regisss/math_qa huggingface dataset:
Problem: find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 10 as quotient and the 10 as remainder
Options: a ) 1234 , b ) 1110 , c ) 1456 , d ) 1200 , e ) 1600
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 10 x + 10 9 x = 990 x = 110 large number = 110 + 1000 = 1110 b"
Answer: b
Problem: the average height of 30 girls out of a class of 40 is 160 cm . and that of the remaining girls is 156 cm . the average height of the whole class is :
Options: a ) 158 cms , b ) 158.5 cms , c ) 159 cms , d ) 159.5 cms , e ) none
Rationale: explanation : average height of the whole class = ( 36 × 160 + 10 × 156 / 40 ) = 159 cms answer c
Answer: c
Problem: what is the units digit of 16 ^ 83 × 13 ^ 82 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 6 correct option : c"
Answer: c
Problem: a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 15000 rs , what is the value of buzness ?
Options: a ) 55000 , b ) 75000 , c ) 65000 , d ) 190000 , e ) 250000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 15000 - > x = 75000 answer : b"
Answer: b
Problem: jaylen was planning to save all summer for a pair of jordan 12 s . they cost $ 250 . jaylen figured that he could cut grass to help with the cost of the sneakers . how many yards would jaylen have to cut if he charges $ 2.15 per yard ?
Options: a ) 116 yards , b ) 226 yards , c ) 97 yards , d ) 115.74 yards , e ) 1 yard
Rationale: d
Answer: d
Problem: what is the total number of integers between 200 and 500 that are divisible by 25 ?
Options: a ) 20 , b ) 25 , c ) 14 , d ) 15 , e ) 18
Rationale: "125 , 150 , 175 , . . . , 450,475 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 475 - 125 ) / ( 25 ) + 1 = 350 / 25 + 1 = 14 + 1 = 15 answer is d"
Answer: d
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 30 million gallons of water . this amount is twice the normal level . if this amount represents 75 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 30 mg = 75 % of total . . total = 30 / . 75 = 40 mg . . normal level = 1 / 2 of 40 = 20 mg . . shortage of normal level = 40 - 20 = 20 mg . . c"
Answer: c
Problem: matt gets a $ 1000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d
Answer: d
Problem: the present worth of $ 169 due in 2 years at 4 % per annum compound interest is ?
Options: a ) $ 145.89 , b ) $ 138.62 , c ) $ 156.25 , d ) $ 160.23 , e ) $ 158.95
Rationale: "present worth = 169 / ( 1 + 4 / 100 ) ^ 2 = 169 * 25 / 26 * 25 / 26 = $ 156.25 answer is c"
Answer: c
Problem: an urn contains 10 black and 5 white balls . two balls are drawn from the urn one after the other without replacement . what is the probability that both drawn balls are black ?
Options: a ) 1 / 5 , b ) 3 / 7 , c ) 2 / 5 , d ) 3 / 5 , e ) 2 / 7
Rationale: let e and f denote respectively the events that first and second ball drawn are black . we have to find p ( e n f ) or p ( ef ) . now p ( e ) = p ( black ball in first draw ) = 10 / 15 also given that the first ball drawn is black , i . e . , event e has occurred , now there are 9 black balls and five white balls left in the urn . therefore , the probability that the second ball drawn is black , given that the ball in the first draw is black , is nothing but the conditional probability of f given that e has occurred . that is p ( f | e ) = 9 / 14 by multiplication rule of probability , we have p ( e n f ) = p ( e ) p ( f | e ) = 10 / 15 × 9 / 14 = 3 / 7 b
Answer: b
Problem: by selling 11 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8.25 , b ) 9.25 , c ) 7.25 , d ) 10.25 , e ) 3.25
Rationale: 90 % - - - 11 120 % - - - ? 90 / 120 * 11 = 8.25 answer : a
Answer: a
Problem: in the first 10 overs of a cricket game , the run rate was only 4.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) 6
Rationale: "10 overs - run rate = 4.2 runs scored in first 10 overs = 42 remaining overs 40 total runs to be scored = 282 42 runs already scored 282 - 42 = 240 240 runs to be scored in 40 overs let required runrate be x 40 * x = 240 x = 240 / 40 x = 6.0 the required runrate is 6.0 answer : e"
Answer: e
Problem: average between two sets of numbers is closer to the set withmore numbers ?
