regisss/math_qa huggingface dataset:
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 49 more . what was his original selling price ?
Options: a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840
Rationale: let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 49 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 49 = > 0.07 x = 49 = > x = $ 700 original purchase price = $ 700 hence , original selling price ( at 10 % of profit ) = 1.1 ( 700 ) = $ 770 option a
Answer: a
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 612 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: difference in c . i . and s . i for 2 years = $ 612 - $ 600 = $ 12 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 12 rate = ( 100 * 12 ) / ( 300 ) = 4 % the answer is b .
Answer: b
Problem: 3 numbers which are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073 . the sum of the 3 numbers is :
Options: a ) 81 , b ) 82 , c ) 85 , d ) 90 , e ) 95
Rationale: since the numbers are co - prime , they contain only 1 as the common factor . also , the given two products have the middle number in common . so , middle number = h . c . f of 551 and 1073 = 29 ; first number = 551 / 29 = 19 third number = 1073 / 29 = 37 . required sum = 19 + 29 + 37 = 85 . answer : c
Answer: c
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 17 km / hr , c ) 60 km / hr , d ) 77 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c"
Answer: c
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 110 mph + 88 mph ) / 2 = 99 mph correct answer is : e"
Answer: e
Problem: a person is traveling at 65 km / hr and reached his destiny in 3 hr then find the distance ?
Options: a ) 205 km , b ) 195 km , c ) 295 km , d ) 115 km , e ) 215 km
Rationale: "t = 3 hrs d = t * s = 65 * 3 = 195 km answer is b"
Answer: b
Problem: find the area of a parallelogram with base 12 cm and height 8 cm ?
Options: a ) 96 cm 2 , b ) 104 cm 2 , c ) 78 cm 2 , d ) 86 cm 2 , e ) 76 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 8 = 96 cm 2 answer : a"
Answer: a
Problem: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1260 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8235 , e ) 9255
Rationale: "you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1260 , we get the answer of 8235 . ( ans d )"
Answer: d
Problem: if the annual increase in the population of a town is 4 % and the present number of people is 15625 , what will the population be in 3 years ?
Options: a ) 15265 , b ) 16458 , c ) 25600 , d ) 17576 , e ) 14785
Rationale: "the required population is = 15625 ( 1 + 4 / 100 ) ^ 3 = 15625 * 26 / 25 * 26 / 25 * 26 / 25 = 17576 answer is d"
Answer: d
Problem: n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 n is divided by 4 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 5
Rationale: "explanation : let n = 4 q + 3 . then 2 n = 8 q + 6 = 4 ( 2 q + 1 ) + 2 . thus , when 2 n is divided by 4 , the remainder is 2 . answer : b"
Answer: b
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 224
Rationale: "white : yellow = x : ( x + 70 ) = 8 : 13 - - > 13 x = 8 x + 560 - - > x = 112 . the total # of balls originally x + x = 112 + 112 = 224 . answer : e ."
Answer: e
Problem: 80 x 100 + 80 x 11 = ?
Options: a ) 7500 , b ) 8880 , c ) 6200 , d ) 5200 , e ) none of them
Rationale: "= 80 x ( 100 + 11 ) ( by distributive law ) = 80 x 111 = 8880 answer is b"
Answer: b
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 3.2 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 397.2
Rationale: "explanation : cost of each share = ( 20 + 3.2 % of 20 ) = rs . 20.64 therefore , number of shares = 8200 / 20.64 = 397.2 answer : e"
Answer: e
Problem: in a school of 850 boys , 44 % of muslims , 14 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 153 , d ) d ) 721 , e ) e ) 272
Rationale: "44 + 14 + 10 = 68 % 100 – 68 = 32 % 850 * 32 / 100 = 272 answer : e"
Answer: e
Problem: the diagonals of a rhombus are 13 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 130 , c ) 150 , d ) 179 , e ) 172
Rationale: "1 / 2 * 13 * 20 = 130 answer : b"
Answer: b
Problem: a train 125 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 51 , d ) 79 , e ) 80
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 45 = > x = 51 km / hr . answer : option c"
Answer: c
Problem: what could be the range of a set consisting of odd multiples of 11 ?
