regisss/math_qa huggingface dataset:
Problem: what is the greatest positive integer x such that 5 ^ x is a factor of 125 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "125 ^ 10 = ( 5 ^ 3 ) ^ 10 = 5 ^ 30 answer : e"
Answer: e
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 35 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 40 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.35 m = = > revenue = price x quantity = 0.40 ( m + w ) = = > profit = 0.40 ( m + w ) - 0.35 m = 0.2 * ( 0.35 m ) [ 20 % of cost ] = = > 0.40 m + 0.40 w - 0.35 m = 0.07 m = = > 0.02 m = 0.40 w = = > m / w = 0.40 / 0.02 = 20 - - or - - w / m = 1 / 20 a is correct ."
Answer: a
Problem: two trains start simultaneously from opposite ends of a 150 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 150 - km trip in 4 hours . train y , travelling at a constant rate , completes the 150 - km trip in 3.5 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 68 , b ) 70 , c ) 72 , d ) 74 , e ) 76
Rationale: if the two trains cover a total distance d , then train x travels ( 7 / 15 ) * d while train y travels ( 8 / 15 ) * d . if the trains travel 150 km to the meeting point , then train x travels ( 7 / 15 ) * 150 = 70 km . the answer is b .
Answer: b
Problem: ( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: ( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ ( m + 1 ) = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 34 answer c
Answer: c
Problem: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 106 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 277 , d ) 122 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 106 x = 122 answer : d"
Answer: d
Problem: a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 1.4 , b ) 1.5 , c ) 1.6 , d ) 1.8 , e ) 1.0
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 18 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 1.8 m / s d"
Answer: d
Problem: if the cost price is 98 % of sp then what is the profit %
Options: a ) 4.07 % , b ) 4 % , c ) 2.7 % , d ) 2.04 % , e ) 2.08 %
Rationale: "sol . sp = rs 100 : then cp = rs 98 : profit = rs 2 . profit = { ( 2 / 98 ) * 100 } % = 2.04 % answer is d ."
Answer: d
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 3 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1.5 , b ) 1.3 , c ) 1.25 , d ) 1.6 , e ) 2
Rationale: "d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 50 t + 50 / 4 = 60 t 10 t = 50 / 4 t = 1.25 or 1 hr , 15 min c"
Answer: c
Problem: the banker â € ™ s discount of a certain sum of money is rs . 78 and the true discount on the same sum for the same time is rs . 66 . the sum due is
Options: a ) 429 , b ) 280 , c ) 360 , d ) 450 , e ) none
Rationale: sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 78 * 66 / 78 - 66 ] = rs . [ 78 * 66 / 12 ] = rs . 429 answer a
Answer: a
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 10 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 152.3 , c ) $ 180 , d ) $ 220 , e ) $ 260
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 10 * ( a + e ) = = > 9 a = 11 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 e / 9 * 11 = 220 + 12 e or ( 121 / 9 - 12 ) e = 220 or 13 / 9 e = 220 e = 220 * 9 / 13 = 152.3 b"
Answer: b
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number q of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average q sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Problem: subtract the absolute value from the local value of 4 in 564823
Options: a ) 196 , b ) 1996 , c ) 2996 , d ) 3996 , e ) 6000
Rationale: explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 - 4 = 3996 answer : option d
Answer: d
Problem: machine a and machine g are each used to manufacture 660 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine g . machine g produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: [ reveal ] spoiler : timeg : 660 / x timea : [ 660 / x + 10 ] 660 / x = [ 660 / x + 10 ] * 110 / 100 660 / x = 66 * 11 / x + 10 660 x + 10 = 66 * 11 * x 660 x + 6600 = 66 * 11 * x x = 100 plug in back to timea 660 / 100 + 10 = > 660 / 110 = 6
Answer: a
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 7 ] * [ 4 ] equivalent to ?
Options: a ) [ 28 ] , b ) [ 84 ] , c ) [ 42 ] , d ) [ 48 ] , e ) [ 14 ]
Rationale: "[ 7 ] * [ 4 ] = 21 * 2 = 42 = ( 1 / 2 ) ( 84 ) = [ 84 ] the answer is b ."
Answer: b
Problem: what is the tens digit of 6 ^ 21 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 21 has the form 5 n + 1 , so the tens digit of 6 ^ 21 is 5 . the answer is c ."