Options: a ) 60 , b ) 80 , c ) 98 , d ) 89 , e ) 91
Rationale: if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b
Answer: b
Problem: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 50 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100
Rationale: "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 50 % , so the manufacturing must have been $ 50 . answer = ( c ) ."
Answer: c
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2240 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 2800 , e ) 11500
Rationale: "p - 2240 = ( p * 5 * 4 ) / 100 p = 2800 answer : d"
Answer: d
Problem: a jeep takes 9 hours to cover a distance of 480 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 52 kmph , c ) 35 kmph , d ) 63 kmph , e ) 65 kmph
Rationale: time = 9 distance = 480 3 / 2 of 9 hours = 9 * 3 / 2 = 13.5 hours required speed = 480 / 13.5 = 35 kmph c )
Answer: c
Problem: what is the tens digit of 6 ^ 22 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 22 has the form 5 n + 2 , so the tens digit of 6 ^ 22 is 3 . the answer is b ."
Answer: b
Problem: in one hour , a boat goes 7 km along the steram and 5 km against the stream . the speed of the boat in still waer ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 12 , e ) 15
Rationale: "sol . speed in still water = 1 / 2 ( 7 + 5 ) kmph = 6 kmph . answer c"
Answer: c
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 36 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 289 m , d ) 299 m , e ) 25 m
Rationale: "speed = 300 / 36 = 25 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 3 = > x = 25 m . answer : e"
Answer: e
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 15 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 250 , b ) $ 340 , c ) $ 640 , d ) $ 440 , e ) $ 540
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 15 a = 15 + b ( 1 ) = = = > c = 45 + 3 b - b = 2 b + 45 = = > 2 b - c = - 45 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 15 = 2.5 b - 15 = = > 2.5 b - c = 15 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 60 b = $ 120 a = $ 135 c = 405 - 120 = $ 285 total amount = 135 + 120 + 285 = $ 540 answer : e"
Answer: e
Problem: the distance between a & b is 1540 km . a person is traveling from a to b at 100 km / hr started at 6 am and another person is traveling from b to a at 120 km / hr and started at same time . then at what time they meet together .
Options: a ) 11 am , b ) 1 pm , c ) 3 pm , d ) 10 am , e ) 9 am
Rationale: "let x hours be they will meet together distance covered by 1 st person + distance covered by 2 nd person = 1540 km 100 x + 120 x = 1540 x = 7 hr they will meet = 6 am + 7 hr = 1 pm answer is b"
Answer: b
Problem: williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 8 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 3 / 7 , b ) 5 / 7 , c ) 6 / 7 , d ) 1 / 7 , e ) 4 / 7
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 8 x total tips for all months = 6 * x + 8 x = 14 x tips for august / total tips for all months = 8 x / 14 x = 4 / 7 answer : e
Answer: e
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 1000 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 1000 km in = 1000 / 50 * 1 = 20 hours answer is c"
Answer: c
Problem: 0.0008 ? = 0.02
Options: a ) 40 , b ) 4 , c ) 0.4 , d ) none of these , e ) 0.04
Rationale: "explanation : required answer = 0.0008 / 0.02 = 0.08 / 2 = 0.04 . answer : option e"
Answer: e
Problem: if each edge of cube increased by 50 % , the percentage increase in
Options: a ) 100 , b ) 114 , c ) 115 , d ) 125 , e ) 105
Rationale: "100 × ( 150 ) / 100 × ( 150 ) / 100 = 225 = > 125 % answer is d ."
Answer: d
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 11 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 642 km , d ) 440 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 11 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 = sum of 11 terms in ap whose first term is 30 and last term is 50 = 11 / 2 [ 30 + 50 ] = 440 km . answer : d"
Answer: d
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 b beats a by 80 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 87 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 20 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.2 ) = 0.13 % ( which means b would have covered 0.13 of the race length during the time in which a has covered 0.2 of the race length . therefore to win , b needs a headstart of ( 1 - 0.13 = ) 0.87 of the race length . so the answer is e"
Answer: e
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12,000 and the marginal cost is $ 200 , and the total cost is $ 16,000 , what is the value of n ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a .
