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Question: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 216 Β° of the circle , what percentage of megatek employees are in manufacturing ?
A.20 %.
B.25 %.
C.30 %.
D.35 %.
e ) 60 %E.
"answer : e 216 Β° divided by 360 Β° equals 0.6 , therefore the sector is equal to 60 % of the total" | null |
Question: in a school of 850 boys , 34 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
A.A.125.
B.B.627.
C.C.153.
D.D.238.
e ) e ) 159D.
"34 + 28 + 10 = 72 % 100 β 72 = 28 % 850 * 28 / 100 = 238 answer : d" | null |
Question: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a third circle ?
A.0.36.
B.3.6.
C.12,000.
D.3,600.
e ) 36,000C.
"1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 120 degrees = 12000 anglets answer - c" | null |
Question: 2 ^ 46655 mod 9 = ?
A.4.
B.5.
C.6.
D.7.
e ) 8B.
by remainder theorem remainder = { [ ( 2 ^ 3 ) ^ 1551 * 2 ^ 2 ] / 9 } = [ { ( - 1 ) ^ 1551 * 4 } / 9 ] = 5 answer : b | null |
Question: a cube has five of its faces painted half red and half white . the other face is completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
['A.6 : 11', 'B.2 : 5', 'C.3 : 4', 'D.5 : 7', 'e ) 2 : 3']D.
let x be the area of each face of the cube . the area painted red is 5 ( x / 2 ) = 5 x / 2 the area painted white is 5 ( x / 2 ) + x = 7 x / 2 x the ratio of red to white is 5 x / 2 : 7 x / 2 which is 5 : 7 . the answer is d . | null |
Question: the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
A.276.
B.299.
C.322.
D.345.
e ) 350E.
"clearly , the numbers are ( 25 x 13 ) and ( 25 x 14 ) . larger number = ( 25 x 14 ) = 350 . answer : option e" | null |
Question: increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
A.31.25.
B.37.5.
C.50.0.
D.52.5.
e ) 62.5E.
we ' re told that the original price of an item is increased by 25 % and then that price is increased by 30 % . . . . if . . . . starting value = $ 100 + 25 % = 100 + . 25 ( 100 ) = 125 + 30 % = 125 + . 30 ( 125 ) = 125 + 37.5 = 162.5 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 62.5 / 100 = 62.50 % final answer : e | null |
Question: the population of a bacteria colony doubles every day . if it was started 10 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
A.512.
B.768.
C.1024.
D.2048.
e ) 4096D.
"2 ^ 10 ( 2 ) = 2 ^ 11 = 2048 the answer is d ." | null |
Question: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,200 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
A.$ 28.
B.$ 82.
C.$ 110.
D.$ 190.
e ) $ 192D.
"this question can be solved easily using a equation model . 150 * p = 16200 ( fixed cost ) + 150 * 80 + 150 * 2 . = 16200 + 12000 + 300 = 28500 p = $ 190 . d" | null |
Question: a certain list consists of 21 different numbers . if n is in the list and n is 6 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
A.1 / 20.
B.1 / 6.
C.1 / 5.
D.3 / 13.
e ) 5 / 21D.
"series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 6 * x hence , a 1 + a 2 + . . + a 20 + n = 26 x so , the fraction asked = 6 x / 26 x = 6 / 26 = 3 / 13 d" | null |
Question: in a sports club with 42 members , 20 play badminton and 23 play tennis and 6 do not play either . how many members play both badminton and tennis ?
A.3.
B.5.
C.6.
D.7.
e ) 8D.
"20 + 23 = 43 but where as total number is 42 - 6 = 36 therefore answer is 43 - 36 = 7 hence answer is d" | null |
Question: a tempo , while travelling at 70 kmph , uses 30 % more petrol than it uses while travelling at 50 kmph for travelling a certain distance . using one litre of petrol , it can travel 19.5 km at 50 kmph . how far can the tempo travel on 10 litres of petrol at a speed of 70 kmph ?
A.150 kms.
B.160 kms.
C.170 kms.
D.180 kms.
e ) 190 kmsA.
@ 50 kmph , one km distance uses 1 / 19.5 ltr petrol . @ 70 kmph , one km dist . uses 1.3 / 19.5 ltr petrol distance travelled with 10 ltrs @ 70 kmph = 10 * 19.5 / 1.3 = 150 kms . answer : a | null |
Question: in an examination it is necessary for a candidate to get 45 % of the maximum marks to pass . a candidate who gets 180 marks , fails by 45 marks . find the maximum marks .
