regisss/math_qa huggingface dataset:
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 130 marks , the no of questions he attempts correctly is :
Options: a ) a ) 35 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 42
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 80 – x ) = 130 = > 5 x = 210 = > x = 42 answer : e"
Answer: e
Problem: what is the least number should be added to 1056 , so the sum of the number is completely divisible by 29 ?
Options: a ) 17 , b ) 27 , c ) 37 , d ) 47 , e ) 57
Rationale: ( 1056 / 29 ) gives remainder 12 17 + 12 = 29 , so we need to add 17 a
Answer: a
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1455 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: ( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a
Answer: a
Problem: if the price of an article went up by 30 % , then by what percent should it be brought down to bring it back to its original price ?
Options: a ) 25 % , b ) 23 1 / 13 % , c ) 16 7 / 3 % , d ) 16 6 / 3 % , e ) 16 2 / 3 %
Rationale: "let the price of the article be rs . 100 . 30 % of 100 = 30 . new price = 100 + 30 = rs . 130 required percentage = ( 130 - 100 ) / 130 * 100 = 30 / 130 * 100 = 23 1 / 13 % answer : b"
Answer: b
Problem: if n is the product of all the integers from 5 to 20 , inclusive , what is the greatest integer k for which 2 ^ k is a factor of n ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: 20 / 2 = 10 10 / 2 = 5 ans : 10 + 5 = 15 answer : e
Answer: e
Problem: the perimeter of an isosceles right triangle is 14 + 14 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9.899
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 14 + 14 sqrt 2 or , a . ( 2 + sqrt 2 ) = 14 ( 1 + sqrt 2 ) , a = 14 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 14 * 2.414 / 3.414 = then hypotenuse = 9.899 e"
Answer: e
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 180 . if the ratio of his marks in english and maths is 1 : 2 , find his marks in science ?
Options: a ) 19 , b ) 77 , c ) 66 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 1 : 2 - - - - - - - - - - - - s : e : m = 1 : 3 : 6 1 / 10 * 190 = 19 answer : a"
Answer: a
Problem: what is 82 % of 3 / 5 ?
Options: a ) 6.9 , b ) 0.492 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "82 % * ( 3 / 5 ) = 0.82 * 0.6 = 0.492 answer : b"
Answer: b
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?
Options: a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500
Rationale: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b
Answer: b
Problem: a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 7 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 73 , b ) b ) 20 , c ) c ) 83 , d ) d ) 21 , e ) e ) 52
Rationale: "explanation : 1 : 2 / 7 = 7 : 2 2 / 9 * 90 = 20 answer : option b"
Answer: b
Problem: the sum of 3 integers is 33 . the largest integer is 3 times the middle integer , and the smallest integer is 23 less than the largest integer . what is the product of the 3 integers ?
Options: a ) 192 , b ) 203 , c ) 214 , d ) 225 , e ) 236
Rationale: let x be the middle integer . then the largest is 3 x and the smallest is 3 x - 23 . 3 x - 23 + x + 3 x = 33 x = 8 the three integers are 1 , 8 , and 24 . the product is 1 * 8 * 24 = 192 the answer is a .
Answer: a
Problem: how many integers between 1 and 10 ^ 19 are such that the sum of their digits is 2 ?
Options: a ) 190 , b ) 210 , c ) 211 , d ) 230 , e ) 231
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 18 and there are 19 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 18 thus , the total number of integers is 1 + 2 + . . . + 18 + 19 = 20 * 19 / 2 = 190 the answer is a ."
Answer: a
Problem: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 70 . he was allowed to drop his lowest score . after doing so , his average test score improved to 75 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 70 . so what we can assume is that we have 4 test scores , each 70 . he dropped his lowest score and the avg went to 75 . this means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 70 . so the lowest score = 70 - 15 = 55 answer ( c )"
Answer: c
Problem: an error 2 % in excess is made while measuring the sideofa square . the % of error in the calculated area of the square is ?
Options: a ) 4 % , b ) 4.04 % , c ) 4.15 % , d ) 5 % , e ) 5.24 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b"
Answer: b
Problem: what is the normal price of an article sold at $ 144 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 184 , b ) $ 192 , c ) $ 200 , d ) $ 208 , e ) $ 216
Rationale: "0.8 * 0.9 * cost price = $ 144 cost price = $ 200 the answer is c ."