Answer: c
Problem: machine x and machine b are each used to manufacture 660 sprockets . it takes machine x 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine x . how many sprockets per hour does machine x produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: i think the correct answer is a . machine x produces at a speed of x sp / hour and b at a speed of b sp / hour . so , 660 / x = ( 660 / b ) + 10 and x = 1,1 x - - - > 1,1 * 660 = 660 + 11 x - - - > a = 6 , so answer a is correct
Answer: a
Problem: a can do a piece of work in 2 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 3
Rationale: "a ' s 1 hour ' s work = 1 / 2 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 2 + 1 / 3 ) = 5 / 6 . b ' s 1 hour ' s work = ( 5 / 6 - 1 / 2 ) = 1 / 3 . therefore a alone will take 3 hours to do the work . e"
Answer: e
Problem: the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person
Options: a ) 11 , b ) 66 , c ) 28 , d ) 30 , e ) 99
Rationale: "let ' s take the present age of the elder person = x and the present age of the younger person = x – 16 ( x – 6 ) = 3 ( x - 16 - 6 ) = > x – 6 = 3 x – 66 = > 2 x = 60 = > x = 60 / 2 = 30 answer : d"
Answer: d
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 10 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.4 % , b ) 9.6 % , c ) 9 % , d ) 9.8 % , e ) 10 %
Rationale: "the amount of chromium in the new 10 + 30 = 40 kg alloy is 0.12 * 10 + 0.08 * 30 = 3.6 kg , so the percentage is 3.6 / 40 * 100 = 9 % . answer : c"
Answer: c
Problem: an automotive test consisted of driving a car the same distance 3 separate times , first at an average rate of 4 miles per hour , then 5 miles per hour , then 6 miles per hour . if the test took 37 hours to complete , how many miles was the car driven during the entire test ?
Options: a ) 100 , b ) 120 , c ) 180 , d ) 200 , e ) 240
Rationale: x is the segment to be traveled x / 4 + x / 5 + x / 6 = 37 or 74 x / 120 = 37 x = 60 miles . total distance = 3 * 60 = 180 miles c
Answer: c
Problem: a can do a work in 12 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 ) 8 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 12 b rate = 1 / 24 ( a + b ) rate = ( 1 / 12 ) + ( 1 / 24 ) = 1 / 8 a & b finish the work in 8 days correct option is c"
Answer: c
Problem: a , b and c invests rs . 2000 , rs . 3000 and rs . 4000 in a business . after 2 year a removed his money ; b and c continued the business for two more year . if the net profit after 3 years be rs . 4000 , then a ' s share in the profit is ?
Options: a ) 460 , b ) 289 , c ) 220 , d ) 400 , e ) 640
Rationale: "2 * 24 : 3 * 36 : 4 * 36 4 : 9 : 12 4 / 25 * 4000 = 640 answer : e"
Answer: e
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 19 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 465 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 19 ) ( x - 8 ) ^ 2 = t + 19 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 465 + 19 = 484 = 22 ^ 2 = ( x - 8 ) ^ 2 hence , x = 30 cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 30 * 31 / 2 = 465 hence , answer is a ."
Answer: a
Problem: the average of 5 quantities is 10 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 19 , b ) 14 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: answer : a ( 5 x 10 - 3 x 4 ) / 2 = 19
Answer: a
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 70 paise per sq m is
Options: a ) rs . 258.80 , b ) rs . 358.80 , c ) rs . 458.80 , d ) rs . 520.80 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 70 / 100 ) = rs . 520.80 answer : d"
Answer: d
Problem: how many odd factors does 520 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 520 = 2 * 5 * 13 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 520 . answer : b ."
Answer: b
Problem: if the sum of two numbers is 22 and the sum of their squares is 460 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 12 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 460 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 460 + 2 xy so xy = 24 / 2 = 12 answer : c"
Answer: c
Problem: what is the value of n if the sum of the consecutive odd integers from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: # of terms = ( n - 1 / 2 ) + 1 { ( last term - first term ) / 2 + 1 | sum = ( 1 + n ) / 2 * # of terms = ( n + 1 ) ^ 2 / 4 = 169 n + 1 = 13 * 2 n + 1 = 26 n = 25 . answer : b
Answer: b
Problem: the total number of plums that grew during each year on a certain plum tree was equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded to the nearest lower integer . ) during its 3 rd year , this plum tree grew 50 plums . how many plums did it grow during its 6 th year ?