A.450.
B.600.
C.500.
D.550.
e ) 650C.
let max . mark = x pass mark = 45 x / 100 180 = 45 x / 100 - 45 x = 180 * 100 - 4500 / 45 = 500 answer : c | null |
Question: in a box of 9 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
A.3 / 10.
B.4 / 11.
C.5 / 12.
D.6 / 13.
e ) 7 / 15C.
p ( neither pen is defective ) = 6 / 9 * 5 / 8 = 5 / 12 the answer is c . | null |
Question: 265.124 x 11.98 Γ£ Β· 8.001 + 32.28 = ?
A.983.578.
B.659.121.
C.781.189.
D.429.966.
e ) 456.512D.
"explanation : ? = 265.124 x 11.98 Γ£ Β· 8.001 + 32.28 Γ’ β° Λ ( 265.124 x 12 / 8 ) + 32.28 Γ’ β° Λ 397.686 + 32.28 Γ’ β° Λ 429.966 answer : option d" | null |
Question: find a two digit number , given that the sum of the digits is 9 and the difference of the digits is 3 . ?
A.75.
B.63.
C.83.
D.94.
e ) 39B.
using elimination method find which of the options fit the description of the number . . . from the option only 63 meets this description sum of digits - - - 6 + 3 = 9 difference of digits - - - 6 - 3 = 3 answer b . | null |
Question: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 25 percent , what is the discount rate on pony jeans ?
A.9 %.
B.10 %.
C.11 %.
D.12 %.
e ) 25 %E.
"x discount on pony jeans , ( 0.25 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.25 - x ) + 2 * 18 x = 9 - - > x = 0.25 = 25 % answer : e ." | null |
Question: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 7 hours ?
A.675.
B.750.
C.1,800.
D.5,900.
e ) 1,575E.
"8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 7 hours ) = 1575 cans . the answer is e ." | null |
Question: if x is an integer and 2.13 Γ 10 ^ x is less than 2100 , what is the greatest possible value for x ?
A.2.
B.6.
C.5.
D.4.
e ) 3A.
"if x = 3 2.13 Γ 10 ^ 3 = 2130 > 2,100 so , x = 2 answer : a" | null |
Question: if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is ?
A.127.
B.688.
C.400.
D.121.
e ) 123C.
"let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : c" | null |
Question: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 525 what is the least possible value of k ?
A.10.
B.14.
C.15.
D.21.
e ) 25A.
"525 = 3 * 5 * 5 * 7 thus k must include numbers at least up to the number 10 so that there are two appearances of 5 . the answer is a ." | null |
Question: find the area of trapezium whose parallel sides are 28 cm and 18 cm long , and the distance between them is 15 cm .
A.227.
B.299.
C.345.
D.161.
e ) 212C.
"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 28 + 18 ) * ( 15 ) = 345 cm 2 answer : c" | null |
Question: joshua and jose work at an auto repair center with 4 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
A.1 / 15.
B.1 / 12.
C.1 / 9.
D.1 / 6.
e ) 1 / 3A.
"1 ) probability of chosing josh first = 1 / 6 probability of chosing jose second = 1 / 5 total = 1 / 30 probability of chosing jose first = 1 / 6 probability of choosing josh second = 1 / 5 total = 1 / 30 final = 1 / 30 + 1 / 30 = 1 / 15 2 ) number of ways two persons can be chosen 6 c 2 = 15 number of ways josh and jose are the two persons = 1 total = 1 / 15 answer will be a ." | null |
Question: 3 candidates in an election and received 6136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
A.46 %.
B.49 %.
C.57 %.
D.59 %.
e ) 61 %A.
"total number of votes polled = ( 6136 + 7636 + 11628 ) = 25400 so , required percentage = 11628 / 25400 * 100 = 46 % a" | null |
Question: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - fourth of the males and one - half of the females in the class ?
['A.128', 'B.136', 'C.144', 'D.152', 'e ) 160']C.
1 / 4 * 2 / 5 + 1 / 2 * 3 / 5 = 2 / 20 + 6 / 20 = 2 / 5 the number of degrees is 2 / 5 * 360 = 144 degrees the answer is c . | null |
Question: 4 liters of a 20 percent solution of alcohol in water are mixed with 5 liters of a 10 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
A.14.4 %.