Options: a ) 21 , b ) 24 , c ) 44 , d ) 62 , e ) 70
Rationale: range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 11 * ( 2 n + 1 ) where n is any positive integer . range = 11 * ( 2 m + 1 ) - 11 * ( 2 n + 1 ) = 11 * 2 * ( m - n ) = 22 * ( m - n ) . m , n - any positive integers the answer must be divisible by 22 , which is only 44 . the correct answer is c
Answer: c
Problem: a train covers a distance of 18 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 , b ) 168 , c ) 120 , d ) 882 , e ) 180
Rationale: "speed = ( 18 / 10 * 60 ) km / hr = ( 108 * 5 / 18 ) m / sec = 30 m / sec . length of the train = 30 * 6 = 180 m . answer : e"
Answer: e
Problem: what quantity of water should be added to reduce 5 litres of 45 % acidic liquid to 25 % acidic liquid ?
Options: a ) 3 litres , b ) 2 litres , c ) 4 litres , d ) 4.5 litres , e ) 5 litres
Rationale: "quantity of acid in 5 litres = 45 * 5 / 100 = 2.25 litres let x litres of water is added to the solution , then there is 2.25 litres of acid in ( 5 + x ) litres of liquid . 25 % of ( 5 + x ) = 2.25 , 25 / 100 * ( 5 + x ) = 2.25 x = 225 - 125 / 25 = 4 answer : d"
Answer: d
Problem: a certain company had a total annual expenditure of 2.55 ∗ 10 ^ 7 on employee salaries last year . if the company employed 425 people , what was the average employee salary ?
Options: a ) $ 60,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 2.55 ∗ 10 ^ 7 on employee salaries total employees = 425 observe that 425 * 6 = 2550 therefore try to bring the numerator in terms of 2550 average salary = ( 2550 * 10 ^ 4 ) / 425 = 6 * 10 ^ 4 = 60,000 option a"
Answer: a
Problem: a no . when divided by 242 gives a remainder 100 , what remainder will be obtainedby dividingthe same no . 18 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "242 + 100 = 342 / 18 = 19 ( remainder ) e"
Answer: e
Problem: if each year the population of the country grows by 40 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 140 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 196 . . . . . . . . . . . . . 2 year elapsed year 2003 : population > 200 . . . . . . . . . . . . . . . . . . 3 year elapsed answer : a"
Answer: a
Problem: two pipes can fill a tank in 18 minutes and 20 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 21 - 1 / 45 = 1 / 12 so , the tank becomes full in 12 minutes . answer : e"
Answer: e
Problem: a certain sum is invested at simple interest at 14 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 14000 , d ) s . 17000 , e ) s . 42000
Rationale: "let the sum be rs . x . ( x * 14 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 28 x / 100 - 24 x / 100 = 840 = > 4 x / 100 = 840 = > x = 42000 . answer : e"
Answer: e
Problem: a box contains 23 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 37 , d ) 21 / 95 , e ) none
Rationale: solution p ( none is defective ) = 19 c 2 / 23 c 2 = 25 / 37 . p ( at least one is defective ) = ( 1 - 25 / 37 ) = 12 / 37 . answer c
Answer: c
Problem: aarti can do a piece of work in 5 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 3 days , e ) 15 days
Rationale: we have the important relation , more work , more time ( days ) a piece of work can be done in 5 days . three times of work of same type can be done in 5 x 3 = 15 days answer e
Answer: e
Problem: a rectangular lawn 70 m × 30 m has two roads each 5 metres wide , running in the middle of it , one parallel to the length and the other parallel to the breadth . find the cost of gravelling the road at the rate of 4 per square metre .