Answer: c
Problem: the length of a room is 6.5 m and width is 2.75 m . what is the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 18725 , b ) rs . 16725 , c ) rs . 30725 , d ) rs . 10725 , e ) rs . 20725
Rationale: "area = 6.5 * 2.75 sq . metre . cost for sq . metre . = rs . 600 hence , total cost = 6.5 * 2.75 * 600 = rs . 10725 answer : d"
Answer: d
Problem: the number of diagonals of a polygon of n sides is given by the formula v = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "v = n ( n - 3 ) v = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Problem: what is the least common multiple of 12,27 and 40
Options: a ) 8521 , b ) 1080 , c ) 368 , d ) 8979 , e ) 6584
Rationale: "factors of 12 = 2 * 2 * 3 factors of 27 = 3 * 3 * 3 factors of 40 = 2 * 2 * 2 * 5 thus the l . c . m is 2 ^ 3 * 3 ^ 3 * 5 = 1080 the answer is b"
Answer: b
Problem: saturn travels around the sun at an approximate speed of 5.82 miles per second . this speed is how many kilometers per hour ? ( 1 km = 0.6 miles )
Options: a ) 30,560 , b ) 31,650 , c ) 32,740 , d ) 33,830 , e ) 34,920
Rationale: the speed is 5.82 miles / s . then 5.82 / 0.6 = 9.7 km / s 9.7 * 3600 = 34,920 kph the answer is e .
Answer: e
Problem: total 30 cows 10 cow gives each 2 liter milk 10 cow gives each 3 / 4 liter milk 10 cow gives each 1 / 4 liter milk this is split into 3 son per each 10 cows & 10 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "10 cow 2 liter each = 20 liter 10 cow 3 / 4 liter each = 3 / 4 = 0.758 * 10 = 7.5 10 cow 1 / 4 liter each = 1 / 4 = 0.25 * 10 = 2.5 add 20 + 7.5 + 2.5 = 30 milk split into 3 son each 10 liter then 30 / 3 = 10 answer : a"
Answer: a
Problem: if 15 % of 30 % of 50 % of a number is 108 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4800 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 108 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 108 = > a = 10 * 20 * 10 * 2 = 4800 . answer : d"
Answer: d
Problem: andy solves problems 75 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 52 , c ) 51 , d ) 50 , e ) 49
Rationale: "125 - 75 + 1 = 51 ' c ' is the answer"
Answer: c
Problem: if a boat goes 7 km upstream in 42 minutes and the speed of the stream is 6 kmph , then the speed of the boat in still water is
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) none of these
Rationale: explanation : rate upstream = ( 7 / 42 ) * 60 kmh = 10 kmph . speed of stream = 6 kmph . let speed in still water is x km / hr then , speed upstream = ( x ï ¿ ½ 6 ) km / hr . x - 6 = 10 or x = 16 kmph answer : e
Answer: e
Problem: a worker earns $ 20 on the first day and spends $ 15 on the second day . the worker earns $ 20 on the third day and spends $ 15 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 80 ?
Options: a ) 24 , b ) 25 , c ) 27 , d ) 30 , e ) 32
Rationale: "every two days , the net total is $ 5 . after 24 days , the worker will have $ 60 . on day 25 , the worker will receive $ 20 for a net total of $ 80 . the answer is b ."
Answer: b
Problem: 6 ) a marketing firm determined that , of 260 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45
Rationale: "180 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 180 = > 4 x = 120 = > x = 30 answer - c"
Answer: c
Problem: 26 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 39 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 26 ã — 13.5 = 351 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 351 â  „ 9 = 39 answer b"
Answer: b
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 22.5 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 22.5 s distance covered , d = vt = ( 400 / 36 ) ã — 22.5 = 250 m distance covered is equal to the length of the train = 250 m correct answer is 250 metres e"
Answer: e
Problem: at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 10 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 20 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 500 , d ) $ 800 , e ) $ 1000
Rationale: "let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 10 ) + 30 ( y - 10 ) = r - . 2 r = > 20 x + 200 + 30 y - 300 = . 8 r = > 20 x + 30 y = . 8 r + 100 . . . . . . . . . . . . ( 2 ) so , r = . 8 r + 100 = > r = 500 the answer is c ."
Answer: c
Problem: it is currently 8 : 12 pm . at what time in the morning was it exactly 205,106 minutes ago ?