B.14.8 %.
C.15.2 %.
D.15.6 %.
e ) 16.0 %A.
"the total amount of alcohol is 0.2 ( 4 ) + 0.1 ( 5 ) = 1.3 liters . the percentage is 1.3 / 9 = 13 / 90 which is about 14.4 % the answer is a ." | null |
Question: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 45 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
A.15.
B.25.
C.13.
D.45.
e ) 75C.
"out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 45 % = 81 responded as satisfied , so remaining satisfied are 120 - 81 = 39 so 39 is what percentage of 300 - 13 % so the answer should be c" | null |
Question: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
A.20 %.
B.40 %.
C.50 %.
D.60 %.
e ) 75 %C.
"soln : - original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.2 c ( 20 % profit ) x = 1.2 / . 8 * c x = 3 / 2 c original selling price is 1.5 c which is 50 % profit answer : c" | null |
Question: solution a is 30 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
A.6 : 4.
B.6 : 14.
C.4 : 4.
D.4 : 6.
e ) 3 : 2E.
"forget the volumes for the time being . you have to mix 30 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 30 ) = 3 / 2 so the volume of the two solutions will be equal . answer has to be 3 : 2 e" | null |
Question: a question paper has 2 parts , a & b , each containing 8 questions . if a student has to choose 8 from part a & 4 from part b , in how many ways can he choose the questions ?
A.110.
B.70.
C.120.
D.130.
e ) 140B.
"there 8 questions in part a out of which 8 question can be chosen as = 8 c 8 . similarly , 4 questions can be chosen from 8 questions of part b as = 8 c 4 . hence , total number of ways , = 8 c 8 * 8 c 4 = [ 8 ! / ( 0 ! 8 ! ) ] * [ 8 ! / ( 4 ! * 4 ! ) ] = { 1 } * { 8 * 7 * 6 * 5 / ( 4 ! ) } = 70 . b" | null |
Question: a can do a piece of work in 80 days . he works at it for 10 days b alone finishes the remaining work in 42 days . in how much time will a and b working together , finish the work ?
A.25.
B.30.
C.20.
D.32.
e ) none of themB.
"work done by a in 10 days = ( 1 / 80 * 10 ) = 1 / 8 remaining work = ( 1 - 1 / 8 ) = 7 / 8 now , 7 / 8 work is done by b in 42 days . whole work will be done by b in ( 42 x 8 / 7 ) = 48 days . a β s 1 day ' s work = 1 / 80 and b ' s 1 day ' s work = 1 / 48 ( a + b ) ' s 1 day ' s work = ( 1 / 80 + 1 / 48 ) = 8 / 240 = 1 / 30 hence , both will finish the work in 30 days . answer is b ." | null |
Question: working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 6 pages a minute more than printer a ?
A.600.
B.800.
C.1000.
D.720.
e ) 1500D.
answer : d . | null |
Question: the monthly rent of a shop of dimension 18 feet Γ 22 feet is rs . 2244 . what is the annual rent per square foot of the shop ? ( a ) rs . 5 ( 2 / 3 )
A.43.
B.56.
C.68.
D.87.
e ) 92C.
"sol . monthly rent per square feet = 2244 / ( 18 * 22 ) & annual rent per square feet = 12 * ( 2244 / ( 18 * 22 ) ) = 68 c" | null |
Question: a grocer has a sale of rs . 5255 , rs . 5840 , rs . 5921 , rs . 6022 and rs . 6499 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?
A.3463.
B.4463.
C.5463.
D.4063.
e ) 5063B.
"total sale for 5 months = rs . ( 5255 + 5840 + 5921 + 6022 + 6499 ) = rs . 29537 . required sale = rs . [ ( 5500 x 6 ) - 29537 ] = rs . ( 33000 - 29537 ) = rs . 3463 . answer : b" | null |
Question: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 135 mangoes .
A.360.
B.380.
C.400.
D.450.
e ) 412D.
mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 135 mangoes = 135 * 3.33 = 450 . answer d | null |
Question: a gambler has won 40 % of his 20 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
A.20.
B.25.
C.30.
D.35.
e ) 40A.
"let x be the number of additional games the gambler needs to play . 0.4 ( 20 ) + 0.8 x = 0.6 ( x + 20 ) 0.2 x = 4 x = 20 the answer is a ." | null |
Question: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 100 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
A.1000.