Options: a ) 2,000
b ) 1,800
c ) 1,900
d ) 1,700
e ) none of these
Rationale: total area of road = area of road which parallel to length + area of road which parallel to breadth – overlapped road = 70 × 5 + 30 × 5 – 5 × 5 = 350 + 150 – 25 = 500 – 25 = 475 m 2 ∴ cost of gravelling the road = 475 × 4 = 1900 answer c
Answer: c
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 11 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 92 , c ) 95 , d ) 88 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 11 total people can seat = 81 + 11 = 92 answer : b"
Answer: b
Problem: in a 300 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 79 , b ) 77 , c ) 85 , d ) 83 , e ) 61
Rationale: "solution simple out of 300 20 % are male i . e 60 and 25 % are female i . e 75 , so total homeowner is 135 . now min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option . so ans is 61 . answer : e"
Answer: e
Problem: two cars , one from austin to dallas and the other from dallas to austin , start simultaneously . after they meet , the cars reach their destinations after 4 hours and 9 hours respectively the ratio of their speeds is
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 3 : 6 , d ) 4 : 5 , e ) none
Rationale: solution let us name the cars as a and b . = ( car a ' s speed ) : ( car b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 4 : â ˆ š 9 = 2 : 3 answer a
Answer: a
Problem: chlorination is used in industry for the purification of water ; 1 gm solution of chlorine will remove half of the germs in 1 liter of water . if water containing less than 0.09 % of germs is considered clean , what is the minimum amount of chlorine required to purify 150 liter of water containing 0.3 liter of harmful substances ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assuming that it ' s supposed to state ` ` 0.3 ' ' liters of harmful substances , here ' s how you can answer this question . first , we have to figure out what . 09 % of 150 liters is . . . 1 % = . 01 . 1 % = . 001 . 09 % = . 0009 so , . 0009 ( 150 ) = . 135 liters we need enough doses of chlorine to get the 0.3 liters down to less than . 135 liters . each ` ` dose ' ' of chlorine will remove half of the harmful substances . . . start = 0.3 liters after 1 st dose = . 15 liters after 2 nd dose = . 075 liters we ' re now below the . 135 liters that we need to be less than . final answer : b
Answer: b
Problem: a train 175 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 49 , b ) 50 , c ) 12 , d ) 13 , e ) 68
Rationale: "speed of the train relative to man = ( 175 / 10 ) m / sec = ( 35 / 2 ) m / sec . [ ( 35 / 2 ) * ( 18 / 5 ) ] km / hr = 63 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 63 = = > x = 68 km / hr . answer : option e"
Answer: e
Problem: on a purchase of $ 127 , a store offered a payment plan consisting of a $ 27 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 18.3 % , b ) 15.3 % , c ) 21.3 % , d ) 22.3 % , e ) 25.3 %
Rationale: "12 * 10 + 27 = 147 ( 27 / 127 ) * 100 = 21.3 answer : c"
Answer: c
Problem: in how many r ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: r = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Problem: 50 men do a work in 100 days . how many men are needed to finish the work in 20 days ?
Options: a ) 50 , b ) 100 , c ) 250 , d ) 300 , e ) 400
Rationale: men required to finish the work in 2 days = 50 * 100 / 20 = 250 answer is c
Answer: c
Problem: what is the rate percent when the simple interest on rs . 900 amount to rs . 160 in 4 years ?
Options: a ) 4.44 , b ) 5.44 , c ) 6.44 , d ) 7.44 , e ) 8.44
Rationale: "160 = ( 900 * 4 * r ) / 100 r = 4.44 % answer : a"
Answer: a
Problem: a car takes 6 hours to cover a distance of 432 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: "time = 6 distence = 432 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 432 / 9 = 48 kmph a"
Answer: a
Problem: in a recent election , james received 5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001
Rationale: "james = ( 5 / 100 ) * 2000 = 100 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 100 = 901 answer : option a"
Answer: a
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 14 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 40 points as end of season we need another 26 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 hence option a - 6"
Answer: a
Problem: find large number from below question the difference of two numbers is 1390 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1665
Rationale: "let the smaller number be x . then larger number = ( x + 1390 ) . x + 1390 = 6 x + 15 5 x = 1375 x = 275 large number = 275 + 1390 = 1665 e"
Answer: e
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 105 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 105 - 55 = 50 n = 10 the answer is b ."