Options: a ) a ) 41 , b ) b ) 38 , c ) c ) 35 , d ) d ) 29 , e ) e ) 28
Rationale: the answer shud be 38 . ( 50 - 3 - 4 - 5 = 38 ) yes , if you go the 50 - 3 way , then it will be 38 . if instead you go the 50 - 4 way ( which they have suggested ) , the answer will be 35 . as i said , there is ambiguity here . answer is c
Answer: c
Problem: a can finish a work in 8 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 3 / 5 , b ) 3 / 6 , c ) 3 / 7 , d ) 3 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 8 b ' s 1 day work = 1 / 4 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 8 + 1 / 4 ) = 3 / 8 so in one day 3 / 8 work will be done answer : d"
Answer: d
Problem: donovan and michael are racing around a circular 500 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 500 / 45 = > 100 / 9 2 . speed / rate of michael = distance / time = > 500 / 40 = > 50 / 4 relative speed between them = 50 / 4 - 100 / 9 = > 25 / 36 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 500 , relative rate = 50 / 36 total time taken by micheal to surpass donovan = distance / rate = > 500 * 36 / 50 = > 3600 / 10 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . a"
Answer: a
Problem: if m = | | n – 3 | – 2 | , for how many values of n is m = 6 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "m = | | n – 3 | – 2 | can be 4 only and only when n - 3 = + / - 8 . so there are 2 values of n answer : e"
Answer: e
Problem: in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of :
Options: a ) 3488 , b ) 6240 , c ) 2776 , d ) 2889 , e ) 7721
Rationale: "explanation : to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 answer : b ) 6240"
Answer: b
Problem: in a group of 68 students , each student is registered for at least one of 3 classes – history , math and english . 20 - one students are registered for history , 20 - 6 students are registered for math , and thirty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: a u b u c = a + b + c - ab - bc - ac + abc 68 = 21 + 26 + 34 - ab - bc - ac + 3 = > ab + bc + ac = 16 exactly two classes = ab + bc + ac - 3 abc = 16 - 3 * 3 = 7 hence e
Answer: e
Problem: 210 reputed college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 18 kmph , find the speed of the stream ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 7 kmph , d ) 6 kmph , e ) 5 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 18 / 3 = 6 kmph . answer : d"
Answer: d
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 62 . if the marks secured by reema was written as 50 instead of 85 then find the correct average marks up to two decimal places .
Options: a ) 63 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 62 = 2170 corrected total marks = 2170 - 50 + 85 = 2205 correct average = 2205 / 35 = 63 answer : a"
Answer: a
Problem: on the xy - coordinate plane , point a lies on the y - axis and point b lies on the x - axis . points a , b , and c form a right triangle with a 90 - degree angle at point c and the triangle has an area of 20 . if ac is parallel to the x - axis , and bc is parallel to the y - axis , which of the following could be the coordinates of point c ?
Options: a ) ( 8 , - 3 )
b ) ( 4 , 5 )
c ) ( - 5 , 7 )
d ) ( - 2 , - 20 )
e ) ( - 15 , - 3 )
Rationale: the area of the triangle formed will be : 1 / 2 * base * height = 1 / 2 * | ( x - coordinate of point c ) | * | ( y - coordinate of point c ) | = 20 thus | product of coordinates of point c | = 40 the answer is d .
Answer: d
Problem: 63 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 ) a ) 87 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 97
Rationale: "( 63 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 140 140 – 63 = 77 answer : b"
Answer: b
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 90 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 70 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 90 * 3 = 270 miles . therefore , total distance covered = 80 + 270 = 350 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 350 / 5 = 70 miles per hour . choice d"
Answer: d
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be odd ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 3 . answer : b ."
Answer: b
Problem: in march mrs bil ' s earnings were 80 percent of the bil family ' s total income . in april mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?
Options: a ) 83 , b ) 56 , c ) 34 , d ) 12 , e ) 26
Rationale: lets say the family income is 100 in may , lee earned 80 family income is 20 in june , lee earned 20 % more than may , so it is ( 80 + 20 * 80 / 100 = 96 ) family income is same 20 in june lee ' s income percent is 96 * 100 / 116 ~ 83 ans is a
Answer: a
Problem: how many prime numbers are between 29 / 4 and 87 / 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 29 / 4 = 7 . xxx 87 / 5 = 17 . xxx so we need to find prime numbers between 7 ( exclusive ) - 16 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b
Answer: b
Problem: in digging a pond 25 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 1750 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1121
Rationale: "25 * 10 * 5 = 1750 answer : a"
Answer: a
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 48 kmph , find the speed of the stream ?