Answer: a
Problem: the mark up between ` ` normal plan ' ' price and ` ` premium plan ' ' price is 30 percent of the ` ` normal plan ' ' price . the markup is what percent of the ` ` premium plan ' ' price ? ( markup = difference between normal and premium price plans )
Options: a ) 8 % , b ) 20 % , c ) 33 1 / 3 % , d ) 45 % , e ) 56 2 / 3 %
Rationale: a = price for normal plan b = price for premium plan mp = 0.5 a b = a + 0.5 a = 1.5 a hence markup = b - a = 0.5 / 1.5 b = 1 / 3 b . hence mp is 33.33 % of b answer c
Answer: c
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 50 % of the total school population of x students , what is x ?
Options: a ) 134 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 50 / 100 * x = > x ^ 2 = 9 * 10000 / 5 = > x = 134 a"
Answer: a
Problem: paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?
Options: a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "let rex ' s income = 100 , then : rex = 100 paul = 60 quentin = 48 sam = 36 rex gives 60 dollars to sam , so now sam has 96 dollars rex gives 40 dollars to quentin , so now quentin has 88 dollars the fraction q / s = 11 / 12 answer : a"
Answer: a
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 8 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 22 , b ) 21 , c ) 88 , d ) 37 , e ) 24
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 8 ) + 6000 ( v - 8 ) < = > 2000 v = 48000 < = > v = 24 answer : e ) 24"
Answer: e
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 7 ?
Options: a ) 70,592 , b ) 64,850 , c ) 64,749 , d ) 149,700 , e ) 156,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 7 seeing the options after dividing an finding the reminder of 2 my answer was a"
Answer: a
Problem: a tyre has two punctures . the first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes . if air leaks out at a constant rate , how long does it take both the punctures together to make it flat ?
Options: a ) 315 min , b ) 325 min , c ) 335 min , d ) 345 min , e ) none of these
Rationale: explanation : do not be confused , take this question same as that of work done question ' s . like work done by 1 st puncture in 1 minute and by second in 1 minute . lets solve it : 1 minute work done by both the punctures = ( 19 + 16 ) = ( 518 ) so both punctures will make the type flat in ( 185 ) mins = 335 mins answer : c
Answer: c
Problem: a sum of money is distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 1000 more than d , what is the b ' s share ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 2500 , d ) $ 2850 , e ) $ 2950
Rationale: "let the shares of a , b , c , d are 5 x , 2 x , 4 x , 3 x 4 x - 3 x = 1000 x = 1000 b ' s share = 2 x = $ 2000 answer is b"
Answer: b
Problem: alex takes a loan of $ 6,000 to buy a used truck at the rate of 8 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 700 , c ) 720 , d ) 480 , e ) 420
Rationale: "from the details given in the problem principle = p = $ 6,000 and r = 8 % or 0.08 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 6,000 x 1 x 0.08 = 480.00 annual interest to be paid = $ 480 answer : d"
Answer: d
Problem: during a certain two - week period , 60 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 6 a , c ) 8 a , d ) 14 a , e ) 20 a
Rationale: "movies : 60 % comedies . 40 % remaining genre . now in this 40 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 3 x . total 4 x . 4 x = 40 ; x = 10 action movies : 10 % drama movies : 30 % we can say that out of 100 z , : comedies : 60 z action : 10 z drama : 30 z now action movies werea this means : a = 10 z . z = ( a / 10 ) comedies : 60 z = 60 * ( a / 10 ) 6 a b is the answer ."