Options: a ) 9 : 14 , b ) 9 : 16 , c ) 9 : 42 , d ) 9 : 44 , e ) 9 : 46
Rationale: convert 205,106 minutes to hours by dividing by 60 : 205,106 / 60 = 3,418 r 26 . that is 3,418 hours and 26 minutes . convert 3,418 hours to days by dividing by 24 : 3,418 / 24 = 142 r 10 . that is 142 days and 10 hours . now , 142 days previous was 8 : 12 pm . another 10 hours previous was 10 : 12 am . another 26 minutes previous was 9 : 46 am ( subtract the 12 minutes of 10 : 12 from 26 to get 14 . then subtract 14 from 60 to get 46 ) . e
Answer: e
Problem: a circular ground whose diameter is 70 metres , has a 2.8 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 540.72 , b ) 740.64 , c ) 640.64 , d ) 620.45 , e ) 725.26
Rationale: "req . area = ï € [ ( 37.8 ) 2 â € “ ( 35 ) 2 ] = 22 â  „ 7 ã — ( 72.8 ã — 2.8 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = 22 ã — 72.8 ã — 0.4 = 640.64 sq m answer c"
Answer: c
Problem: a 70 kg metal bar made of alloy of tin and silver lost 7 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 7 kg when 70 kg alloy is immersed . this is a loss of ( 7 / 70 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Problem: what is the rate percent when the simple interest on rs . 720 amount to rs . 180 in 4 years ?
Options: a ) 6.25 , b ) 7.25 , c ) 8.25 , d ) 9.25 , e ) 10.25
Rationale: "180 = ( 720 * 4 * r ) / 100 r = 6.25 % answer : a"
Answer: a
Problem: when 242 is divided by a certain divisor the remainder obtained is 15 . when 698 is divided by the same divisor the remainder obtained is 27 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?
Options: a ) 11 , b ) 17 , c ) 13 , d ) 23 , e ) 37
Rationale: let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27 . now 242 - 15 = 227 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 27 = 671 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 227 + 671 ) + 15 + 27 = x ( k + l ) + 42 when we divide this number by x then remainder will be equal to remainder of ( 42 divided by x ) = 5 hence x = 42 - 5 = 37 hence e
Answer: e
Problem: if 25 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 4 : 3 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 25 % of a = 1 / 3 b then 25 a / 100 = 1 b / 3 a / 4 = b / 3 a / b = 4 / 3 a : b = 4 : 3 answer is a"
Answer: a
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 15 times as heavy as water ?
Options: a ) 3 : 2 , b ) 3 : 8 , c ) 5 : 7 , d ) 3 : 7 , e ) 3 : 6
Rationale: "let us say , water weighs 1 kg / 1 liter . then gold weighs 19 kgs and copper weighs 9 kgs . assume x kgs of gold and y kgs of copper required to get the required alloy . we use weighted average formula = ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 therefore , 15 = x . 19 + y . 9 x + y 15 = x . 19 + y . 9 x + y 15 x + 15 y = 19 x + 9 y 4 x = 6 y ⇒ x / y = 3 : 2 so gold and copper should be mixed in the ratio 3 : 2 . answer : a"
Answer: a
Problem: find the cost of fencing around a circular field of diameter 32 m at the rate of rs . 2 a meter ?
Options: a ) 201 , b ) 132 , c ) 772 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 16 = 100.5 100.5 * 2 = rs . 201 answer : a"
Answer: a
Problem: how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 40 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 100 / 3 , d ) 8 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 40 % of ( 100 + x ) or 20 + x = ( 100 + x ) 2 / 5 100 + 5 x = 200 + 2 x 3 x = 100 x = 100 / 3 ans : c"
Answer: c
Problem: a bookseller has two display windows . she plans to display 3 new fiction books in the left window , and 3 new non - fiction books in the right window . assuming she can put the 4 fiction books in any order , and separately , the 3 non - fiction books in any order , how many total configurations will there be for the two display windows ?
Options: a ) 24 , b ) 72 , c ) 144 , d ) 36 , e ) 420
Rationale: the left window will have permutations of the 3 fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 the right window will have permutations of the 3 non - fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 any of the 24 displays of the left window could be combined with any of the 6 displays of the right window , so the total number of configurations is 6 * 6 = 36 answer : d .
