regisss/math_qa huggingface dataset:
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 5 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 5 = 19 the answer is a ."
Answer: a
Problem: a can run 288 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 36 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 288 / 32 = 9 m / s distance covered by b in 4 seconds = speed ã — time = 9 ã — 4 = 36 metre i . e . , a beat b by 36 metre answer is e"
Answer: e
Problem: 417 x 417 + 383 x 383 = ?
Options: a ) 320578 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 417 ) ^ 2 + ( 383 ) ^ 2 = ( 400 + 17 ) ^ 2 + ( 400 - 17 ) ^ 2 = 2 [ ( 400 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 160000 + 289 ] = 2 x 160289 = 320578 answer is a"
Answer: a
Problem: if x / y = 7 / 4 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 11 / 3 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5
Rationale: "any x and y satisfying x / y = 7 / 4 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 4 , then ( x + y ) / ( x - y ) = ( 7 + 4 ) / ( 7 - 4 ) = 11 / 3 . answer : b ."
Answer: b
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.50 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 8.00
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.5 ) = $ 7 ( as the charge is 0.5 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 7 = 8 answer is e ."
Answer: e
Problem: if 1.5 x = 0.04 y , then the value of ( y - x ) ( y + x ) is :
Options: a ) 1405.25 , b ) 1305.25 , c ) 1205.25 , d ) 1505.25 , e ) 1605.25
Rationale: "let us assume x = 1 and y = 37.5 then 1.5 ( x ) = 0.04 ( y ) that is 1.5 ( 1 ) = 0.04 ( 37.5 ) = 1.5 = 1.5 therfore from given equation ( 37.5 - 1 ) ( 37.5 + 1 ) = ( 36.5 ) ( 38.5 ) = 1405.25 answer : a"
Answer: a
Problem: of the families in city x in 1956 , 25 percent owned a personal computer . the number of families in city x owning a computer in 1960 was 15 percent greater than it was in 1956 , and the total number of families in city x was 5 percent greater in 1956 than it was in 1960 . what percent of the families in city x owned a personal computer in 1960 ?
Options: a ) 50 % , b ) 51.22 % , c ) 5.26 % , d ) 7.20 % , e ) 27.38 %
Rationale: "say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 number of families owning computer in 1960 = 25 * 115 / 100 = 28.75 number of families in 1960 = 105 the percentage = 28.75 / 105 * 100 = 27.38 % . option : e"
Answer: e
Problem: if the cost price is 91 % of sp then what is the profit %
Options: a ) 9.89 % , b ) 8.90 % , c ) 9.00 % , d ) 8.00 % , e ) 9.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 91 : profit = rs 9 . profit = { ( 9 / 91 ) * 100 } % = 9.89 % answer is a ."
Answer: a
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 24 , find the sum of money ?
Options: a ) 288 , b ) 262 , c ) 72 , d ) 123 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 24 41 - - - - ? = > rs . 123 answer : d"
Answer: d
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a girl sitting at window seat in the slower train in 32 seconds . find the length of the faster train ?
Options: a ) 170 m , b ) 100 m , c ) 270 m , d ) 320 m , e ) 350 m
Rationale: "explanation : relative speed = ( 72 - 36 ) x 5 / 18 = 2 x 5 = 10 mps . distance covered in 32 sec = 32 x 10 = 320 m . the length of the faster train = 320 m . answer is d"
Answer: d
Problem: tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?
Options: a ) 6 , b ) 7 , c ) 12 , d ) 16 , e ) 24
Rationale: number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e
Answer: e
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 . 44000 . what is the share of c ?
