more than the average expenditure of all 7 people . what was the total amount of money that the 7 people spent ?
Options: a ) $ 80 , b ) $ 81 , c ) $ 82 , d ) $ 83 , e ) $ 84
Rationale: let t be the total amount of money spent . 6 * 11 + ( t / 7 + 6 ) = t 72 = 6 t / 7 t = ( 7 * 72 ) / 6 = 84 the answer is e .
Answer: e
Question (gain): on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 32 ) = 32 hence answer will be ( d )"
Answer: d