Answer: b
Problem: if 15 % of a is the same as 40 % of b , then a : b is :
Options: a ) 5 : 4 , b ) 8 : 3 , c ) 7 : 16 , d ) 2 : 17 , e ) 3 : 5
Rationale: "expl : 15 % of a i = 40 % of b = 15 a / 100 = 40 b / 100 = 8 / 3 = 8 : 3 answer : b"
Answer: b
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6500 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9503 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6500 1 = 6500 / 68.4 100 = ( 6500 * 100 ) / 68.4 = rs . 9503 . answer : option d"
Answer: d
Problem: if a man walks at a rate of 10 kmph , he misses a train by 14 minutes . however , if he walks at the rate of 12 kmph , he reaches the station 10 minutes before the arrival of the train . find the distance covered by him to reach the station .
Options: a ) 6 , b ) 15 , c ) 12 , d ) 4 , e ) 8
Rationale: "let the required distance x km difference in the times taken at two speeds = 12 min = 1 / 5 hr ( x / 10 ) - ( x / 12 ) = 1 / 10 x = 6 the required distance is 6 km answer is a"
Answer: a
Problem: of 32 applicants for a job , 14 had at least 4 years ' experience , 18 had degrees , and 7 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 32 - 7 = 25 aub = a + b - aib aib = 18 + 14 - 25 = 7 answer d"
Answer: d
Problem: a box contains 10 tablets of medicine a and 10 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 15 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 10 + 2 = 12 tablets . answer : a ."
Answer: a
Problem: express a speed of 63 kmph in meters per second ?
Options: a ) 10 mps , b ) 14 mps , c ) 17.5 mps , d ) 19.4 mps , e ) 10.8 mps
Rationale: "63 * 5 / 18 = 17.5 mps answer : c"
Answer: c
Problem: if w / x = 2 / 3 and w / y = 3 / 5 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 9 / 10 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "w / x = 2 / 3 x = > x = 3 / 2 w and w / y = 3 / 5 = > y = 5 / 3 w ( x + y ) / y = ( 3 / 2 w + 5 / 3 w ) / ( 5 / 3 x ) = 9 / 10 correct option : b"
Answer: b
Problem: what least number must be subtracted from 42739 so that remaining no . is divisible by 15
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 42739 by 15 we get the remainder 4 , so 4 should be subtracted option b"
Answer: b
Problem: 18 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 279 , d ) 90 , e ) 45
Rationale: "there are 18 business exec and in each handshake 2 business execs are involved . hence 18 c 2 = 153 also , each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake . total = 153 + 126 = 279 ans : c"
Answer: c
Problem: for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?
Options: a ) $ 48 , b ) $ 54 , c ) $ 60 , d ) $ 66 , e ) $ 72
Rationale: "the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 40 * $ 1.50 = $ 60 the answer is c ."
Answer: c
Problem: the probability of two events a and b are 0.20 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.55 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 20 + . 40 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : d"
Answer: d
Problem: of the diplomats who attended a summit conference : 20 spoke japanese , 32 did not speak russian and 20 % of the diplomats spoke neither japanese nor russian . if 10 % of the diplomats spoke both japanese and russian , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Problem: if n = 2.0423 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0023 , c ) 0.0007 , d ) 0.0047 , e ) 0.0153
Rationale: n * = 2.04 n * - n = 2.04 - 2.0423 - 0.0023 answer : b
Answer: b
Problem: carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 6 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 3 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 36 / 12 = 3 answer is c"
Answer: c
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 49 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 120 , c ) 140 , d ) 147 , e ) 168
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 49 t or 5 t + 6 = 7 t or t = 3 distance travelled by car x from the time car y began traveling until both cars stopped is 35 x 3 = 105 miles answer : - a"
Answer: a
Problem: in a restaurant , the profit is 160 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 57 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 160 , s . p . = rs . 260 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 260 . profit = rs . ( 260 - 112 ) = rs . 148 . required percentage = ( 148 / 260 * 100 ) % = 57 % appox answer : b"
Answer: b
Problem: a train 250 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 150 m long ?