Options: a ) 16 kmph , b ) 19 kmph , c ) 14 kmph , d ) 11 kmph , e ) 13 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 48 / 3 = 16 kmph . answer : a"
Answer: a
Problem: what is the total number of integers between 100 and 500 ( exclusive ) that are divisible by 5 ?
Options: a ) 51 , b ) 63 , c ) 79 , d ) 66 , e ) 42
Rationale: 105 , 110 , 115 , . . . , 490,495 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 495 - 105 ) / ( 5 ) + 1 = 78 + 1 = 79 answer is c
Answer: c
Problem: a shopkeeper sold 10 articles at the cost price of 12 articles . then find the profit % or lost %
Options: a ) - 10 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: here 10 articles selling price = 12 articles cost price so the difference = 12 - 10 = 2 % of profit = 2 * 100 / 10 = 20 % correct option is d
Answer: d
Problem: venus travels around the sun at a speed of approximately 21.9 miles per second . the approximate speed is how many miles per hour ?
Options: a ) 64,420 , b ) 78,840 , c ) 83,160 , d ) 88,970 , e ) 94,320
Rationale: 21.9 * 3600 = 78,840 the answer is b .
Answer: b
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: 150 ml solution contains 45 ml sulphuric acid 400 ml solution contains 48 ml sulphuric acid adding 550 ml solution contains 93 ml sulphuric acid 93 / 550 ≈ 90 / 540 = 1 / 6 answer is d
Answer: d
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 18 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 9 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 18 = > x = 3 so deepak age is = 3 ( 3 ) = 9 answer : d"
Answer: d
Problem: a and b can do a piece of work in 8 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ?
Options: a ) 3.33 days , b ) 8.33 days , c ) 3.99 days , d ) 7.38 days , e ) 2.88 days
Rationale: a + b = 1 / 8 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 8 + 1 / 12 + 1 / 16 = 13 / 48 a + b + c = 13 / 96 96 / 13 = 7.38 days answer : d
Answer: d
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 19 % home electronics ; 10 % food additives ; 24 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 90 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "14 % microphotonics ; 19 % home electronics ; 10 % food additives ; 24 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 19 + 10 + 24 + 8 ) = 25 % basic astrophysics . 25 % of 360 ° is 90 ° . answer : b ."
Answer: b
Problem: a will was written such that an estate would be divided among 4 beneficiaries with the remainder donated to charity . one stipulation in the will is that no one beneficiary can receive an amount within 20 % of another ' s amount . if one of the beneficiaries received $ 40000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 4 beneficiaries ?
Options: a ) $ 12436 , b ) $ 13344 , c ) $ 71234 , d ) $ 15736 , e ) $ 19403
Rationale: 1 st - 40,000 . 2 nd - 0.8 * 40,000 = 32,000 3 rd - 0.8 * 32,000 = 25,600 4 th - 0.8 * 25,600 = ~ 20,480 range = 40,000 - 20,480 = 19520 answer : e .
Answer: e
Problem: a box contains 2 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 7 / 5 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 5 black balls be bbbbb and 2 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 5 ! x 2 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 6 slots and 4 black ( bbbb ) and 2 red ( rrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 2 ! ) hence required probability = [ ( 7 ! ) / ( 5 ! x 2 ! ) ] / [ ( 6 ! ) / ( 4 ! x 2 ! ) ] = 7 / 5 b"
Answer: b
Problem: sachin is younger than rahul by 4 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?
Options: a ) 24.9 , b ) 24.6 , c ) 24.2 , d ) 24.8 , e ) 24.5
Rationale: "let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . ( x - 7 ) / x = 7 / 9 2 x = 63 = > x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : e"
Answer: e
Problem: if a ( a + 5 ) = 6 and b ( b + 5 ) = 6 , where a ≠ b , then a + b =
Options: a ) − 5 , b ) − 9 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 1 then b = - 6 or if a = - 6 then b = 1 but in each case a + b = - 6 + 1 = - 5 answer : option a"
Answer: a
Problem: the l . c . m . of two numbers is 36 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 36 or x = 6 . the numbers are 12 and 18 . hence , required sum = ( 12 + 18 ) = 30 . answer : option b"
Answer: b
Problem: a man can do a piece of work in 6 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 the son alone can do the work in 6 days answer is c"
Answer: c
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 70 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 240 , c ) 385 , d ) 440 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 70 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 70 = 315 . total area = 70 + 315 = 385 answer : c ."