B.1400.
C.1200.
D.800.
e ) 1000D.
"volume of pool = 60 * 100 * 10 cu . ft , 80 % full = 60 * 100 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 100 * 10 * 0.8 / 60 min = 800 min d" | null |
Question: walking at 4 / 5 of her normal speed , a worker is 10 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
A.30.
B.35.
C.40.
D.45.
e ) 50C.
"let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 10 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 10 ) t / 5 = 8 t = 40 the answer is c ." | null |
Question: find the length of the longest pole that can be placed in a room 12 m long , 8 m broad and 9 m high .
A.10 m.
B.12 m.
C.17 m.
D.19 m.
e ) noneC.
solution length of longest pole = length of the diagonal of the room = β ( 12 ) 2 + 82 + 92 βΉ = βΊ β 289 = 17 m . answer c | null |
Question: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 4 m , the volume of the box ( in m 3 ) is :
A.4480.
B.5120.
C.6420.
D.8960.
e ) 7960A.
"clearly , l = ( 48 - 8 ) m = 40 m , b = ( 36 - 8 ) m = 28 m , h = 8 m . volume of the box = ( 40 x 28 x 4 ) m 3 = 4480 m 3 . answer : option a" | null |
Question: find the value of x in ( x + 1 ) / ( x + 3 ) = 5
A.2.5.
B.- 2.5.
C.3.0.
D.3.5.
e ) - 3.5E.
"( x - 1 ) / ( x + 3 ) = 5 multiplying both sides with x + 3 gives x + 1 = 5 ( x + 3 ) = x + 1 = 5 x + 15 subtracting x from both sides gives 4 x + 15 = 1 subtracting 15 from both sides gives 4 x = - 14 dividing by 4 on both sides gives x = - 3.5 answer : e" | null |
Question: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 15 days , a finished the remaining work . in how many days a alone can finish the job ?
A.10.
B.25.
C.60.
D.30.
e ) 20E.
"a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 15 days whole work will be done by a in 15 * 4 / 3 = 20 days answer is e" | null |
Question: if the radius of a cylinder is made 3 times and height is doubled , what is the new volume of the cylinder divided by the old one ?
A.18 ..
B.2 ..
C.6 ..
D.4 ..
e ) 10 .A.
let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 2 h ) v ' = 18 v a ) 18 | null |
Question: a train 110 m long is running with a speed of 82 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
A.7 sec.
B.6 sec.
C.8 sec.
D.4.5 sec.
e ) 2 secD.
"speed of train relative to man = 82 + 6 = 88 km / hr . = 88 * 5 / 18 = 24.44 m / sec . time taken to pass the men = 110 / 24.44 = 4.5 sec . answer : d" | null |
Question: the average marks of a class of 35 students is 40 and that of another class of 45 students is 60 . find the average marks of all the students ?
A.52.6.
B.52.4.
C.52.1.
D.51.2.
e ) 52.9D.
"sum of the marks for the class of 35 students = 35 * 40 = 1400 sum of the marks for the class of 45 students = 45 * 60 = 2700 sum of the marks for the class of 80 students = 1400 + 2700 = 4100 average marks of all the students = 4100 / 80 = 51.2 . answer : d" | null |
Question: abcd is a square where ab = β 2016 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
A.3008.
B.2002.
C.1008.
D.2016.
e ) 3000C.
note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 2016 / 2 = 1008 . correct answer c | null |
Question: chris age after 9 years will be 5 times his age 5 years back . what is the present age of chris ?
A.A.20.
B.B.25.
C.C.15.
D.D.22.
e ) e ) 16E.
"chris present age = x after 9 years = x + 9 5 years back = x - 5 x + 9 = 5 ( x - 5 ) x = 16 answer is e" | null |
Question: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8600 for a computer table , then what was the cost price of the computer table ?
A.rs . 6289.
B.rs . 6298.
C.rs . 6290.
D.rs . 7166.
e ) rs . 7708D.
"cp = sp * ( 100 / ( 100 + profit % ) ) = 8600 ( 100 / 120 ) = rs . 7166 . answer : d" | null |
Question: what is the perimeter , in meters , of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
A.48.
B.56.
C.60.
D.56.
e ) 192D.
"say length of garden is l meters . then ( l * 16 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 12 meters . perimeter of garden = 2 * ( 12 + 16 ) = 56 meter . answer is d" | null |
Question: mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 19 of them answered question 1 correctly . if 24 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
A.3.