Options: a ) 45 sec , b ) 42 sec , c ) 32 sec , d ) 48 sec , e ) 25 sec
Rationale: "total length = 250 + 150 = 400 speed = 45 km / h = ( 45 * 5 ) / 18 = 25 / 2 m / s time = ( 400 * 2 ) / 25 = 32 sec . answer : c"
Answer: c
Problem: a can complete the job in 5 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 8 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 8
Answer: a
Problem: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 35 and 200 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14
Rationale: "given : 35 < x ( x + 1 ) < 200 . now , it ' s better to test the answer choices here rather than to solve : if x = 5 then x ( x + 1 ) = 30 > 35 - - > so , the least value is 5 . test for the largest value : if x = 14 then x ( x + 1 ) = 14 * 15 = 210 > 200 answer : e ."
Answer: e
Problem: 25 * 25 * 25 * 25 * 25 = 5 ^ ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 3 , e ) 10
Rationale: "solution : 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 = 5 ^ ( 2 + 2 + 2 + 2 + 2 ) = 5 ^ 10 answer : e"
Answer: e
Problem: what quantity of water should taken out to concentrate 21 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 7 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 21 ( 60 - 40 ) / 60 = 7 liters answer is c"
Answer: c
Problem: a and b together can do a work in 6 days . if a alone can do it in 10 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 15 , c ) 77 , d ) 55 , e ) 21
Rationale: "1 / 6 – 1 / 10 = 1 / 15 = > 15 answer : b"
Answer: b
Problem: sam and nik start from a and b respectively at the same time and travel towards each other at constant speeds along the same route . sam meets nik at point c on the road which is 600 m away from starting point a and 400 m away from point b . the speed of sam is 50 m / m ( meter / minute ) . how much time did sam take to cover the distance between a and b ?
Options: a ) 10 minutes , b ) 15 minutes , c ) 20 minutes , d ) 22 minutes , e ) 17 minutes
Rationale: total distance from a to b - a - c = 600 m , b - c = 400 m ; therefore a - b = 1000 m ; vs = 50 m / m ; therefore , t = 1000 / 50 = 20 minutes . option c
Answer: c
Problem: subtract . simplify your answer and write it as a proper fraction or as a whole or mixed number . 4 / 5 - 1 / 5 =
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 5
Rationale: here ' s how to subtract 1 / 5 from 4 / 5 : 4 / 5 − 1 / 5 since our denominators match , we can subtract the numerators . 4 − 1 = 3 so the answer is : 3 / 5 answer : c
Answer: c
Problem: ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?
Options: a ) 378 , b ) 180 , c ) 820 , d ) 734 , e ) 840
Rationale: explanation : 3 x + 4 x = 420 x = 60 = > 3 x = 180 answer : option b
Answer: b
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 30 , what is the greatest possible value of q minus r ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 30 . the greatest multiple of 9 which is less than 30 is 27 . the answer is e .
Answer: e
Problem: what is the square root of 121 ?
Options: a ) 11 , b ) 12 , c ) 16 , d ) 18 , e ) 25
Rationale: "11 x 11 = 121 answer a"
Answer: a
Problem: if equation | x / 5 | + | y / 5 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 200 , d ) 100 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 10 | + | y / 10 | = 1 , so these are lines in four quadrants with x and y intercept as 10 , so it is a rhombus with diagonals of 20 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 20 * 20 = 200 . answer c .
Answer: c
Problem: in a vehicle ' s repair shed , 3 men and 8 boys can do a piece of work in 15 days ; 4 men and 9 boys can do the same work in 12 days . then , 5 men and 5 boys can do double the amount of this work in :
Options: a ) 20 days , b ) 33 days , c ) 24 days , d ) 28 days , e ) none of these
Rationale: explanation : solution : ( 3 * 15 ) men + ( 8 * 15 ) boys = ( 4 * 12 ) men + ( 9 * 12 ) boys 45 m + 120 b = 48 m + 108 b < = > 3 m = 12 b = > 1 m = 4 b . . ' . 3 m + 8 b = ( 3 * 4 ) b + 8 b = 20 b . 5 m + 5 b = ( 5 * 4 ) b + 5 b = 25 b . let the required number of days be x . now , more boys , less days ( ip ) more work , more days ( dp ) boys 25 : 20 } : : 15 : x work 1 : 2 . ' . ( 25 * 1 * x ) = ( 20 * 2 * 15 ) = > x = 40 * 15 / 25 = 24 . answer : c
Answer: c
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 50 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 50
Rationale: "amount earned by james = 40 * x + 10 * 2 x = 60 x therefore , amount earned by james = 60 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 60 x ] ] so x * ( 1.5 y - 45 + 30 ) = 60 x or x * ( 1.5 y - 15 ) = 60 x so 1.5 y - 15 = 60 so 1.5 y = 75 so y = 50 answer is e"
Answer: e
Problem: increasing the original price of an article by 8 percent and then increasing the new price by 8 percent is equivalent to increasing the original price by
Options: a ) 16.16 % , b ) 16.32 % , c ) 16.64 % , d ) 17.26 % , e ) 18.56 %
Rationale: "1.08 * 1.08 * x = 1.1664 * x the answer is c ."