Answer: b
Problem: a company sells pens and pencils . the revenue from pens in 2007 was up 5 % from 2006 . the revenue from pencils declined 13 % over the same period . overall revenue was down 1 % from 06 to 07 . what was the ratio of pencil revenue to pen revenue in 2006
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: let the revenue of pens be ' x ' let the revenue of pencils be ' y ' the revenue of pens up from 2006 by 5 % = > 105 % the revenue of pencils down from 2006 by 13 % = > 87 % overall revenue down by 1 % = > 99 % hence the ratio of pencils to pens = 6 / 12 = 1 / 2 answer : a
Answer: a
Problem: a family made a down payment of $ 300 and borrowed the balance on a set of encyclopedias that cost $ 750 . the balance with interest was paid in 9 monthly payments of $ 57 each and a final payment of $ 21 . the amount of interest paid was what percent of the amount borrowed ?
Options: a ) 6 % , b ) 12 % , c ) 14 % , d ) 18.66 % , e ) 20 %
Rationale: interest paid = 57 * 9 + 21 - 450 = 84 % off the balance = ( 84 / 450 ) * 100 = 18.66 % answer is d .
Answer: d
Problem: there are 10 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 50
Rationale: "10 c 2 = 45 the answer is d ."
Answer: d
Problem: consider a quarter of a circle of radius 20 . let r be the radius of the circle inscribed in this quarter of a circle . find r .
Options: a ) 20 * ( sqr 2 - 1 )
b ) 8 * ( sqr 3 - 1 )
c ) 4 * ( sqr 7 - 1 )
d ) 12 * ( sqr 7 - 1 )
e ) none of these
Rationale: i got 20 / ( sqr 2 + 1 ) and just forgot to multiply by ( sqr 2 - 1 ) . answer a
Answer: a
Problem: what two - digit number is less than the sum of the square of its digits by 12 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 12 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 12 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 99 thus the answer is b"
Answer: b
Problem: if x is to be chosen at random from the integers between 1 to 5 , inclusive , and y is to be chosen at random from the integers between 7 and 10 , inclusive , what is the probability that x + y will be even ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 2 / 5 * 2 / 4 = 1 / 5 p ( x and y are both odd ) = 3 / 5 * 2 / 4 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a .
Answer: a
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 8 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 62 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 8 ^ 2 - 2 = 62 . thus , the answer is c ."
Answer: c
Problem: the perimeter of a rhombus is 52 units . one of its diagonal is 24 units . what is its second diagonals length ?
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: when the perimeter of a triangle is 52 units each side is 13 units next , the diagonal of a rhombus bisect each other at 90 degree thus the half of the diagonal is 12 units now in a right angle triangle so formed , the perpendicular is 12 and the hypptenuse is 13 ( that is the side of the triangle ) finding the base ( which is half of the other diagonal ) : 13 ^ 2 - 12 ^ 2 = 25 thus half of the diagonal is 5 and the diagonal is 10 units answer : b
Answer: b
Problem: how much is 60 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 4 , b ) 6 , c ) 10 , d ) 8 , e ) 13
Rationale: "60 / 100 ) * 40 â € “ ( 4 / 5 ) * 25 24 - 20 = 4 answer : a"
Answer: a
Problem: if x and y are integers , what is the least positive number of 24 x + 18 y ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "24 x + 21 y = 6 ( 4 x + 3 y ) which will be a minimum positive number when 4 x + 3 y = 1 . 4 ( 1 ) + 3 ( - 1 ) = 1 then 6 ( 4 x + 3 y ) can have a minimum positive value of 6 . the answer is b ."
Answer: b
Problem: the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.2 minutes , b ) 5.21 minutes , c ) 5.25 minutes , d ) 5.28 minutes , e ) 6 minutes
Rationale: let both of them meet after tt min 4500 m are covered by suresh in 60 m . in tt min he will cover 4500 t 604500 t 60 likewise , in tt min suresh ' s wife will cover 3750 t 603750 t 60 given , 4500 t 60 + 3750 t 60 = 7264500 t 60 + 3750 t 60 = 726 tt = 5.28 minutes option ( d ) is correct
Answer: d
Problem: a boatman goes 3 km against the current of the stream in 3 hour and goes 1 km along the current in 30 minutes . how long will it take to go 3 km in stationary water ?