B.9.
C.11.
D.17.
e ) 19E.
"total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 19 . number of students who answered both q 1 & q 2 correctly = 19 . answer : e" | null |
Question: the distance between west - town to east - town is 10 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
A.3 ..
B.8 ..
C.10 ..
D.12 ..
e ) 15 .B.
"time taken by the birds to meet = 10 / ( 4 + 1 ) = 2 mins distance traveled by the bird traveling from west - town = 4 * 2 = 8 answer : b" | null |
Question: if m is a positive integer and m ^ 2 is divisible by 33 , then the largest positive integer that must divide m is ?
A.3.
B.6.
C.8.
D.11.
e ) 16D.
"m ^ 2 is divisible by 33 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 11 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 33 then answer should be 16 . is the question right ? or am i missing some thing ? d" | null |
Question: β 2 percent of 2 β 2 =
A.5.0.
B.0.05.
C.1.0.
D.2.0.
e ) 4.0B.
"the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : β 2 β 1.4 so , β 2 percent of 2 β 2 β 1.4 percent of ( 2 ) ( 1.4 ) β ( 1.4 / 100 ) ( 2.8 ) β 3.92 / 100 β 0.03 check the answer choices to see that b is the only answer that ' s close . answer : b" | null |
Question: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 6 : 3 and b : c = 6 : 5 . if the total runs scored by all of them are 118 , the runs scored by b are ?
A.24.
B.20.13.
C.30.93.
D.20.93.
e ) 10.93A.
"a : b = 6 : 3 b : c = 6 : 5 a : b : c = 36 : 18 : 15 12 / 59 * 118 = 24 answer : a" | null |
Question: a man swims downstream 90 km and upstream 55 km taking 5 hours each time ; what is the speed of the current ?
A.3.8.
B.3.5.
C.3.3.
D.3.2.
e ) 1.6B.
"90 - - - 5 ds = 18 ? - - - - 1 55 - - - - 5 us = 11 ? - - - - 1 s = ? s = ( 18 - 11 ) / 2 = 3.5 answer : b" | null |
Question: from a total of 5 boys and 6 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
A.16.
B.24.
C.60.
D.120.
e ) 150E.
answer = e = 150 no of 4 person committees that can be formed = 5 c 2 * 6 c 2 = 150 answer e | null |
Question: the simple interest on a sum of money will be rs . 1400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
A.2800.
B.3799.
C.1200.
D.2693.
e ) 1732A.
"p - - - 10 - - - - 1400 p - - - 5 - - - - - 700 3 p - - - 5 - - - - - 2100 - - - - - - = > 2800 answer : a" | null |
Question: if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 3 d =
A.540.
B.570.
C.619.
D.649.
e ) 710E.
"before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 3 d = 3 * 270 = 710 answer : option e" | null |
Question: two cars start at the same time from opposite ends of a highway that is 175 miles long . one car is riding at 25 mph and the second car is riding at 45 mph . how long after they begin will they meet ?
A.2.
B.2.5.
C.3.
D.3.5.
e ) 4B.
"as cars are moving in opposite directions their speeds will be added . so their relative speeds : 45 + 25 = 70 mph total distance to be covered = 175 miles . time taken would be : 175 miles / 70 mph = 2.5 hours b is the answer ." | null |
Question: how many seven - digit numbers that do not contain the digits 2 or 9 are there ?
A.178546.
B.44786544.
C.435786.
D.1599678.
e ) 1835008E.
"we can have 7 digits ( 1 , 3,4 , 5,6 , 7,8 ) for the first place ( million ' s place ) . and similarly 8 digits for hundred thousands , ten thousands , thousands , hundred ' s , tenth ' s and unit digit . ( 0,1 , 3,4 , 5,6 , 7,8 ) so in total 7 * 8 * 8 * 8 * 8 * 8 * 8 = 1835008 hence e" | null |
Question: the sum of two consecutive number is 67 . which is the larger number ?
A.34.
B.43.
C.44.
D.45.
e ) 46A.
"let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 67 2 x + 1 = 67 2 x = 66 x = 33 therefore larger number is x + 1 = 34 answer : a" | null |
Question: a and b together can do a piece of work in 1 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
A.0.35 days.
B.0.45 days.
C.0.55 days.