Answer: d
Problem: find a two digit number , given that the sum of the digits is 11 and the difference of the digits is 5 . ?
Options: a ) 78 , b ) 53 , c ) 89 , d ) 83 , e ) 99
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 83 meets this description sum of digits - - - 8 + 3 = 11 difference of digits - - - 8 - 3 = 5 answer d ."
Answer: d
Problem: what is the remainder when 43 ^ 87 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 87 has the form 4 k + 3 so the units digit of 43 ^ 87 is 7 . the remainder when dividing by 5 is 2 . the answer is c ."
Answer: c
Problem: if julie rows 32 km upstream and 72 km down steam taking 4 hours each , then the speed of the stream
Options: a ) 1.5 kmph , b ) 0.5 kmph , c ) 0.4 kmph , d ) 1.6 kmph , e ) 2.5 kmph
Rationale: speed upstream = 32 / 4 = 8 kmph speed down stream = 72 / 8 = 9 kmph speed of stream = ½ ( 9 - 8 ) = 0.5 kmph answer : b
Answer: b
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of odd all the integers between 10 and 100 ?
Options: a ) 1345 , b ) 1576 , c ) 2475 , d ) 2578 , e ) 1895
Rationale: "numbers are 11 , 13,15 - - - - - - - , 97,99 average of the set : ( largest + smallest ) / 2 = ( 99 + 11 ) / 2 = 55 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 99 - 11 ) / 2 + 1 = 45 the sum = 45 * 55 = 2475 answer : c"
Answer: c
Problem: two numbers are in the ratio of 7 : 6 . if 18 be subtracted from each , they are in the ratio of 6 : 5 . find the numbers ?
Options: a ) 5,9 , b ) 7,9 , c ) 4,7 , d ) 7,6 , e ) 6,9
Rationale: "( 7 x - 18 ) : ( 6 x - 18 ) = 6 : 5 x = 1 = > 7,6 answer : d"
Answer: d
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 7 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 11 / 30 , b ) 29 / 42 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 7 x = 6 / 7 x so if gold card balance is transferred then the rest unspent will be 6 / 7 x - x / 6 = 29 / 42 x so the ans is b"
Answer: b
Problem: of all the homes on gotham street , 1 / 3 are termite - ridden , and 4 / 7 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 7 * 1 / 3 = 1 / 7 the answer is e ."
Answer: e
Problem: if the average ( arithmetic mean ) of x + 2 , x + 3 , and x + 4 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 2 + x + 3 + x + 4 ) / 3 = 0 = > 3 x + 9 = 0 = > x = - 3 answer b"
Answer: b
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 6
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 7
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 answer e"
Answer: e
Problem: 54671 - 14456 - 31466 = ?
Options: a ) 2449 , b ) 5449 , c ) 8749 , d ) 8449 , e ) 6468
Rationale: "c if we calculate we will get 8749"
Answer: c
Problem: what is the minimum value of | x - 4 | + | x + 5 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 10
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 5 | > = 0 - - > minimum occurs at x = - 5 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 5 - - > result = 9 + 0 + 10 = 19 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 9 + 1 = 10 x = 5 - - > result = 1 + 10 + 0 = 11 so minimum value of the expression occurs at x = 4 and the resultant value = 10 answer : e"
Answer: e
Problem: sravan travelled for 15 hours . he covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph . find the distance travelled by sravan ?
Options: a ) 520 , b ) 540 , c ) 550 , d ) 560 , e ) 440
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 45 + ( x / 2 ) / 30 = 15 = > x / 90 + x / 60 = 15 = > ( 2 x + 3 x ) / 180 = 15 = > x = 540 km answer : b
Answer: b
Problem: 50 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 100 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 50 = 66.67 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 66.67 = 100 litres . answer c"
Answer: c
Problem: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 10 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 18.25 , b ) 20.75 , c ) 22.25 , d ) 24.25 , e ) 26.75
Rationale: "let x be the length of the size 8 shoe . then 0.1 x = 9 / 4 x = 90 / 4 inches the size 15 shoe has a length of 90 / 4 + 7 / 4 = 97 / 4 = 24.25 inches the answer is d ."
Answer: d
Problem: a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 18 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 65.0 , b ) 67.5 , c ) 70.0 , d ) 72.5 , e ) 75.0
Rationale: "let x be the distance from his house to the school . x / 10 = x / 18 + 3 9 x = 5 x + 270 4 x = 270 x = 67.5 km the answer is b ."