Options: a ) rs . 12000 , b ) rs . 13375 , c ) rs . 11750 , d ) rs . 11625 , 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 ) × 44000 ] = rs . 12000 answer : option a"
Answer: a
Problem: in a 400 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 ) 81 , b ) 147 , c ) 145 , d ) 143 , e ) 141
Rationale: "solution simple out of 400 20 % are male i . e 80 and 25 % are female i . e 100 , so total homeowner is 180 . now min number homeowner is 80 and max is 180 so question ask us to find least and 81 has least value among all option . so ans is 81 . answer : a"
Answer: a
Problem: a sum of rs . 100 is lent at simple interest of 3 % p . a . for the first month , 9 % p . a . for the second month , 27 % p . a . for the third month and so on . what is the total amount of interest earned at the end of the year approximately
Options: a ) rs . 797160 , b ) rs . 791160 , c ) rs . 65930 , d ) rs . 66430 , e ) rs . 67430
Rationale: total amount of interest is i = p / 100 * 1 [ 3 / 12 + 9 / 12 + 27 / 12 … . 312 / 12 where p = 100 ; i = 1 / 12 ( 3 + 9 + … . . 312 ) i = 1 / 12 ( 3 ( 312 - 1 ) ) / 3 - 1 = 531440 * 3 / 12 * 2 = rs . 66430 answer : d
Answer: d
Problem: suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 10 , e ) 12
Rationale: the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the “ back ” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b .
Answer: b
Problem: the side of a square has the length of 6 . what is the area of the region shaded ?
Options: a ) 48 - 8 π
b ) 48 - 6 π
c ) 24 + 6 π
d ) 16 + 8 π
e ) 64 - 8 π
Rationale: the area of a square whose side is 6 – ( the area of a square whose side is 4 + the area of the semi - circle whose side is 4 ) = the area of the region shaded the correct answer is b .
Answer: b
Problem: how many positive integer solutions does the equation 4 x + 5 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 5 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 4 * 5 ) = 5 answer : d"
Answer: d
Problem: a man bought 10 crates of mangoes for $ 40 total . if he lost 2 of the crates , at what price would he have to sell each of the remaining crates in order to earn a total profit of 20 percent of the total cost ?
Options: a ) $ 6 , b ) $ 8 , c ) $ 10 , d ) $ 12 , e ) $ 14
Rationale: as given , after lost , the remaining 8 crates total cost = $ 40 so , 1 crate cost = 40 / 8 = 5 to get 20 % profit , 1 crate cost should be = 5 + 5 * 20 / 100 = $ 6 answer : a
Answer: a
Problem: a train passes a station platform in 32 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 887 , d ) 166 , e ) 180
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 32 = 15 = > x = 180 m . answer : e"
Answer: e
Problem: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 170 cookies , what percent of the cookies did irin bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 12.5 % , d ) 53.5 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 170 cookies x = 170 / 16.4 = 10 ( approx ) so , irin baked 10 * 9.18 cookies or 91 cookies ( approx ) % share = 91 / 170 = 53.5 approx hence , answer is d ."
Answer: d
Problem: how many four - digit numbers that do not contain the digits 3 or 6 are there ?
Options: a ) 2401 , b ) 3584 , c ) 4096 , d ) 5040 , e ) 7200
Rationale: "1 st digit can be filled up by the numbers - { 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 7 ways 2 nd digit can be filled up by the numbers - { 0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways 3 rd digit can be filled up by the numbers - { 0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways so , total no of ways is 7 * 8 * 8 = > 3584 hence answer will be ( b )"
Answer: b
Problem: a number increased by 30 % gives 650 . the number is ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 650 ( 130 ã — 5 = 650 ) 100 % - - - - - - - > 400 ( 100 ã — 5 = 500 ) option ' d '"
Answer: d
Problem: the positive numbers w , x , y , and z are such that x is 25 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.2 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16.2 - answer b"
Answer: b
Problem: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 20 days .
Options: a ) 12 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 20 * 6 / 10 = 12 days . answer : a"
Answer: a
Problem: if ' x ' is a positive integer exactly divisible by 6 or 15 but not divisible by 12 . what could possibly be the value of ' x ' ?
Options: a ) 120 , b ) 60 , c ) 36 , d ) 90 , e ) 54
Rationale: 120 and 60 are both divisible by 6 and 15 but also by 12 . so they are not the right answer . 36 and 54 are both clearly not divisible by 15 ( not correct ) 90 is both divisible by 6 and 15 but not by 12 . answer : ( d ) 90
Answer: d
Problem: if rs . 450 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) 227 , b ) 299 , c ) 270 , d ) 585 , e ) 271
Rationale: "90 = ( 450 * 4 * r ) / 100 r = 5 % i = ( 450 * 6 * 5 ) / 100 = 135 450 + 135 = 585 answer : c"
Answer: c
Problem: on a sum of money , the simple interest for 2 years is rs . 324 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 9.87 % , d ) 10.5 % , e ) 11.5 %
Rationale: "the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 324 = 16 ( r ã — si ) / ( 2 ã — 100 ) = 16 ( r ã — 324 ) / ( 2 ã — 100 ) = 16 r = 9.87 % answer : option c"
Answer: c
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 10 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.10 t + 0.08 ( p - t ) = 1440 - - - - > t = 1600 . a is the correct answer ."