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 1 hours
Rationale: "explanation : speed upstream = 3 / 3 = 1 km / hr speed downstream = 1 / ( 30 / 60 ) = 2 km / hr speed in still water = 1 / 2 ( 2 + 1 ) = 3 / 2 km / hr time taken to travel 3 km in still water = 3 / ( 3 / 2 ) = 6 / 3 = 2 hours answer : option d"
Answer: d
Problem: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?
Options: a ) 39 , b ) 27 , c ) 30 , d ) 26 , e ) 29
Rationale: "20 + 24 + 8 * 2 = 60 / 2 = 30 answer : c"
Answer: c
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 20 m long and 16 1 / 2 m board ?
Options: a ) 66 , b ) 18 , c ) 16 , d ) 10 , e ) 15
Rationale: "20 * 33 / 2 = 5 / 2 * 2 * x = > x = 66 answer : a"
Answer: a
Problem: a corporation paid $ 5 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 140 % , e ) 43 %
Rationale: difference in ratios = ( 30 / 150 ) - ( 5 / 50 ) = ( 5 / 50 ) % change = ( change ( 5 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 140 % answer - d
Answer: d
Problem: a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 69 / 70 ) â ˆ ’ 150000 ã — ( 69 / 70 ) â ˆ ’ 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,000 = > rs . 5,000 . answer : d
Answer: d
Problem: there are 5 thieves , each loot a bakery one after the other such that the first one takes 1 / 2 of the total no . of the breads plus 1 / 2 of a bread . similarly 2 nd , 3 rd , 4 th and 5 fth also did the same . after the fifth one no . of breads remained are 3 . initially how many breads were there ?
Options: a ) 124 , b ) 125 , c ) 126 , d ) 127 , e ) 128
Rationale: let the number of breads initial be x you should go in reverse order as left bread is 3 i . e x = ? after 1 st person ate a = x - ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - x ) / 2 - ( 1 / 2 ) i . e a = ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - 2 ) / 4 i . e a = ( x - 1 ) / 2 like wise - - - - after 2 nd person ate b = ( a - 1 ) / 2 like wise - - - - after 3 rd person ate c = ( b - 1 ) / 2 like wise - - - - after 4 th person ate d = ( c - 1 ) / 2 like wise - - - - after 5 th person ate e = ( d - 1 ) / 2 now as after 5 th person ate the value of remaining bread is - - - 3 therefore the value of e = 3 ; now go reverse from botom to top to get the value of x after calcuating value of d = 7 value of c = 15 value of b = 31 value of a = 63 value of x = 127 so the final answer is 127 breads were there answer : d
Answer: d
Problem: in an examination 35 % of the students passed and 260 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 260 65 x / 100 = 260 x = 260 * 100 / 65 = 400 answer is b"
Answer: b
Problem: if 8 women can color 400 m long cloth in 5 days , then 10 women can color 500 m long cloth in ?
Options: a ) 6 days , b ) 4 days , c ) 5 days , d ) 15 days , e ) 10 days
Rationale: "the length of cloth painted by one woman in one day = 400 / 8 × 5 = 10 m no . of days required to paint 500 m cloth by 10 women = 500 / 10 × 10 = 5 days answer : c"
Answer: c
Problem: average of 6 numbers comes out to be 3.95 . average of two of the numbers is 3.4 while the average of other two is 3.85 . determine the average of the two numbers left .
Options: a ) 4.7 , b ) 4.8 , c ) 4.3 , d ) 4.6 , e ) 4.9
Rationale: explanation : in the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers . = > 3.95 ( average of 1 st and 2 nd number ) = > 3.85 ( average of 3 rd and 4 th number ) = > 3.4 ( average of 5 th and 6 th number ) 3.95 = ( 3.4 + 3.85 + x ) / 3 x = 4.6 answer d
Answer: d
Problem: the average weight of 8 person ' s increases by 4 kg when a new person comes in place of one of them weighing 55 kg . what might be the weight of the new person ?