Answer: b
Problem: excluding stoppages , the average speed of a bus is 75 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 28 min
Rationale: "in 1 hr , the bus covers 75 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 75 - 40 ) km i . e 35 km at 75 km / hr . stoppage time = 35 / 75 hrs = 28 min answer : e"
Answer: e
Problem: find the area of a parallelogram with base 26 cm and height 16 cm ?
Options: a ) 297 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 416 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 26 * 16 = 416 cm 2 answer : d"
Answer: d
Problem: by selling an article at rs . 600 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 360 , b ) s . 480 , c ) s . 500 , d ) s . 450 , e ) s . 550
Rationale: "sp = 600 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / 125 ] = 480 loss = 25 % = 25 % of 480 = rs . 120 sp = cp - loss = 480 - 120 = rs . 360 answer : a"
Answer: a
Problem: a man invests some money partly in 15 % stock at 105 and partly in 8 % stock at 40 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 7 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 15 % stock at 105 , investment = rs . ( 105 / 15 ) = rs . 7 . for an income of rs . 1 in 8 % stock at 40 , investment = rs . ( 40 / 8 ) = rs . 5 . ∴ ratio of investments = 7 : 5 = 7 : 5 answer c"
Answer: c
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 12375 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 600 × 20.625 ) = 12375 . answer a"
Answer: a
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 15,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 4,500 , c ) s . 5,700 , d ) s . 6,500 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 15000 x 3 / 10 = rs . 4,500 . b"
Answer: b
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 14 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: @ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 14 . then 4 n < 14 and n < 3.5 . the largest possible integer is n = 3 . the answer is c .
Answer: c
Problem: if x ^ 2 – 4 x = 5 , then one possible value of x – 2 =
Options: a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 5
Rationale: "x ^ 2 – 4 x = 5 i . e . x ^ 2 – 4 x - 5 = 0 i . e . x ^ 2 – 5 x + x - 5 = 0 i . e . ( x - 5 ) ( x + 1 ) = 0 i . e . x = 5 or - 1 i . e . x - 2 = 5 - 2 or - 1 - 2 i . e . x - 2 = 3 or - 3 answer : option c"
Answer: c
Problem: if 9 workers can build 9 cars in 9 days , then how many days would it take 7 workers to build 7 cars ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "9 workers can build 1 car per day on average . 1 worker can build 1 / 9 of a car per day . 7 workers can build 7 / 9 car per day . the time required to build 7 cars is 7 / ( 7 / 9 ) = 9 days the answer is d ."
Answer: d
Problem: the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.20 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.55 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 20 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : c"
Answer: c
Problem: a bakery has 6 employees . it pays annual salaries of $ 19,000 to each of 2 employees , $ 21,000 to 1 employee , and $ 22,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 20,200 , b ) $ 20,500 , c ) $ 20,800 , d ) $ 21,000 , e ) $ 21,400
Rationale: average = 2 ( 19000 ) + ( 21000 ) + 3 ( 22000 ) / 6 = $ 20,833 the answer is c .
Answer: c
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 300 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?
Options: a ) 65 , b ) 13.42 , c ) 18 , d ) 16 , e ) 14
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 300 / 5 = 60 sq m l b = 60 i . e . , l * l / 3 = 60 l 2 = 180 = > l = 13.42 answer : b"
Answer: b
Problem: the s . i . on a certain sum of money for 5 years at 10 % per annum is half the c . i . on rs . 5000 for 2 years at 12 % per annum . the sum placed on s . i . is ?
Options: a ) 1585 , b ) 1454 , c ) 1656 , d ) 2458 , e ) 1272
Rationale: c . i . = [ 5000 * ( 1 + 12 / 100 ) 2 - 5000 ] = ( 5000 * 28 / 25 * 28 / 25 - 5000 ) = rs . 1272 . sum = ( 636 * 100 ) / ( 5 * 10 ) = rs . 1272 answer : e
Answer: e
Problem: the sum of all two digit numbers divisible by 8 is
Options: a ) 910 , b ) 510 , c ) 611 , d ) 616 , e ) 810
Rationale: "required numbers are 16,24 . . . . . 96 this is an a . p . in which a = 16 , d = 8 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 16 + ( n - 1 ) * 8 = 96 16 + 8 n - 8 = 96 8 + 8 n = 96 8 n = 96 - 8 n = 88 / 8 then n = 11 . required sum = n / 2 ( a + l ) = 11 / 2 ( 16 + 96 ) = 616 answer is d"
Answer: d
Problem: dropbox charges $ 3.10 for first 1 / 5 of a month for 500 gb storage , plus $ 0.40 for each additional 1 / 5 of a month . what would dropbox charge for a data storage of 500 gb for 8 months ?