Answer: c
Problem: what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 8 ?
Options: a ) 0 , b ) 2 , c ) 0 , d ) 3 , e ) none of these
Rationale: "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 48 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : c"
Answer: c
Problem: the sum of the present ages of a , b , c is 57 years . 3 years ago their ages were in the ratio 1 : 2 : 3 . what is the present age of a ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: three years ago : a : b : c = 1 : 2 : 3 let a = 1 x , b = 2 x , and c = 3 x . today : ( x + 3 ) + ( 2 x + 3 ) + ( 3 x + 3 ) = 57 x = 8 so the present age of a is x + 3 = 11 the answer is d .
Answer: d
Problem: a parking garage rents parking spaces for $ 12 per week or $ 30 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 264
Rationale: "12 $ per week ! an year has 52 weeks . annual charges per year = 52 * 12 = 624 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 30 = 360 $ 624 - 360 = 264 ans e"
Answer: e
Problem: the profit earned by selling an article for rs . 753 is equal to the loss incurred when the same article is sold for rs . 455 . what should be the sale price for making 50 % profit ?
Options: a ) 706 , b ) 786 , c ) 906 , d ) 896 , e ) 696
Rationale: "let c . p = rs . x then as given , ( 753 - x ) = ( x - 455 ) 2 x = 1208 x = 604 there fore s . p = 150 % of 604 = > rs . = rs . 906 answer : c"
Answer: c
Problem: the sum of a number and its square is 1406 . what is the number ?
Options: a ) 1409
b ) 1402
c ) 1221
d ) 1406
e ) 8828
Rationale: explanation : by option verification 37 + 37 × 37 = 1406 answer : d
Answer: d
Problem: 1 , 1 , 2 , 1 , 2 , 3 , 1 , 2 , 3 , 4 , 1 , 2 , __ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "1,1 , 2,1 , 2,3 , 1,2 , 3,4 , 1,2 , __ ? looking at the series 1 12 123 1234 12 ( 3 ) 45 so the answer is 3 . answer : c"
Answer: c
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 756 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1806 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 756 × 100 ) / ( 6 × 12 ) = rs . 1050 bg = bd – td = > 756 = bd - 1050 = > bd = 1050 + 756 = 1806 answer : option d"
Answer: d
Problem: one fourth of one third of two fifth of a number is 35 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 420 , c ) c ) 180 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 35 then x = 35 * 30 = 1050 40 % of 1050 = 420 answer : option b"
Answer: b
Problem: a flagstaff 17.5 m high casts a shadow of length 40.25 m . what will be the height of a building , which casts a shadow of length 28.75 m under similar conditions ?  
Options: a ) 12.5 m , b ) 10.5 m , c ) 14 , d ) 12 , e ) 10
Rationale: explanation : let the required height of the building be x meter more shadow length , more height ( direct proportion ) hence we can write as ( shadow length ) 40.25 : 28.75 : : 17.5 : x ⇒ 40.25 × x = 28.75 × 17.5 ⇒ x = 28.75 × 17.5 / 40.25 = 2875 × 175 / 40250 = 2875 × 7 / 1610 = 2875 / 230 = 575 / 46 = 12.5 answer : option a
Answer: a
Problem: in a party every person shakes hands with every other person . if there were a total of 153 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 153 n ( n - 1 ) / 2 = 153 â ˆ ´ n = 18 answer : option d"
Answer: d
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 1 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 1 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 4 - - - > 5 = 2 k + 4 - - - > k = 1 / 2 . the answer is , therefore , ( a ) ."
Answer: a
Problem: if a lends rs . 25000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 1125 , b ) 1225 , c ) 1325 , d ) 1145 , e ) 2125
Rationale: "( 25000 * 1.5 * 3 ) / 100 = > 1125 answer : a"
Answer: a
Problem: 50 is what percent of 125 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 50 / 125 × 100 = 50 % answer : b
Answer: b
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 10 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 5 , b ) 5 / 15 , c ) 6 / 15 , d ) 3 / 10 , e ) 4 / 15
Rationale: p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.1 * 300 / 450 = 30 / 450 = 1 / 15 the sum of the probabilities is 6 / 15 = 2 / 5 the answer is c .