Options: a ) 80 kg , b ) 87 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 55 + 32 ) kg = 87 kg . b )"
Answer: b
Problem: a 900 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 1000 , b ) 1050 , c ) 1060 , d ) 370 , e ) 380
Rationale: "speed = 900 / 18 = 50 / 1 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 50 / 1 = > x = 1950 m . l = 1950 - 900 = 1050 answer : option b"
Answer: b
Problem: a horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2
b ) 308 m 2
c ) 150 m 2
d ) 407 m 2
e ) none of these
Rationale: area of the shaded portion = 1 ⁄ 4 × π × ( 14 ) 2 = 154 m 2 answer a
Answer: a
Problem: reeya obtained 55 , 67 , 76 , 82 and 55 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 67 , d ) 85 , e ) 90
Rationale: "explanation : ( 55 + 67 + 76 + 82 + 55 / 5 ) = 67 option c"
Answer: c
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 8 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1
b ) 2
c ) 4
d ) 8
e ) 16
Rationale: as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 8 ( pir ^ 2 ) pir ^ 2 = 16 pir r = 16 answer : e
Answer: e
Problem: at the end of the first quarter , the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 60 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33.33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 60 = 20 + b + 20 b / 100 b = 33.33 answer ( d )"
Answer: d
Problem: the class mean score on a test was 50 , and the standard deviation was 15 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 20 , b ) 31 , c ) 45 , d ) 90 , e ) 89
Rationale: "1 sd from the mean ranges from 35 to 65 , where 65 is within sd above the mean and 35 within 1 sd below the mean 2 sd = 15 twice = 30 from the the mean , which is 80 to 20 , where 80 is within 2 sd above the mean and 20 is within 2 sd below the mean . answer = a"
Answer: a
Problem: find the area of a cuboid of length 4 cm , breadth 6 cm . and height 5 cm .
Options: a ) 120 cm cube
b ) 110 cm cube
c ) 220 cm cube
d ) 430 cm cube
e ) 480 cm cube
Rationale: area of a cuboid = lxbxh = 4 cm x 6 cm x 5 cm = 120 cm cube answer : a
Answer: a
Problem: a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 660 , b ) 680 , c ) 720 , d ) 760 , e ) 800
Rationale: "total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 600 = 1800 5 x / 3 = 1200 x = 720 km the answer is c ."
Answer: c
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 55000 . what is the share of c ?
Options: a ) rs . 12250 , b ) rs . 13375 , c ) rs . 16750 , d ) rs . 15000 , e ) none of these
Rationale: explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 55000 ] = rs . 15000 answer : option d
Answer: d
Problem: the average runs of a cricket player of 5 innings was 20 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?
Options: a ) 12 , b ) 42 , c ) 44 , d ) 76 , e ) 84
Rationale: "explanation : average after 6 innings = 23 required number of runs = ( 24 * 6 ) – ( 20 * 5 ) = 144 – 100 = 44 answer c"
Answer: c
Problem: the sum of three consecutive even numbers is 20 more than the first of these numbers . what is the middle number ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) can not be determined , e ) none of these
Rationale: "solution let the numbers be x , x + 2 and x + 4 . then , x + ( x + 2 ) + ( x + 4 ) = x + 20 ⇔ 2 x = 14 ⇔ x = 7 . ∴ middle number = x + 2 = 9 . answer b"
Answer: b
Problem: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 600 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 2778 , d ) 2800 , e ) 5000
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 600 = > 36 x / 100 - 24 x / 100 = 600 = > 12 x / 100 = 600 = > x = 5000 . answer : e"
Answer: e
Problem: there are 100 freshmen at a particular college , all of whom must take at least one of the 3 core classes : art , biology , and calculus . of these freshmen , 17 take only biology , 10 take only calculus , 9 take all 3 classes , and 20 take art and exactly one of the other two core classes . if the number of freshmen who take only art is 3 times the number of freshmen who take every core class except art , how many freshmen take art ?