Answer: c
Problem: if 6 women can color 180 m long cloth in 3 days , then 5 women can color 200 m long cloth in ?
Options: a ) 6 days , b ) 5 days , c ) 4 days , d ) 2 days , e ) 3 days
Rationale: the length of cloth painted by one woman in one day = 180 / 6 × 3 = 10 m no . of days required to paint 200 m cloth by 5 women = 200 / 5 × 10 = 4 days answer : c
Answer: c
Problem: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 210 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.64 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
Rationale: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 210 - - > x = 1.308 . 1.25 x = ~ 1.64 . answer : b ."
Answer: b
Problem: if x ⁄ 2 + 9 ⁄ 4 = 5 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "x ⁄ 2 + 9 ⁄ 4 = 5 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 9 = 5 2 x = - 4 x = - 2 the answer is a ."
Answer: a
Problem: how many zeros does 65 ! end with ?
Options: a ) 20 , b ) 15 , c ) 25 , d ) 30 , e ) 32
Rationale: "according to above 65 ! has 65 / 5 + 65 / 25 = 13 + 2 = 15 trailing zeros . answer : b ."
Answer: b
Problem: the price of a certain painting increased by 30 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 110.5 % , d ) 112.5 % , e ) 100 %
Rationale: easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.15 = 130 * 0.85 = 110.5 hence required answer = ( 110.5 / 100 ) * 100 % = 110.5 % answer is c .
Answer: c
Problem: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 27 more than the correct answer . find the number .
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 27 25 x = 16 x + 540 9 x = 540 x = 60 the answer is c .
Answer: c
Problem: in a forest 150 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 20 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 ) 6,000 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 20 / 50 * 100 = 40 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 150 * 40 = 6,000 . answer : b"
Answer: b
Problem: the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 5 days ago , the water level was at w inches . what will be the water level exactly 3 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 126 , b ) w − 56 , c ) w − 112 , d ) w + 14 , e ) w + 126
Rationale: "drop = 14 inches / day 5 days ago = w , means now it ' s equal w - 70 and in 3 days = w - 70 - 42 = w - 112 answer c"
Answer: c
Problem: what is 15 % of 2 / 3 of 0.6 ?
Options: a ) 0.06 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 6 / 10 ) = 180 / 3000 = 0.06 option a"
Answer: a
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 150 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 110 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 150 newborn 150 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 110 is expected to survive . answer : a ."
Answer: a
Problem: the units digit of ( 35 ) ^ ( 7 ) + ( 93 ) ^ ( 45 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term takes a little more work . we can ignore the tens digit , and just treat this base as 3 . here is the units digit patter for the powers of 3 . 3 ^ 45 has a units digit of 3 of course 5 + 3 = 8 , d"
Answer: d
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 7 : 3 . if 70 % of the toyota bought and 30 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 76 % , b ) 58 % , c ) 68 % , d ) 89 % , e ) 49 %
Rationale: let total no of vehicles bought be 100 , toyota 70 and honda 30 , so total number of suv ' s bought for toyota and honda respectively 70 * 70 / 100 = 49 and 30 * 30 / 100 = 9 so total 58 suv ' s were bought out of 100 vehicles bought . . so required % is 58 % answer : b
Answer: b
Problem: how many 4 - digit numbers are completely divisible by 7 ?