Answer: c
Problem: the least number by which 72 must be multiplied in order to produce a multiple of 112 , is
Options: a ) 6 , b ) 12 , c ) 14 , d ) 18 , e ) 20
Rationale: "solution required numbers is divisible by 72 as well as by 112 , if it is divisible by their lcm , which is 1008 . now , 1008 when divided by 72 , gives quotient = 14 . required number = 14 . answer c"
Answer: c
Problem: find the number , difference between number and its 3 / 5 is 58 .
Options: a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 146
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 58 , = > ( 2 / 5 ) x = 58 = > 2 x = 58 * 5 , = > x = 145 answer : option d"
Answer: d
Problem: the unit digit in the product ( 891 * 781 * 912 * 463 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 1 * 1 * 2 * 3 ) = 6 answer : c"
Answer: c
Problem: find the value of 3 + 2 . ( 8 - 3 )
Options: a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 19
Rationale: "3 + 2 . ( 8 - 3 ) = 3 + 2 ( 5 ) , = 3 + 2 * 5 , = 3 + 10 , = 13 , correct answer : ( d )"
Answer: d
Problem: two numbers a and b are such that the sum of 5 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 3 , b ) 1 : 1 , c ) 3 : 4 , d ) 4 : 3 , e ) 5 : 5
Rationale: "5 / 100 a + 4 / 100 b = 2 / 3 ( 6 / 100 a + 8 / 100 b ) = > 1 / 20 a + 1 / 25 b = 1 / 25 a + 4 / 75 b = > ( 1 / 20 - 1 / 25 ) b = 1 / 25 a + 4 / 75 b ( 1 / 20 - 1 / 25 ) a = ( 4 / 75 - 1 / 25 ) b 1 / 100 a = 1 / 75 b a / b = 100 / 75 = 4 / 3 req ratio = 4 : 3 answer d"
Answer: d
Problem: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 5 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 360 , c ) 400 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 5 of 300 = 60 total amount in her account = 360 answer b"
Answer: b
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "9 / 7 * 32 = 41.1 the answer is c ."
Answer: c
Problem: a man ' s speed with the current is 22 km / hr and the speed of the current is 5 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 22 - 5 ) km / hr = 17 km / hr . man ' s rate against the current = ( 17 - 5 ) km / hr = 12 km / hr . answer : d"
Answer: d
Problem: machine z takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine z to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of z is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and a reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of z . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Problem: a certain pair of used shoes can be repaired for $ 13.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 17.69 , b ) 14.85 , c ) 21.3 , d ) 16.5 , e ) 18.51
Rationale: "1 ) cost of repairing = 13.5 ( for one year ) , therefore for 2 years it would be $ 27 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 32 - 27 ) / ( 27 ) * 100 = 18.51 % . ans is e"
Answer: e
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 31 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 31 kg joins the group , total weight of boys = 20 x + 31 so 20 x + 31 = 21 ( x + 1 ) = > x = 10 . answer : e"
Answer: e
Problem: if x = 55 + 2 q and y = 4 q + 41 , then for what value of q , x is equal to y ?
Options: a ) - 14 , b ) 14 , c ) - 7 , d ) 7 , e ) 0
Rationale: explanation : x = y < = > 55 + 2 q = 4 q + 41 < = > 2 q = 14 < = > q = 7 . answer : d
Answer: d
Problem: a man can swim in still water at 4 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.9 , c ) 1.1 , d ) 1.5 , e ) 0.75
Rationale: "m = 4 s = x ds = 4 + x us = 4 + x 4 + x = ( 4 - x ) 2 4 + x = 8 - 2 x 3 x = 4 x = 0.75 answer : e"
Answer: e
Problem: there are 10 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 90
Rationale: "every team plays with 9 teams . . . so total no of matches = 10 x 9 = 90 . now , each match is played twice = > 90 x 2 but 2 teams play a match = > 90 x 2 / 2 = 90 . answer : e"
Answer: e
Problem: a sum fetched a total simple interest of rs . 100 at the rate of 5 p . c . p . a . in 4 years . what is the sum ?
Options: a ) 800 , b ) 600 , c ) 500 , d ) 1000 , e ) 300
Rationale: "sol . principal = rs . [ 100 * 100 / 5 * 4 ] = rs . [ 10000 / 20 ] = rs . 500 . answer c"
Answer: c
Problem: an auction house charges a commission of 18 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 200,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.18 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 200,000 ( 18 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c ."