Answer: a
Problem: a taxi leaves point a 2 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .
Options: a ) 42 , b ) 48 , c ) 44 , d ) 50 , e ) 40
Rationale: "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 4 hrs and taxi a total of 2 hrs . hence 4 * ( v - 20 ) = 2 v 4 v - 80 = 2 v 2 v = 80 v = 40 mph e"
Answer: e
Problem: a man walking at a constant rate of 12 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 24 miles per hour . the woman stops to wait for the man 10 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 13 , b ) 10 , c ) 15 , d ) 11 , e ) 9
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 10 * 24 / 60 = 4 miles and the man walks the distance mm , which is 10 * 12 / 60 = 2 mile . the difference of 4 - 2 = 2 miles ( mw ) will be covered by the man in ( 2 ) / 9 = 2 / 9 of an hour , which is ~ 13 minutes . answer a ."
Answer: a
Problem: if | 5 x - 5 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 2 , d ) - 3 , e ) 4
Rationale: "| 5 x - 5 | = 100 5 x - 5 = 100 or 5 x - 5 = - 100 5 x = 105 or 5 x = - 95 x = 21 or x = - 19 sum = 21 - 19 = 2 answer is c"
Answer: c
Problem: a bag of potatoes weighs 39 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 13 lb , e ) 5 lb
Rationale: "sol . 39 ÷ 3 = 13 . answer : d"
Answer: d
Problem: a person saved $ 50 in buying an item on sale . if he spent $ 500 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 1.8 %
Rationale: "actual price = 500 + 50 = $ 550 saving = 10 / 550 * 100 = 100 / 55 = 1.8 % approximately answer is e"
Answer: e
Problem: the difference between a number and its two - fifth is 510 . what is 20 % of that number ?
Options: a ) 58 , b ) 170 , c ) 95 , d ) 100 , e ) 120
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 20 % of 850 = 170 . answer : b"
Answer: b
Problem: monica planned her birthday party . she prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra . after the party , it turned out that one of the guests did n ' t come but every one of the guests that did come ate 6 muffins and 6 muffins remained . how many guests did monica plan on ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 7 .
Rationale: let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a
Answer: a
Problem: a boy rides his bicycle 10 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately ?
Options: a ) 10.7 km / hr , b ) 10.8 km / hr , c ) 17.8 km / hr , d ) 10.5 km / hr , e ) 30.8 km / hr
Rationale: total distance traveled = 10 + 12 = 22 km / hr . total time taken = 10 / 12 + 12 / 10 = 61 / 30 hrs . average speed = 22 * 30 / 61 = 10.8 km / hr . answer : b
Answer: b
Problem: if 3 ^ x = 2 , then 3 ^ ( 4 x + 3 ) =
Options: a ) 429 , b ) 454 , c ) 432 , d ) 438 , e ) 108
Rationale: 3 ^ x = 2 3 ^ 4 x = 2 ^ 4 3 ^ 4 x = 16 3 ^ ( 4 x + 3 ) = 3 ^ 4 x * 3 ^ 3 = 16 * 27 = 432 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 360 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 24 sec , e ) 1 min
Rationale: "they meet every 360 / 7 + 8 = 24 sec answer is d"
Answer: d
Problem: carol spends 1 / 3 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 9 , d ) 1 / 2 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 3 ) s amount spent on television = ( 1 - 1 / 3 ) ( 1 / 3 ) s = ( 2 / 3 ) * ( 1 / 3 ) * s = ( 2 / 9 ) s ( stereo + tv ) / total savings = s ( 1 / 3 + 2 / 9 ) / s = 5 / 9 answer : c"
Answer: c
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 36 . what is the value of x ?