Options: a ) 1354 , b ) 1286 , c ) 1178 , d ) 1224 , e ) none
Rationale: "solution : 4 - digit numbers divisible by 7 are : 1001 , 1008 , 1015 … . . 9996 . this is an a . p . in which a = 1001 , d = 7 , l = 9996 . let the number of terms be n . then tn = 9996 . . ' . a + ( n - 1 ) d = 9996 = > 1001 + ( n - 1 ) 7 = 9996 = > ( n - 1 ) 7 = 8995 = > ( n - 1 ) = 8995 / 7 = 1285 = > n = 1286 . . ' . number of terms = 1286 . answer b"
Answer: b
Problem: what is the units digit of ( 3 ^ 16 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 16 = 3 ^ 4 * 4 =  3 ^ 0 = 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 16 ) ( 4 ^ 13 )  ( 3 ^ 0 ) ( ~ 4 ) = ( ~ 1 ) ( ~ 4 ) = ~ 4 . therefore , the answer is b ."
Answer: b
Problem: a can do a piece of work in 10 days , b in 15 days . they work for 5 days . the rest of work finished by c in 2 days . if they get rs 1500 for the whole work , the daily wages of b and c are ?
Options: a ) 225 , b ) 276 , c ) 126 , d ) 187 , e ) 1267
Rationale: explanation : let the total work = 30 units . then capacity of a = 3 units , b = 2 units . now they worked for 5 days . so they must have completed 25 units . rest of the work 5 units done by c in 2 days . so c capacity = 5 / 2 = 2.5 units . given that toatal wages are rs . 1500 for 30 units . so for 1 unit of work they get rs . 50 . now b and c per day work = ( 2 + 2.5 ) = 4.5 units . so their daily wages = 4.5 × 50 = rs . 225 answer : a
Answer: a
Problem: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 20 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100
Rationale: cost + profit = income ( selling price ) profit now = 0.5 x or x - 50 0.5 x = x - 50 50 = 0.5 x x = 100 $ is selling price so , profit before was 0.2 * 100 = 20 $ cost = 100 - 20 = 80 $ answer : d
Answer: d
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 900 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 1300 , b ) 1350 , c ) 1400 , d ) 1450 , e ) 1500
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 900 x = 1500 the answer is e ."
Answer: e
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 18 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.18 0.2 x = 0.08 x = 0.4 = 40 % the answer is c ."
Answer: c
Problem: find the value o f 72519 x 9999 = m ?
Options: a ) 434539873 , b ) 355797990 , c ) 435453490 , d ) m = 725117481 , e ) 873430134
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Problem: ( 4 ! ) ^ n is a factor of 12 ! , but ( 4 ! ) ^ ( n + 1 ) is not factor of 12 ! . what is the value of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 12 ! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 4 ! = 24 question can be rephrased as how many 24 ' s are there in 12 ! 12 * 2 = 24 4 * 6 = 24 3 * 8 = 24 value of n = 3 answer : c
Answer: c
Problem: a motorcyclist goes from bombay to pune , a distance of 256 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 1 , e ) 5 : 8
Rationale: "t = 256 / 32 = 8 h t = 8 - 3 = 5 time ratio = 8 : 5 speed ratio = 5 : 8 answer : e"
Answer: e
Problem: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years x in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) x = 25 , c ) x = 30 , d ) x = 35 , e ) 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Problem: when the positive integer y is divided by 9 , the remainder is 5 . what is the remainder when 3 y is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6
Rationale: lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y = 9 k + 5 multiplying by 3 will give 3 y = 27 k + 15 we can also write 3 y = 27 k + 9 + 6 now 27 k and 9 are divisible by 9 leaving the remainder as 6 hence e is the answer .
Answer: e
Problem: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 70 th number in this set ?