Options: a ) $ 15.60 , b ) $ 16.00 , c ) $ 17.80 , d ) $ 18.70 , e ) $ 19.10
Rationale: first 1 / 5 month charge = $ 3.10 rest of the months = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the months = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 answer is d .
Answer: d
Problem: find the simple interest on rs . 72,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 9000 , d ) 9500 , e ) none of them
Rationale: "p = rs . 72000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 72,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9000 answer is c ."
Answer: c
Problem: if it would take one machine 20 minutes to fill a large production order and another machine 30 minutes to fill the same order , how many minutes would it take both machines working together , at their respective rates , to fill the order ?
Options: a ) 10 min , b ) 12 min , c ) 15 min , d ) 20 min , e ) 18 min
Rationale: this question can be solved using the work formula : work = ( a ) ( b ) / ( a + b ) where a and b are the individual completion rates of the respective entities ( for the same job ) . we ' re told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job . plugging in those values gets us . . . ( 20 ) ( 30 ) / ( 20 + 30 ) = 600 / 50 = 12 minutes answer is b
Answer: b
Problem: how many digits are required to number a book containing 220 pages ?
Options: a ) 674 , b ) 604 , c ) 552 , d ) 372 , e ) 250
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 220 - ( 90 + 9 ) = 121 pages will require 121 * 3 = 363 digits . the total number of digits is 9 + 180 + 363 = 552 . the answer is c ."
Answer: c
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent w of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is w = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 5 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 60
Rationale: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 5 x = 5 * 8 = 40 . hence c ."
Answer: c
Problem: a rectangular box of volume v has width , depth and height in the ratio of 2 : 1 : 3 ( in that order ) . what is the height as a function of v ?
Options: a ) ( v / 2 ) ^ ( 1 / 3 )
b ) ( 2 v / 6 ) ^ ( 1 / 3 )
c ) ( 9 v / 2 ) ^ ( 1 / 3 )
d ) ( 4 v / 3 ) ^ ( 1 / 3 )
e ) ( 4 v / 2 ) ^ ( 1 / 3 )
Rationale: we are given width = 2 , depth = 1 , height = 3 . then volume v = width x depth x height = 2 * 1 * 3 = 6 i . e . v = 6 the correct option should result in 3 ( the height ) on substituting the value of v = 6 . checking options with v = 6 : a ) ( v / 2 ) ^ ( 1 / 3 ) = ( 6 / 2 ) ^ ( 1 / 3 ) = 3 ^ ( 1 / 3 ) incorrect answer b ) ( 2 v / 6 ) ^ ( 1 / 3 ) = ( 12 / 6 ) ^ ( 1 / 3 ) = 2 ^ ( 1 / 3 ) incorrect answer c ) ( 9 v / 2 ) ^ ( 1 / 3 ) = ( 54 / 2 ) ^ ( 1 / 3 ) = 3 correct answer d ) ( 4 v / 3 ) ^ ( 1 / 3 ) = ( 24 / 3 ) ^ ( 1 / 3 ) = 8 ^ ( 1 / 3 ) = 2 incorrect answer e ) ( 4 v / 2 ) ^ ( 1 / 3 ) = ( 24 / 2 ) ^ ( 1 / 3 ) = 12 ^ ( 1 / 3 ) incorrect answer answer : option c
Answer: c
Problem: calculate the amount that an investor needs to be invest to earn $ 1005 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 11 % compounded semi - annually ?