Options: a ) 25 , b ) 32 , c ) 36 , d ) 48 , e ) 62
Rationale: make a venn diagram to get a clear picture . look at the diagram : each letter represents only one color . b represents the people who take only art . d represents people who take only art and bio etc . d + f = 20 ( people who take art and one other class ) b = 3 e ( people who take only art is 3 times the people who take bio and calculus ) 17 + 10 + 9 + b + d + e + f = 100 ( total people ) b + b / 3 = 44 b = 33 number of freshmen who take art = 33 + 20 + 9 = 62 answer e
Answer: e
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 512 , b ) 656 , c ) 740 , d ) 896 , e ) 972
Rationale: "there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 14 * 64 = 896 . the answer is d ."
Answer: d
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 228 , b ) 2000 , c ) 267 , d ) 270 , e ) 274
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 250 ) / 26 = 20 x = 270 m . answer : d"
Answer: d
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.0168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 5 digits after decimal total no . of decimals = 7 req . no . of digits = ( n - 1 ) = ( 7 - 1 ) = 6 answer : b"
Answer: b
Problem: a goods train runs at the speed of 72 km / hr and crosses a 150 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 277 , c ) 276 , d ) 370 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 150 ) / 26 = 20 x = 370 m . answer : d"
Answer: d
Problem: if w is the set of all the integers between 49 and 76 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 19 , b ) 91 , c ) 41 , d ) 18 , e ) 14
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 75 , the smallest is 51 ) : 75 - 51 = 24 step 2 . divide by 3 : 24 / 3 = 8 step 3 . add 1 : 8 + 1 = 9 . so there are 9 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 76 , the smallest is 50 ) : 76 - 50 = 26 step 2 . divide by 2 : 26 / 2 = 13 step 3 . add 1 : 13 + 1 = 14 . so there are 14 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 9 multiples of 3 and the 14 multiples of 2 : 9 + 14 = 23 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 9 + 14 = 23 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 23 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 72 - 54 = 18 step 2 . divide by 6 : 18 / 6 = 3 step 3 . add 1 : 3 + 1 = 4 . so there are 4 multiples of 6 within the range : we counted 4 numbers twice . subtract the 4 multiples of 6 from the sum of the multiples of 2 and 3 : = 9 + 14 - 4 = 23 - 4 = 19 therefore , the final number of multiples of 2 , 3 or 6 is 19 . hence , this is the correct answer . ( a )"
Answer: a
Problem: the ratio between the sale price and the cost price of an article is 10 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 7 , d ) 2 : 0 , e ) 2 : 1
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 10 x . then , gain = rs . 3 x required ratio = 3 x : 7 x = 3 : 7 answer : c"
Answer: c
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 300 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 50 sec , e ) 1 min
Rationale: they meet every 300 / 7 + 8 = 20 sec answer is a
Answer: a
Problem: what annual installment will discharge a debt of rs . 1344 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 345 , c ) 325 , d ) 335 , e ) 400
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1344 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1344 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1344 * 25 ) x = ( 1344 * 25 ) / 84 = rs . 400 . therefore , each installment = rs . 400 . answer is e ."
Answer: e
Problem: city x has a population 5 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 10 : 1
Rationale: "x = 5 y , y = 2 * z x : y , y : z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 so , x : z = 10 : 1 ( e )"
Answer: e
Problem: a working mom wakes up every day at 7 am and goes to sleep at 11 pm . she works 8 hours a day . spends 2 hours working out at the gym . she spends 1.5 hours cooking dinner and doing dishes . she spends . 5 of an hour giving her daughter a bath . she spends 1 hour helping with homework and getting her daughter ready for bed . she spends another . 5 of an hour packing lunches for the family for the next day . she spends . 5 of an hour cleaning the house and 2 hours taking a shower and reading or watching t . v . before she goes to sleep . what percent of her day does she spend at work ?