Answer: c
Problem: if one person completes a journey in 10 hrs . he travels 1 st half of the journey at the rate of 21 km / hr and 2 nd half at therate of 24 km / hr . find the total journey in km .
Options: a ) 200 km , b ) 212 km , c ) 224 km , d ) 230 km , e ) 256 km
Rationale: distance = speed x time let time taken to travel the first half = x hr then time taken to travel the second half = ( 10 - x ) hr distance covered in the the first half = 21 x distance covered in the the second half = 24 ( 10 - x ) but distance covered in the the first half = distance covered in the the second half = > 21 x = 24 ( 10 - x ) = > 21 x = 240 - 24 x = > 45 x = 240 = > 9 x = 48 = > 3 x = 16 ⇒ x = 163 hence distance covered in the the first half = 21 x = 21 × 163 = 7 × 16 = 112 kmtotal distance = 2 × 112 = 224 km c
Answer: c
Problem: m = { - 6 , - 5 , - 4 , - 3 , - 2 , - 1 } t = { - 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 1 / 4 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: we will have a negative product only if 1 or 2 are selected from set t . p ( negative product ) = 2 / 8 = 1 / 4 the answer is b .
Answer: b
Problem: the radius of a cylinder is 6 m , height 21 m . the total surface area of the cylinder is ?
Options: a ) 525 , b ) 528 , c ) 522 , d ) 529 , e ) 521
Rationale: "total surface area of the cylinder is = 2 π r ( r + h ) = 2 × 22 / 7 × 6 ( 6 + 8 ) = 2 × 22 / 7 × 6 ( 14 ) = 44 × 12 = 528 m ( power 2 ) answer is b ."
Answer: b
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 $ 2,160 , 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 = 2160 = > x = 6 total lens = 6 + ( 6 + 5 ) = 17 answer d"
Answer: d
Problem: what is the tenth digit of ( 5 ! * 5 ! - 5 ! * 3 ! ) / 5 ?
Options: a ) 1 , b ) 2 , c ) 0 , d ) 6 , e ) 7
Rationale: ( 5 ! * 5 ! + 5 ! * 3 ! ) / 5 = 5 ! ( 5 ! + 3 ! ) / 5 = 120 ( 120 + 6 ) / 5 = 3024 units digit of the above product will be equal to 2 answer b
Answer: b
Problem: 30 pens and 75 pencils were purchased for 570 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 570 – 150 ) = 360 ∴ average price of a pen = 420 ⁄ 60 = 14 answer e"
Answer: e
Problem: if 20 typists can type 42 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 189 , b ) 72 , c ) 144 , d ) 216 , e ) 400
Rationale: "20 typists can type 42 letters , so 30 typists can type = 42 * 30 / 20 42 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 42 * 30 * 60 / 20 * 20 = 189 a is the answer"
Answer: a
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates q apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates q / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 18 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 18 + 11 - - > { bike } = 53 - - > # those who have bike only is { bike } - { both } = 53 - 18 = 35 . answer : b ."
Answer: b
Problem: two trains of equal are running on parallel lines in the same direction at 42 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 30 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 42 - 36 = 6 km / hr . = 6 * 5 / 18 = 5 / 3 m / sec . 2 x / 36 = 5 / 3 = > x = 30 . answer : a"
Answer: a
Problem: a customer pays 70 dollars for a coffee maker after a discount of 20 dollars what is the original price of the coffe maker ?
Options: a ) 50 , b ) 40 , c ) 90 , d ) 60 , e ) 20
Rationale: let x be the original price . x - 20 = 70 x - 20 + 20 = 70 + 20 x + 0 = 90 x = 90 answer is c
Answer: c
Problem: if 40 % of a certain number is 160 , then what is 50 % of that number ?
Options: a ) 270 , b ) 380 , c ) 200 , d ) 360 , e ) 290
Rationale: "explanation : 40 % = 40 * 4 = 160 50 % = 50 * 4 = 200 answer : option c"
Answer: c
Problem: a man can row his boat with the stream at 12 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 4 kmph , c ) 98 kmph , d ) 6 kmph , e ) 4 kmph
Rationale: "ds = 12 s = ? s = ( 12 - 4 ) / 2 = 4 kmph answer : e"
Answer: e