D.0.25 days.
e ) 0.95 daysE.
"b = 1 / 1 β 1 / 20 = 0.95 days answer : e" | null |
Question: in a school of 850 boys , 46 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
A.A.136.
B.B.627.
C.C.153.
D.D.721.
e ) e ) 159A.
"46 + 28 + 10 = 84 % 100 β 84 = 16 % 850 * 16 / 100 = 136 answer : a" | null |
Question: 45 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
A.100.
B.200.
C.300.
D.350.
e ) 943E.
"45 x / 100 - x / 3 = 110 7 x / 60 = 110 x = 943 answer : e" | null |
Question: there are 7 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
A.25.
B.28.
C.30.
D.32.
e ) 35A.
"the total number of ways to form a team of 4 is 7 c 4 = 35 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 5 c 2 = 10 . the number of ways to form an acceptable team is 35 - 10 = 25 . the answer is a ." | null |
Question: a / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 6 . what is the largest possible value of the expression ?
A.2 / 18.
B.6 / 3.
C.30 / 2.
D.18 / 2.
e ) 6 / 18D.
a / ( b / c ) = ( a * c ) / b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 6 * 3 ) / 2 = 18 / 2 answer d | null |
Question: a work as fast as b . if b can complete a work in 8 days independently , the number of days in which a and b can together finish the work in ?
A.2 days.
B.2 2 / 3 days.
C.4 days.
D.5 days.
e ) 6 daysB.
"ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 8 a + b 1 day work = 1 / 4 + 1 / 8 = 3 / 8 = > 8 / 3 = 2 2 / 3 a and b can finish the work in 2 2 / 3 days answer is b" | null |
Question: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent . overall he make a .
A.50.
B.288.
C.27.
D.200.
e ) 881A.
"let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . answer : a" | null |
Question: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
A.39.
B.88.
C.26.
D.87.
e ) 11A.
"explanation : consider the avg for first 16 innings is x . then total runs scored till 16 innings is 16 x . total runs after 17 innings = 16 x + 87 . thus , 16 x + 8717 = x + 316 x + 8717 = x + 3 β x = 36 so his average after 17 innings = 39 . answer : a" | null |
Question: the area of a square is equal to five times the area of a rectangle of dimensions 32 cm * 10 cm . what is the perimeter of the square ?
['A.289 cm', 'B.160 cm', 'C.829 cm', 'D.288 cm', 'e ) 289 cm']B.
area of the square = s * s = 5 ( 32 * 10 ) = 1600 = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b | null |
Question: working alone , mary can pave a driveway in 4 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?
A.2 hours.
B.4 hours.
C.5 hours.
D.6 hours.
e ) 7 hoursA.
initial working rates : mary = 1 / 4 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 4 + ( 1 / 3 * 1 / 4 ) = 1 / 3 per hour hillary = 1 / 3 - ( 1 / 2 * 1 / 3 ) = 1 / 6 per hour together they work 1 / 3 + 1 / 6 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a . | null |
Question: if y is a positive number and 1 / 2 the square root of x is the cube root of y , then y =
A.64.
B.32.
C.16.
D.4.
e ) 1A.
1 / 2 the square root of x is cube root of y . if y = 64 . . then 1 / 2 the square root of y = 4 and cube of y is 64 . option a . | null |
Question: the perimeter of a semi circle is 180 cm then the radius is ?
A.22.
B.28.
C.35.
D.37.
e ) 13C.
"36 / 7 r = 180 = > r = 35 answer : c" | null |
Question: the sum of the ages of 4 children born at the intervals of 1 years each is 12 years . what is the age of the youngest child ?
A.2.5.
B.1.5.
C.1.
D.3.5.
e ) 4.5B.
"let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 we know that the sum of their ages is 12 so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 12 therefore the youngest child is 1.5 years old answer : b" | null |
Question: what is the decimal equivalent of ( 1 / 2 ) ^ 2 ?
A.0.0016.
B.0.0625.
C.0.16.
D.0.25.
e ) 0.5D.
"( 1 / 2 ) Β² = ( 1 / 2 ) ( 1 / 2 ) = 1 / 4 approach # 1 : use long division to divide 4 into 1 to get 1 / 4 = 0.25 d" | null |
Question: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 3 ] = ?
A.[ 22 ].
B.[ 44 ].
C.[ 45 ].
D.[ 28 ].
e ) [ 10 ]D.