Options: a ) 8000 , b ) 8100 , c ) 8900 , d ) 8600 , e ) 8400
Rationale: "the approach is substitution , our interest requirement is $ 1005 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 8900 yielded $ 1005 using the formula a = p ( 1 + r / n ) nt hence answer is c"
Answer: c
Problem: a reduction of 42 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.15 , b ) 8.15 , c ) 7.15 , d ) 3.15 , e ) 1.15
Rationale: "explanation : 40 * ( 42 / 100 ) = 16.8 - - - 64 ? - - - 12 = > rs . 3.15 answer : d"
Answer: d
Problem: a train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 m , c ) 250 m , d ) 600 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 1500 + l ( while crossing the bridge ) time = 70 seconds i . e . speed = distance / time = ( 1500 + l ) / 70 case - 2 : distance = l ( while passing the lamp post ) time = 20 seconds i . e . speed = distance / time = ( l ) / 20 but since speed has to be same in both cases so ( 1500 + l ) / 70 = ( l ) / 20 i . e . 1500 + l = 3.5 l i . e . 2.5 l = 1500 i . e . l = 600 answer : option d"
Answer: d
Problem: what will be the cost of building a fence around a square plot with area equal to 289 square feet , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 3932 , c ) 3929 , d ) 3926 , e ) 3902
Rationale: "let the side of the square plot be a foot a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 foot cost of building the fence = 68 * 58 = rs . 3944 . answer : a"
Answer: a
Problem: for a race a distance of 224 meters can be covered by p in 28 seconds and q in 56 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 224 m , c ) 244 m , d ) 231 m , e ) 236 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 28 = 8 m / s = > speed of q = 224 / 56 = 4 m / s = > difference in time taken = 28 seconds therefore , distance covered by p in that time = 8 m / s x 28 seconds = 224 metres answer : b"
Answer: b
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives d = 1 / 9 . a"
Answer: a
Problem: the dimensions of a field are 20 m by 10 m . a pit 8 m long , 5 m wide and 2 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 1 m
b ) 2 m
c ) 0.5 m
d ) 0.75 m
e ) 1.5 m
Rationale: the volume of the earth removed is 8 * 5 * 2 = 80 m ^ 3 . the remaining area of the field is 20 * 10 - 8 * 5 = 160 m ^ 2 . 80 m ^ 3 of the earth evenly spread over the area of 160 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 80 / 160 = 0.5 m . answer : c
Answer: c
Problem: the grade point average of the entire class is 90 . if the average of one third of the class is 96 , what is the average of the rest ?
Options: a ) 92 , b ) 89 , c ) 88 , d ) 87 , e ) 86
Rationale: "let us take number of students on the class as ' x ' . avg grade point = sum of all grade points / x sum of all grade points = avg grade point * x = 90 x average of one third of the class = 96 = sum of one third grade points of the class / ( x / 3 ) sum of one third grade points of the class = 96 * ( x / 3 ) = 32 x sum of rest two third grade points of the class = sum of all grade points - sum of one third grade points of the class sum of rest two third grade points of the class = 90 x - 32 x = 58 x avg of two third of the class = sum of rest two third grade points of the class / ( x * 2 / 3 ) = 58 x / ( 2 x / 3 ) = 29 * 3 = 87 . hence , answer is d"
Answer: d
Problem: last year department store x had a sales total for december that was 6 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 6 / 17 , b ) 4 / 15 , c ) 1 / 3 , d ) 4 / 11 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 60 year total = 11 * 10 + 60 = 170 answer = 60 / 170 = 6 / 17 = a"
Answer: a
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9
b ) 1 / 8
c ) 1 / 6
d ) 1 / 5
e ) 1 / 3
Rationale: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a
Answer: a
Problem: if x is the median of the set { 9 / 2 , 11 / 3 , x , 28 / 9 , 21 / 5 } , x could be
Options: a ) 16 / 5 , b ) 17 / 5 , c ) 4 / 7 , d ) 30 / 7 , e ) 4
Rationale: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( e )"
Answer: e
Problem: a can do a piece of work in 4 days . b can do it in 7 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 28 / 3 days , c ) 67 days , d ) 17 / 5 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 7 = 3 / 28 = > 28 / 3 days answer : b"
Answer: b
Problem: how many integers from 101 to 200 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 20 , b ) 25 , c ) 28 , d ) 30 , e ) 40
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 101 to 200 , inclusive is ( 189 - 105 ) / 21 + 1 = 5 ; 33 - 5 = 28 . answer : c ."
