regisss/math_qa huggingface dataset:
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 9 years investment will become $ 8,000 * 2 = $ 16,000 and in another 9 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ."
Answer: c
Problem: the average ( arithmetic mean ) of the even integers from 0 to 120 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 60 inclusive ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 60
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 120 is 120 / 2 = 60 the average of the even numbers from 0 to 60 is 60 / 2 = 30 the answer is d ."
Answer: d
Problem: a batsman scored 120 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 50 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 120 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 120 - 60 = 60 required % = ( 60 / 120 ) × 100 = 50 % answer : option b"
Answer: b
Problem: the average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years . find the average age of the women ?
Options: a ) 37 , b ) 26 , c ) 34 , d ) 18 , e ) 11
Rationale: explanation : 24 + 26 + 6 * 3 = 68 / 2 = 34 answer : c
Answer: c
Problem: | 9 - 4 | - | 12 - 14 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 9 - 4 | - | 12 - 14 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a"
Answer: a
Problem: a school has received 80 % of the amount it needs for a new building by receiving a donation of $ 600 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) 100 , c ) $ 105 , d ) $ 250 , e ) $ 300
Rationale: "let us suppose there are 100 people . 40 % of them donated $ 24000 ( 600 * 40 ) $ 24000 is 80 % of total amount . so total amount = 24000 * 100 / 80 remaining amount is 20 % of total amount . 20 % of total amount = 24000 * ( 100 / 80 ) * ( 20 / 100 ) = 6000 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 6000 / 60 = $ 100 answer : b"
Answer: b
Problem: if 4 ^ k = 5 , then 4 ^ ( 2 k + 2 ) =
Options: a ) 400 , b ) 540 , c ) 100 , d ) 830 , e ) 420
Rationale: "4 ^ k = 5 4 ^ 2 k = 5 ^ 2 4 ^ 2 k = 25 4 ^ ( 2 k + 2 ) = 4 ^ 2 k * 4 ^ 2 = 25 * 16 = 400 answer : a"
Answer: a
Problem: there are 16 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 306
Rationale: the total number of stations = 18 from 18 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 18 p ₂ ways . 18 p ₂ = 18 * 17 = 306 . answer : e
Answer: e
Problem: an auction house charges a commission of 15 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: say the price of the house was $ x , then 0.15 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 215,000 ( 15 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c
Answer: c
Problem: a man travelled for 13 hours . he covered the first half of the distance at 20 kmph and remaining half of the distance at 25 kmph . find the distance travelled by the man ?
Options: a ) 168 km , b ) 864 km , c ) 200 km , d ) 240 km , e ) 460 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 20 + ( x / 2 ) / 25 = 13 = > x / 40 + x / 50 = 13 = > ( 5 x + 4 x ) / 200 = 13 = > x = 200 km answer : c
Answer: c
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 4 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 3000
Rationale: sugar : flour = 5 : 4 = 25 : 20 ; flour : soda = 10 : 1 = 20 : 2 ; thus we have that sugar : flour : soda = 25 x : 20 x : 2 x . also given that 20 x / ( 2 x + 60 ) = 8 / 1 - - > x = 120 - - > sugar = 25 x = 3,000 answer : e .
Answer: e
Problem: a can do a work in 2 days . b can do the same work in 3 days . both a & b together will finish the work and they got $ 500 from that work . find their shares ?
Options: a ) 100,200 , b ) 400,100 , c ) 300,150 , d ) 300,200 , e ) 250,250
Rationale: "ratio of their works a : b = 2 : 3 ratio of their wages a : b = 3 : 2 a ' s share = ( 3 / 5 ) 500 = 300 b ' s share = ( 2 / 5 ) 500 = 200 correct option is d"
Answer: d
Problem: a fruit seller had some apples . he sells 40 % apples and still has 420 apples . originally , he had
Options: a ) 588 apples , b ) 600 apples , c ) 672 apples , d ) 700 apples , e ) none
Rationale: "solution suppose originally he had x apples . then , ( 100 - 40 ) % of x = 420 . ‹ = › 60 / 100 × x = 420 x ‹ = › ( 420 × 100 / 60 ‹ = › 700 . answer d"
Answer: d
Problem: the cost price of a radio is rs . 1890 and it was sold for rs . 1500 , find the loss % ?
Options: a ) 18 , b ) 20 , c ) 77 , d ) 66 , e ) 41
Rationale: "1890 - - - - 390 100 - - - - ? = > 20 % answer : b"
Answer: b
Problem: if the price of petrol increases by 44 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 44 ) i . e 144 . now , his consumption should be reduced to : - = ( 144 − 100 ) / 144 ∗ 100 . hence , the consumption should be reduced to 30.6 % . answer : e"
Answer: e
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) rs . 7000 , b ) rs . 9000 , c ) rs . 14000 , d ) rs . 17000 , e ) rs . 27000
Rationale: let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 30 x / 100 - 24 x / 100 = 840 = > 6 x / 100 = 840 = > x = 14000 . answer : c
Answer: c
Problem: what is 35 % of 4 / 13 of 715 ?