[ 6 ] * [ 3 ] = ( 6 / 2 + 1 ) ( 3 * 2 + 1 ) = [ 28 ] . ans - d | null |
Question: the sum of all the integers a such that - 26 < a < 24 is
A.0.
B.- 2.
C.- 25.
D.- 49.
e ) - 51D.
easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 10 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 a = - 49 . d is the answer . | null |
Question: in what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way ?
A.3 sec.
B.4 sec.
C.8 sec.
D.6 sec.
e ) 7 secC.
t = 52 / 24 * 18 / 5 = 8 sec answer : c | null |
Question: find the smallest number which should be multiplied with 36963 to make it a perfect square .
A.4.
B.7.
C.4.
D.3.
e ) 6D.
"36963 = 111 * 111 * 3 required smallest number = 3 3 is the smallest number which should be multiplied with 36963 to make it a perfect square . answer : d" | null |
Question: one computer can upload 100 megabytes worth of data in 2 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 10 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
A.6.6.
B.7.
C.9.
D.11.
e ) 13A.
"since the first computer can upload 100 megabytes worth of data in 2 seconds then in 2 * 10 = 20 seconds it can upload 10 * 100 = 1000 megabytes worth of data , hence the second computer in 20 seconds uploads 1300 - 1000 = 300 megabytes worth of data . the second computer can upload 100 megabytes of data in 6.6 seconds . answer : a ." | null |
Question: 6 / 9 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
A.64 %.
B.41 %.
C.45 %.
D.72 %.
e ) 78 %A.
total population = 90 ( assume ) . 6 / 9 * 90 = 60 people from montague . 3 / 9 * 90 = 30 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 12 + 21 ) = ~ 64 . answer : a | null |
Question: if a 2 - b 2 = 10 and a * b = 5 , find a 4 + b 4 .
A.50.
B.100.
C.150.
D.92.
e ) 25C.
a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 5 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 100 : substitute a 4 + b 4 = 150 correct answer c | null |
Question: in an office , totally there are 2800 employees and 25 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
A.390.
B.490.
C.400.
D.460.
e ) none of theseB.
number of male employees = 2800 * 25 / 100 = 700 required number of male employees who are less than 50 years old = 700 * ( 100 - 30 ) % = 700 * 70 / 100 = 490 . answer : b | null |
Question: when 3 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
A.32.
B.81.
C.60.
D.27.
e ) 90E.
explanation : let the number be 3 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 3 = a / 30 = > a = 90 answer : e | null |
Question: how many integers between 314,700 and 458,600 have tens digit 1 and units digit 3 ?
A.10,300.
B.10,030.
C.1,353.
D.1,352.
e ) 1,439E.
"there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 314,700 and 458,600 is 458,600 - 314,700 = 143,900 - one number per each hundred gives 143,900 / 100 = 1,439 numbers . answer : e ." | null |
Question: a certain psychologist charges $ 20 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 300 , what is the total charge to a patient who receives only 3 hours of therapy ?
A.$ 120.
B.$ 135.
C.$ 150.
D.$ 165.
e ) $ 188E.
"let the charge for first hour = x + 20 then charge for each additional hour = x x + 20 + 4 x = 300 = > 5 x = 280 = > x = 56 total charge for patient for 3 hours of therapy = x + 20 + 2 x = 3 x + 20 = 188 $ answer e" | null |
Question: 4 athletes , wendy , michelle , brenda , and jamal , scored in a soccer ( football ) game . if michelle scored 1 more goal than brenda did , jamal scored 3 less than wendy did , and wendy scored 3 more than michelle did , how many fewer goals did brenda score than jamal ?
A.- 8.
B.- 6.
C.- 2.
D.- 1.
e ) - 3D.
in this word problem , the first key is to turn the story into equations : michelle scored 1 more than brenda did : m = 1 + b jamal scored 3 less than wendy did : j = w - 3 wendy scored 3 more than michelle did : w = 3 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more goals did brenda score than jamal did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 1 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 3 + m so that both b and j are in terms of m : j = ( 3 + m ) - 3 . so if b = m - 1 and j = m , then : b - j = ( m - 1 ) - ( m ) b - j = m - 1 - m ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is d . | null |
Question: a bus trip of 550 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
A.40.
B.45.
C.50.