Options: a ) 80 , b ) 96 , c ) 100 , d ) 108 , e ) 120
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 36 ( y / 100 ) * x = 36 ( x / 400 ) * x = 36 x ^ 2 = 36 * 400 x = 120 the answer is e ."
Answer: e
Problem: a van takes 6 hours to cover a distance of 540 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 ) 40 kmph , b ) 50 kmph , c ) 60 kmph , d ) 75 kmph , e ) 860 kmph
Rationale: "time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )"
Answer: c
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ?
Options: a ) 1 / 3 , b ) 5 / 9 , c ) 7 / 9 , d ) 19 / 27 , e ) 23 / 27
Rationale: "p ( missing all 3 ) = ( 2 / 3 ) ^ 3 = 8 / 27 p ( success on at least one attempt ) = 1 - 8 / 27 = 19 / 27 the answer is d ."
Answer: d
Problem: if an object travels 90 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 30.68 , b ) 32.34 , c ) 34.56 , d ) 36.72 , e ) 38.95
Rationale: "90 feet / 2 seconds = 45 feet / second ( 45 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 30.68 ( approximately ) the answer is a ."
Answer: a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25 % . find his false weight age ?
Options: a ) 338 , b ) 278 , c ) 800 , d ) 269 , e ) 112
Rationale: "25 = e / ( 1000 - e ) * 100 1000 - e = 4 e 1000 = 5 e = > e = 200 1000 - 200 = 800 answer : c"
Answer: c
Problem: 16.02 ã — 0.1 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.1 = 1.602 the answer is c ."
Answer: c
Problem: the population of a village is 13400 . it increases annually at the rate of 21 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 19619 , d ) 18989 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 13400 × 121 / 100 × 121 / 100 = 19619 c"
Answer: c
Problem: if the cost price is 90 % of sp then what is the profit %
Options: a ) 1.10 % , b ) 1.11 % , c ) 1.15 % , d ) 1.17 % , e ) 1.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 90 : profit = rs 10 . profit = { ( 10 / 90 ) * 100 } % = 1.11 % answer is b ."
Answer: b
Problem: a box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 42 , c ) 54 , d ) 108 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is ."
Answer: b
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 5,500 meters of fabric ?
Options: a ) $ 7,360 , b ) $ 8,540 , c ) $ 9,720 , d ) $ 10,570 , e ) $ 11,680
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 2000 = $ 3720 the total price is $ 4000 + $ 2850 + $ 3720 = $ 10,570 the answer is d ."
Answer: d
Problem: sonika deposited rs . 7000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 2277 , c ) 9620 , d ) 2774 , e ) 1212
Rationale: "( 7000 * 3 * 2 ) / 100 = 420 9200 - - - - - - - - 9620 answer : c"
Answer: c
Problem: a ’ s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 7 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 13 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 13 meters ) to reach the finish line . so b should get a head start of 7 / 20 th of the race . answer ( d )"
Answer: d
Problem: if 4 spiders make 3 webs in 9 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 9 , b ) 12 , c ) 27 , d ) 24 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 4 : 1 ( webs ) 1 : 9 } : : x : 3 â ‡ ’ 4 ã — 1 ã — 9 = 1 ã — 3 ã — x â ‡ ’ x = 12 answer : option b"
Answer: b
Problem: what is the largest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?
Options: a ) 9600 , b ) 5200 , c ) 362 , d ) 958 , e ) 258
Rationale: explanation : largest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , largest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : a
Answer: a
Problem: what will be the cost of building a fence around a square plot with area equal to 64 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2882 , c ) 2999 , d ) 1856 , e ) 2121
Rationale: "let the side of the square plot be a ft . a 2 = 64 = > a = 8 length of the fence = perimeter of the plot = 4 a = 32 ft . cost of building the fence = 32 * 58 = rs . 1856 . answer : d"
Answer: d
Problem: a 6 litre sol is 20 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3.6 , e ) e . 5.4
Rationale: "20 % of 6 = 1.2 50 % of 6 = 3 shortage is 1.8 so we need to have 1.8 / 50 % to get 50 % alcohol content . = 3.6 d"
Answer: d
Problem: if 45 % of z is 60 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 60 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 60 / 100 ) * ( 3 / 4 ) x i . e . z = ( 60 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1 ) x = ( 100 / 100 ) x i . e . z is 100 % of x answer : option c"
Answer: c
Problem: how many odd 3 - digit integers greater than 800 are there such that all their digits are different ?