Options: a ) 557 , b ) 608 , c ) 613 , d ) 616 , e ) 621
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 70 th number = 8 * ( 70 - 1 ) + 5 = 557 answer = a"
Answer: a
Problem: find the minimum value of 5 cosa + 12 sina + 12
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) none of these
Rationale: "solution : 5 cosa + 12 sina + 12 = 13 ( 5 / 13 cosa + 12 / 13 sina ) + 12 now , for any values of b we can get sinb = 5 / 13 and we can replace cosb = 12 / 13 . we see that our assumption is right because we satisfy the condition sin ^ 2 b + cos ^ 2 b = 1 so we get 13 ( sinbcosa + cosbsina ) + 12 = 13 ( sin ( a + b ) ) + 12 . therefore we know that minimum value of sinx = - 1 and greatest is 1 so the least value of the expression becomes when sin ( a + b ) = - 1 then the value of the whole term becomes 13 . ( - 1 ) + 12 = - 13 + 12 = - 1 answer a"
Answer: a
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 122 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 2200 , e ) 3600
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 2 yearned with the compound interest is the percent yearned on percent . so , $ 2 is yearned on $ 60 , which means that the interest = 30 % . this on the other hand means that half of the savings = 60 * 30 = $ 1800 . twice of that = $ 3,600 . answer : e ."
Answer: e
Problem: when positive integer n is divided by 7 , the remainder is 1 . when n is divided by 11 , the remainder is 5 . what is the smallest positive integer k such that k + n is a multiple of 77 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 7 p + 1 = 11 q + 5 n + 6 = 7 p + 7 = 11 q + 11 n + 6 is a multiple of 7 and 11 , so it is a multiple of 77 . the answer is c ."
Answer: c
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m ?
Options: a ) 29000 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27991
Rationale: "29 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 29 = 1 / 100 * x = > x = 29000 answer : a"
Answer: a
Problem: on a map , 1 inch represents 28 miles . how many b inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: b inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c
Answer: c
Problem: a worker is paid a regular rate of rs . 30 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 20 % higher than her regular rate . if she completed 50 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 2200 , b ) 1100 , c ) 2500 , d ) 2800 , e ) 3300
Rationale: "amount earned using her cell phone = 50 * 36 = 1800 earned for remaining surveys = 50 * 30 = 1500 total earning = 3300 answer : e"
Answer: e
Problem: a man goes from a to b at a speed of 20 kmph and comes back to a at a speed of 30 kmph . find his average speed for the entire journey ?
Options: a ) 11 , b ) 24 , c ) 55 , d ) 66 , e ) 71
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 20 ) + ( d / 30 ) ] = ( 2 d ) / [ 5 d / 60 ) = > 24 kmph . answer : b"
Answer: b
Problem: find the maximum value of the function f ( x ) = x − 5 if x is a number between - 5 and 13 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) none
Rationale: solution : since f ( x ) is a linear function whose slope is 1 , a positive number , it is strictly increasing for all x . therefore its maximal value is reached for the largest value of x , x = 13 and f ( x ) = 13 - 5 = 8 . answer c
Answer: c
Problem: a shopkeeper sold 30 articles at the cost price of 35 articles . then find the profit % or lost %
Options: a ) 12 % , b ) 15 % , c ) 16.67 % , d ) 18 % , e ) 22 %
Rationale: "here 30 articles selling price = 35 articles cost price so the difference = 35 - 30 = 5 % of profit = 5 * 100 / 30 = 16.67 % correct option is c"
Answer: c
Problem: a cycle is bought for rs . 900 and sold for rs . 1140 , find the gain percent ?
Options: a ) 11 , b ) 27 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 240 100 - - - - ? = > 27 % answer : b"
Answer: b
Problem: the average of 5 quantities is 12 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 24 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 12 - 3 x 4 ) / 2 = 24"
Answer: a
Problem: a trained covered x km at 30 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22.5 , b ) 99 , c ) 24 , d ) 66 , e ) 887
Rationale: "total time taken = x / 30 + 2 x / 20 hours = 2 x / 15 hours average speed = 3 x / ( 2 x / 15 ) = 22.5 kmph answer : a"
Answer: a
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 28,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 124000 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 28,000 is made = 96,000 + 28,000 = rs . 1 , 24,000 answer : d"
Answer: d