D.55.
e ) 60C.
the time is the distance / speed . the time difference is 1 hour . 550 / v - 550 / ( v + 5 ) = 1 550 ( v + 5 ) - 550 v = ( v ) ( v + 5 ) 2750 = ( v ) ( v + 5 ) 50 * 55 = ( v ) ( v + 5 ) v = 50 mph the answer is c . | null |
Question: the sum of the squares of 3 consecutive natural number is 2030 . what is the middle number ?
A.25.
B.26.
C.27.
D.28.
e ) 29B.
let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26 | null |
Question: ( β 112 + β 567 ) / β 175 = ?
A.2 β 2.
B.13 / 5.
C.3 β 2.
D.3 β 3.
e ) β 2B.
( β 112 + β 567 ) / β 175 = ( 4 β 7 + 9 β 7 ) / 5 β 7 = 13 / 5 hence , the correct answer is b . | null |
Question: a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 percent is cut away . in the second week 20 percent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?
A.105 kg.
B.103 kg.
C.108 kg.
D.125 kg.
e ) 117 kgA.
"a 105 kg 250 Γ 0.7 Γ 0.8 Γ 0.75 = 105 kg ." | null |
Question: dan can do a job alone in 12 hours . annie , working alone , can do the same job in just 9 hours . if dan works alone for 8 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
A.2.
B.3.
C.4.
D.5.
e ) 6B.
dan can complete 1 / 12 of the job per hour . in 8 hours , dan completes 8 ( 1 / 12 ) = 2 / 3 of the job . annie can complete 1 / 9 of the job per hour . to complete the job , annie will take 1 / 3 / 1 / 9 = 3 hours . the answer is b . | null |
Question: two cars start from the opposite places of a main road , 105 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
A.65.
B.38.
C.20.
D.28.
e ) 21C.
answer : c ) 20 km | null |
Question: 4 dice are thrown simultaneously on the board . find the probability show the same face ?
A.2 / 113.
B.1 / 215.
C.1 / 216.
D.3 / 113.
e ) 4 / 113C.
"the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 Γ 6 Γ 6 Γ 6 = 64 = 6 Γ 6 Γ 6 Γ 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c" | null |
Question: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 126 , how many more green disks than blue disks are in the bag ?
A.25.
B.28.
C.30.
D.35.
e ) 40D.
let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 126 - - > x = 7 . g - b = 8 x - 3 x = 5 x = 35 . the answer is d . | null |
Question: ben left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?
A.40.
B.200.
C.266.
D.267.
e ) 600D.
in order not to lose money because of the change ben ' s total commission must beat least $ 75,000 - $ 45,000 = $ 30,000 , so total sales must beat least $ 30,000 / 0.15 = $ 200,000 . which means that he must makeat least $ 200,000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d . | null |
Question: if there are 86 workers in a factory , and on a certain day , 72 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
A.82.7 %.
B.81.7 %.
C.83.7 %.
D.89.7 %.
e ) 88.7 %C.
"72 / 86 * 100 = 83.72 83.7 % correct answer c" | null |
Question: x does a work in 20 days . y does the same work in 40 days . in how many days they together will do the same work ?
A.10.
B.12.
C.20.
D.30.
e ) 13.33E.
x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 40 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 40 ) = 1 / 13.33 both together will finish the work in 13.33 days . correct option is e | null |
Question: in a school the ratio of boys and girls are in the ration 5 : 6 . 25 % of boys will get scholar ship and 20 % of girls will get scholar ship what % of students wont get scholarship ?
A.60 %.
B.78 %.
C.88 %.
D.98 %.
e ) 99 %B.
boys : girls = > 5 x : 6 x total no . of students including boys nd girls = 5 x + 6 x = 11 x 25 % of boys = > 5 x * 25 / 100 = 5 x / 4 20 % of girls = > 6 x * 20 / 100 = 6 x / 5 no . of students who are getting scholarship = > 5 x / 4 + 6 x / 5 = 49 x / 20 no . of students who are not getting scholarship = 11 x - 49 x / 20 = 171 x / 20 % of students not getting scolorship = > 171 x / 20 / 11 x * 100 = > 100 * 171 x / 220 x = 77.7 % answer : b | null |
Question: a start walking from a place at a uniform speed of 7 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
A.4.7 kmph.
B.7.6 kmph.
C.4 kmph.
D.7 kmph.
e ) 5.3 kmphB.
distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 7 + 5 / 9 = 7.55 answer b | null |
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