Options: a ) 40 , b ) 56 , c ) 72 , d ) 81 , e ) 104
Rationale: in the range 800 - 900 : 1 choice for the first digit : 8 ; 5 choices for the third digit : 1 , 3 , 5 , 7 , 9 ( as the number is odd ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 5 * 8 = 40 . in the range 900 - 999 : 1 choice for the first digit : 9 ; 4 choices for the third digit : 1 , 3 , 5 , 7 ( 9 is out as it ' s the first digit ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 4 * 8 = 32 . total : 40 + 32 = 72 . answer : c
Answer: c
Problem: the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 40 x = 8 and the number of spinsters is 2 ( 8 ) = 16 . the answer is b ."
Answer: b
Problem: 33 1 / 3 % of 240 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 240 = 80 a )"
Answer: a
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 60 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 980 , e ) $ 1,240
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 30 tickets = 30 * 26 = 780 revenue generated from sales of 60 tickets = 120 + 340 + 780 = 1240 $ answer e"
Answer: e
Problem: if x is a number such that x ^ 2 + 5 x - 6 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =
Options: a ) - 1 , b ) 1 , c ) 4 , d ) - 6 , e ) 6
Rationale: "x ^ 2 + 5 x - 6 = ( x + 6 ) ( x - 1 ) = 0 then x = - 6 or x = 1 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 1 . the answer is b ."
Answer: b
Problem: one pump drains one - half of a pond in 7 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 7 hours so 14 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 14 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 14 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 14 + 1 / a ) = 1 / 2 solving u get a = 14 / 13 = 1.1 hence answer is b"
Answer: b
Problem: what is the area of square field whose side of length 18 m ?
Options: a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 324 sq m , e ) 296 sq m
Rationale: "18 * 18 = 324 sq m answer : d"
Answer: d
Problem: how much is 80 % of 40 is greater than 4 / 5 of 30 ?
Options: a ) 12 , b ) 27 , c ) 8 , d ) 12 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 32 - 24 = 8 answer : c"
Answer: c
Problem: how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15
Rationale: "the odd numbers less than 60 are 1 , 3,5 , . . . 59 some of them are equal to product of 5 and odd number hence odd multiples of 5 which are less than 60 are 5,15 , 25,35 , 45,55 ( total = 6 ) ; answer : b"
Answer: b
Problem: in a sports club with 30 members , 17 play badminton and 18 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 18 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"
Answer: a
Problem: a line that passes through ( – 3 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 3 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !"
Answer: c
Problem: the length of a train and that of a platform are equal . if with a speed of 90 kmph the train crosses the platform in one minute , then the length of the train in metres is
Options: a ) 500 , b ) 600 , c ) 750 , d ) 900 , e ) 950
Rationale: "2 x will be the distance travelled by the train if the length of the train = the length of the platform = x as distance = speed * time distance = 2 x speed in kmph = 90 speed in mps = 90 * 5 / 18 as dist = speed * time 2 x = ( 90 * 5 / 18 ) * ( 60 sec ) on solving x = 900 mts answer : d"
Answer: d
Problem: a group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 46 , c ) 49 , d ) 53 , e ) 86
Rationale: "4 x + 2 = 5 y + 2 . . . . . . . . . . . ie : 4 x - 5 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x is fraction if y = 4 thus x = 5 n = 22 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 42 summation 22 + 42 = 64 c"
Answer: c
Problem: in a forest 140 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,400 , e ) 2,500
Rationale: the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 140 tagged deers comprise 10 % of total # of deers - - > total # of deers = 140 * 10 = 1,400 . answer : d .
Answer: d
Problem: working at their respective constant rates , machine a makes 100 copies in 15 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 650 , d ) 700 , e ) 750
Rationale: "machine a can produce 100 * 30 / 15 = 200 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 650 copies . c is the answer"
Answer: c
Problem: the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ?