Options: a ) 60 , b ) 50 , c ) 70 , d ) 55 , e ) 40
Rationale: 8 + 2 + 1.5 + . 5 + 1 + . 5 + . 5 + 2 = 16 = total number of hours 8 / 16 = . 05 = 50 percemt the answer is b
Answer: b
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1400 employees , then the no . of female employees who are computer literate ?
Options: a ) 588 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1400 female employees , 60 % of 1400 . = ( 60 * 1400 ) / 100 = 840 . then male employees , = 560 50 % of male are computer literate , = 280 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1400 ) / 100 = 868 computer literate . thus , female computer literate = 868 - 280 = 588 . answer : option a"
Answer: a
Problem: sales price is $ 81 , gross profit is 170 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 33 , c ) 39 , d ) 40 , e ) 51
Rationale: "cost + profit = sales cost + ( 170 / 100 ) cost = 81 cost = 30 profit = 81 - 30 = 51 answer ( e )"
Answer: e
Problem: if the product of two numbers is 17820 and their h . c . f . is 12 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1485 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 17820 , because we know product of two numbers = product of hcf and lcm lcm = 17820 / 12 = 1485 option c"
Answer: c
Problem: thabo owns exactly 160 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 25 , c ) 35 , d ) 46 , e ) 50
Rationale: i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 160 3 x + 60 + x = 160 x = 25 answer ( b . )
Answer: b
Problem: if x + y = 2 x - 2 z , x - 2 y = 4 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4.5 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 2.5 .
Rationale: given : x + y = 2 x - 2 z , - - > eq 1 x - 2 y = 4 z - - > eq 2 x + y + z = 21 - - > eq 3 . now we are asked to find the value of y / z . now let choose some option randomly , take c , which is 3 , i randomly chose this value as it is positive : ) y / z = 3 , this is the value we need to get . then y = 3 z - - eq 4 sub this in eq 1 . x + 3 z = 2 x - 2 z = > x = 5 z - - > eq 5 . sub x and y value in eq 3 . 5 z + 3 z + z = 21 = > z = 21 / 9 . now sub this value to get y , we get y = 21 / 3 . then y / z = 21 / 3 / 21 / 9 = we get 3 again . so this option is correct . answer : option c is correct .
Answer: c
Problem: evaluate 100 / . 25
Options: a ) 400 , b ) 510 , c ) 500 , d ) none of these , e ) 506
Rationale: explanation : 100 / . 25 = 10000 / 25 = 400 option a
Answer: a
Problem: the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously ?
Options: a ) 5 kg , b ) 12,5 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 10 kg . as the price falls by 20 % , new price for 10 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 10 = rs . 8 per kg . rice can bought now at = 100 / 8 = 12,5 kg . answer : option b"
Answer: b
Problem: what is the smallest integer that is the sum of 2 distinct prime integers , each greater than 70 ?
Options: a ) 147 , b ) 142 , c ) 173 , d ) 144 , e ) 186
Rationale: a prime number ( or a prime ) is a natural number greater than 1 that has no positive divisors other than 1 and itself . here are the first few prime numbers : 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197 , 199 , etc . immediate two prime numbers after 70 are - 71 and 73 sum = 71 + 73 = 144 answer - d
Answer: d
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 940 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 24 , b ) 22 , c ) 16 , d ) 18 , e ) 20
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 940 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest noall factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( opps / / it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which haslength of integeris 9 . now , since x = 512 , x + 3 y < 940 so , 3 y < 428 = = > y < 428 / 3 so , y can take any value which is less than 428 / 3 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . c"
Answer: c
Problem: how many 7 in between 1 to 100 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 , 87,97 20 7 ' s between 1 to 100 answer : b"
Answer: b
Problem: the perimeter of a semi circle is 162 cm then the radius is ?
Options: a ) 31.5 , b ) 28 , c ) 98 , d ) 37 , e ) 13
Rationale: "36 / 7 r = 162 = > r = 31.5 answer : a"
Answer: a