Answer: c
Problem: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 30 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 50 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 84 , c ) 132 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 84 min b"
Answer: b
Problem: what is the remainder when 7 ^ 74 - 10 ^ 74 is divided by 24 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 0 , e ) none of these
Rationale: "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : d"
Answer: d
Problem: what least no . must be subtracted from 101054 so that remaining no . is divisible by 10 ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : on dividing 101054 by 10 we get the remainder 4 , so 4 should be subtracted option b"
Answer: b
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 8 years ?
Options: a ) 6 % , b ) 2.5 % , c ) 4 % , d ) 5 % , e ) 3.5 %
Rationale: 150 = ( 750 * 8 * r ) / 100 r = 2.5 % answer : b
Answer: b
Problem: machine – x produces 50 % of the total output and machine - y produces 75 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - x and two unit of 500 units produced by machine - x prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?
Options: a ) 0.008 , b ) 0.1 , c ) 0.12 , d ) 0.006 , e ) 0.007
Rationale: suppose machine x produce 1000 units total defective = 9 machine y then produces = 1500 units total defective = 6 probability = 15 / 2500 = 0.006 answer : d
Answer: d
Problem: what is the units digit of ( 5 ! * 4 ! + 6 ! * 5 ! ) / 2 ?
Options: a ) 4 , b ) 3 , c ) 0 , d ) 1 , e ) 2
Rationale: "( 5 ! * 4 ! + 6 ! * 5 ! ) / 2 = 5 ! ( 4 ! + 6 ! ) / 2 = 120 ( 24 + 720 ) / 2 = ( 120 * 744 ) / 2 = 120 * 372 units digit of the above product will be equal to 0 answer c"
Answer: c
Problem: find the cost of fencing around a circular field of diameter 22 m at the rate of rs . 2.50 a meter ?
Options: a ) 188 , b ) 172 , c ) 278 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 11 = 69 69 * 2 1 / 2 = rs . 172 answer : b"
Answer: b
Problem: two cycles are standing side - by - side . one cycle , which is 2.5 feets tall , casts a shadow that is 5 feets long . the other cycle is 2 feets tall . compute , in feets , the length of the shadow that the shorter cycle casts .
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: the ratio of shadow to height is constant , so if x is the length of the shadow , then 2.5 / 5 = 2 / x and x = 4 . correct answer b
Answer: b
Problem: stacy has a 12 page history paper due in 12 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 1 , e ) 6
Rationale: "12 / 12 = 1 answer : d"
Answer: d
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 10 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 110 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 110 - 80 ) / 80 * 100 = 10 % answer : d ."
Answer: d
Problem: on a two - dimensional coordinate plane , the line a = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s a = x ^ 2 - x ^ 3 instead of a = x ^ 2 - a ^ 3 . in this case : the x - intercept is the value ( s ) of x for a = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Problem: if the wages of 6 men for 15 days be rs . 2100 , then find the wages of for 12 days .
Options: a ) rs . 2420 , b ) rs . 2500 , c ) rs . 2520 , d ) rs . 2020 , e ) rs . 2650
Rationale: . let the required wages be rs . x . more men , more wages ( direct proportion ) less days , less wages ( direct proportion ) men 6 : 9 : : 2100 : x days 15 : 12 therefore ( 6 x 15 x x ) = ( 9 x 12 x 2100 )  x = ( 9 x 12 x 2100 ) / ( 6 x 15 ) = 2520 hence the required wages are rs . 2520 . answer is c
Answer: c
Problem: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 40 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 5 % , b ) 70 % , c ) 25 % , d ) 40 % , e ) 55 %
Rationale: "the complete round trip consists of driving to the service center and then back home again . so , once the technician drives to the service center he / she has already competed 50 % of the entire trip . since the technician completes a portion of the trip back home , the correct answer must be greater than 50 % so 0.5 + 0.5 * 0.4 = 0.70 answer : b"
Answer: b
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "number divisible by 11 : - 1000 / 11 = 90 numbers divisible by 35 : - 1000 / 35 = 28 numbers divisible by both 11 and 35 = 2 total numbers divisible by both 11 and 28 = 90 + 28 - 2 = 116 ( because we counted 2 in both 90 and 28 ) total numbers not divisible by 11 or 35 = 1000 - 116 = 884 answer : a"
Answer: a
Problem: convert the 15 / 36 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 1.3 , d ) 1.1 , e ) 1.2
Rationale: "15 / 36 m / s = 15 / 36 * 18 / 5 = 3 / 2 = 1.5 kmph . answer : b"
Answer: b