Options: a ) 11 years , b ) 17 years , c ) 26 years , d ) 14 years , e ) 12 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 240 - 214 ) = 26 years . answer : c"
Answer: c
Problem: company a imported 10,500 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported ?
Options: a ) 480 , b ) 840 , c ) 1050 , d ) 420 , e ) 2100
Rationale: "answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are red and 40 % are blue . since we know that there are only three colors , the remaining 40 % must be green . 40 % blue of 10 % brass widgets leads to 4 % green brass widgets out of the total 10,550 widgets . 10,500 / 100 * 4 = 420 . answer d ."
Answer: d
Problem: a train 250 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 100 , b ) 60 , c ) 55 , d ) 50 , e ) 45
Rationale: "speed of the train relative to man = 250 / 20 m / sec = 25 / 2 m / sec . = 25 / 2 x 18 / 5 km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 10 ) km / hr . x - 10 = 45 = 55 km / hr . answer : c"
Answer: c
Problem: you collect baseball cards . suppose you start out with 17 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 17 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 17 + 1 which is 9 , so you ' re left with 17 - 9 = 8 . peter takes 1 baseball card from you : 8 - 1 = 7 baseball cards . paul triples the number of baseball cards you have : 7 ã — 3 = 21 baseball cards . so you have 21 at the end . correct answer : e"
Answer: e
Problem: a bakery has 6 employees . it pays annual salaries of $ 19000 to each of 2 employees , $ 21000 to 1 employee , and $ 22000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 20,200 , b ) $ 20,500 , c ) $ 20,800 , d ) $ 21,000 , e ) $ 21,400
Rationale: average = 2 ( 19000 ) + ( 21000 ) + 3 ( 22000 ) / 6 = $ 20,833 the answer is c .
Answer: c
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 15.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 336 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 15 = 16 * 15 = 240 $ total charge = 126 + 240 = 366 $ answer a"
Answer: a
Problem: one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .
Options: a ) 120 , b ) 147 , c ) 251 , d ) 451 , e ) 258
Rationale: "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a"
Answer: a
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 50 billion gallons to 75 billion gallons . if the storm increased the amount of water in the reservoirs to 37.5 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 90 , b ) 114 , c ) 124 , d ) 120 , e ) 127
Rationale: after the reservoir is filled to 75 gallons the amount of water is at 37.5 % - which means that 62.5 % of the reservoir is empty . to figure out what that 62.5 % is approximate : 75 gallons / 37.5 percent = x gallons / 62.5 percent , therefore , x = 125 gallons , answer choices a , b , c , d are below 125 . we know that the reservoir must be short more than 125 gallons , therefore , the only possible choice is e .
Answer: e
Problem: a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scale ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
Rationale: first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c
Answer: c
Problem: the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number .
Options: a ) 72 , b ) 64 , c ) 84 , d ) 12 , e ) 92
Rationale: let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 .
Answer: a
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Problem: how many litres of pure acid are there in 15 litres of a 20 % solution
Options: a ) 4 , b ) 5 , c ) 2 , d ) 3 , e ) 1
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 15 * 20 / 100 = 3 answer : option d
Answer: d
Problem: rs . 385 were divided among x , y , z in such a way that x had rs . 20 more than y and z had rs 15 more than x . how much was y ’ s share ?
Options: a ) rs . 130 , b ) rs . 145 , c ) rs . 154 , d ) rs . 160 , e ) rs . 164
Rationale: let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r ’ s share = rs ( 110 + 35 ) = rs . 145 b
Answer: b
Problem: when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a
Answer: a
Problem: a group of men decided to do a work in 20 days , but 8 of them became absent . if the rest of the group did the work in 28 days , find the original number of men ?
Options: a ) 60 , b ) 28 , c ) 40 , d ) 50 , e ) 25
Rationale: "original number of men = 8 * 28 / ( 28 - 20 ) = 28 answer is b"
Answer: b
Problem: three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 32 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters
Rationale: "280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) ."
Answer: b
Problem: mr . x , a mathematician , defines a number as ' connected with 6 if it is divisible by 6 or if the sum of its digits is 6 , or if 6 is one of the digits of the number . other numbers are all ' not connected with 6 ' . as per this definition , the number of integers from 1 to 60 ( both inclusive ) which are not connected with 6 is
Options: a ) 18 , b ) 22 , c ) 42 , d ) 43 , e ) 45
Rationale: explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such uncommon numbers . numbers from 1 to 60 , which have 6 as one of the digits are 6 , 16 , 26 , 36 , 46 , 56 , 60 . clearly , there are 4 such uncommon numbers . so , numbers ' not connected with 6 ' = 60 - ( 10 + 3 + 4 ) = 43 . answer : d
Answer: d
Problem: a camera lens filter kit containing 5 filters sells for $ 67.50 . if the filters are purchased individually , 2 of them are priced at $ 7.45 each , 2 at $ 10.05 each , 1 at $ 14.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 25.66 % , b ) 26.66 % , c ) 27.66 % , d ) 28.66 % , e ) 29.66 %
Rationale: "cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b ."
Answer: b
Problem: the largest 4 digit number exactly divisible by 90 is ?
Options: a ) 9935 , b ) 9939 , c ) 9944 , d ) 9954 , e ) 9990
Rationale: "largest 4 - digit number = 9999 90 ) 9999 ( 111 9990 - - - - - - - - - - - - largest number divisible by 90 is 9990 answer : e"
Answer: e
Problem: if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ? .
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: 20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d
Answer: d
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 4 by bus and the remaining 4 km on foot . his total journey is
Options: a ) 18 km , b ) 16 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b"
Answer: b
Problem: what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
Options: a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 7 / 15 , e ) none of these
Rationale: "explanation : since every third number starting from 10 will be divisible by 3 , so total number of numbers divisible by 3 are 90 / 3 = 30 numbers which are divisible by 3 and 5 both are numbers which are multiple of 15 . for the range 10 to 99 , 15 is the first number divisible by 15 and 90 is the last number . so total number of numbers divisible by 15 are : ( 90 - 15 ) / 15 + 1 = 5 + 1 = 6 number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6 . so number of numbers divisible by 3 and not by 5 are : 30 - 6 = 24 so total probability = 24 / 90 = 4 / 15 answer : c"
Answer: c
Problem: bhanu spends 30 % of his income on petrol on scooter 21 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 797 , e ) 147
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 21 % ( 700 ) = rs . 147 answer : e"
Answer: e
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 35 meters deep by working for 6 hours ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 35 x = 70 total workers 70 - 45 = 30 new workers the answer is c ."
Answer: c
Problem: one - third less than 25 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b"
Answer: b
Problem: if an object travels at 8 feet per second , how many feet does it travel in forty five minutes ?
Options: a ) 18000 , b ) 24000 , c ) 21600 , d ) 18000 , e ) 22000
Rationale: "if an object travels at 8 feet per second it covers 8 x 60 feet in one minute , and 8 x 60 x 45 feet in forty five minutes . answer = 21600 answer : c"
Answer: c
Problem: in arun ’ s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun ’ s weight is greater than 60 kg but less than 70 kg . his mother ’ s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what is the average of different probable weights of arun ?
Options: a ) 66 kg , b ) 67 kg , c ) 68 kg , d ) 69 kg , e ) none of these
Rationale: explanation : let arun ’ s weight by x kg . according to arun , 65 < x < 72 according to arun ’ s brother , 60 < x < 70 . according to arun ’ s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b
Answer: b
Problem: there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 65
Rationale: approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e
Answer: e
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 500 . then his monthly salary is
Options: a ) rs . 2500 , b ) rs . 3500 , c ) rs . 1500 , d ) rs . 500 , e ) rs . 2000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 500 â ‡ ” 20 / 100 x = 500 â ‡ ” x = 500 ã — 5 = 2500 . answer a"
Answer: a
Problem: there are 418 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 242 , d ) 171 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 418 = 242 answer : c"
Answer: c
Problem: robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert borrowed rs . 7280 / - from company . but robert forget that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the incentive amount given to robert ?
Options: a ) 9500 , b ) 12500 , c ) 10780 , d ) 10500 , e ) 8600
Rationale: "total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c"
Answer: c
Problem: what number has a 3 : 4 ratio to the number 400 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 300 , e ) 120
Rationale: "3 : 4 = x : 200 4 x = 3 * 400 x = 300 answer : d"
Answer: d