Options: a ) 44 , b ) 55 , c ) 66 , d ) 77 , e ) 88
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 715 , or 1 / 9 of 715 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 715 is about 720 , so ( 1 / 9 ) * 715 will be a bit less than 80 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 77 , so this is the answer to choose . the answer is d ."
Answer: d
Problem: 16 welders work at a constant rate they complete an order in 8 days . if after the first day , 9 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 4 , e ) 16
Rationale: "1 . we need to find out the time taken by 7 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 16 * 8 = 128 days 4 . but on day 1 sixteen workers had already worked finishing 1 / 8 of the job . so 7 workers have to finish only 7 / 8 of the job . 5 . total time taken by 7 workers can be got from formula used at ( 2 ) . i . e . , 7 * total time taken = 128 . total time taken by 7 workers to finish the complete job is 128 / 7 = 18.286 days . 6 . time taken by 7 workers to finish 7 / 8 of the job is 7 / 8 * 18.286 = 16 days . the answer is choice e"
Answer: e
Problem: if the radius of a circle is decreased by 50 % , find the percentage decrease in its area .
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 95 % , e ) none of them
Rationale: "let original radius = r . new radius = ( 50 / 100 ) r = ( r / 2 ) original area = 22 / 7 ( r ) 2 = and new area =  ( ( r / 2 ) ) 2 = (  ( r ) 2 ) / 4 decrease in area = ( ( 3 ( 22 / 7 ) ( r ) 2 ) / 4 x ( 1 / ( 22 / 7 ) ( r ) 2 ) x 100 ) % = 75 % answer is c ."
Answer: c
Problem: what is the least number of squares tiles required to pave the floor of a room 8 m 82 cm long and 2 m 52 cm broad ?
Options: a ) 14 , b ) 20 , c ) 40 , d ) 44 , e ) 48
Rationale: "length of largest tile = h . c . f . of 882 cm and 252 cm = 126 cm . area of each tile = ( 126 x 126 ) cm 2 . required number of tiles = 882 x 252 / ( 126 ^ 2 ) = 14 . answer : a"
Answer: a
Problem: a coin is tossed 8 times . what is the probability of getting exactly 7 heads ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Rationale: "the number of possible outcomes is 2 ^ 8 = 256 there are 8 ways to get exactly 7 heads . p ( exactly 7 heads ) = 8 / 256 = 1 / 32 the answer is c ."
Answer: c
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 30 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 105 , b ) 45 , c ) 85 , d ) 95 , e ) 90.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 30 % , therefore bringing down the price to $ 52.5 . 4 ) now 52.5 has to be added byx % in order to equal the original price . 52.5 + ( x % ) 52.5 = 100 . solving this eq for x , we get x = 90.5 ans is e"
Answer: e
Problem: tough and tricky questions : word problems . mike , sarah and david decided to club together to buy a present . each of them gave equal amount of money . luckily sarah negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: answer c . we know that sarah negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before sarah negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 .
Answer: c
Problem: if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 356,580 , b ) 358,680 , c ) 360,780 , d ) 362,880 , e ) 364,980
Rationale: "9 ! = 362,880 the answer is d ."
Answer: d
Problem: 8 ^ 100 is divisible by 17 . find the remainder ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Problem: in a competitive examination in a state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 8000 , b ) 7540 , c ) 6500 , d ) 9100 , e ) 6000
Rationale: let the number of candidates appeared be x then , 7 % of x - 6 % of x = 80 1 % of x = 80 x = 80 * 100 = 8000 answer is a
Answer: a
Problem: how many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
Options: a ) 13 , b ) 25 , c ) 87 , d ) 49 , e ) 63
Rationale: explanation : required numbers are 24 , 30 , 36 , 42 , . . . , 96 this is an a . p . in which a = 24 , d = 6 and l = 96 let the number of terms in it be n . then tn = 96 a + ( n - 1 ) d = 96 24 + ( n - 1 ) x 6 = 96 ( n - 1 ) x 6 = 72 ( n - 1 ) = 12 n = 13 required number of numbers = 13 . a )
Answer: a
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 9 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 8
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 3 / 4 * 4 / 9 x = 1 / 3 x % loaded by day crew = x / ( x + 1 / 3 x ) = 3 / 4 answer c"
Answer: c
Problem: a bowl was filled with 10 ounces of water , and 0.0008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 %
Rationale: total amount of water evaporated each day during a 50 - day period = . 0008 * 50 = . 0008 * 100 / 2 = . 08 / 2 = . 04 percent of the original amount of water evaporated during this period = ( . 04 / 10 ) * 100 % = 0.4 % answer c
Answer: c
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 5 ¤ √ 5 =
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "x = √ 5 and y also = √ 5 applying the function ( √ 5 + √ 5 ) ^ 2 - ( √ 5 - √ 5 ) ^ 2 = ( 2 √ 5 ) ^ 2 - 0 = 4 x 5 = 20 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 5 and y = √ 5 you get the answer 20 answer is e ."
Answer: e
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 16 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 27 , e ) d ) 36
Rationale: lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 16 = 27 . . d
Answer: d
Problem: which number should replace both the asterisks in ( * / 20 ) x ( * / 180 ) = 1 ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 90 , e ) 120
Rationale: "let ( y / 20 ) x ( y / 180 ) = 1 y ^ 2 = 20 x 180 = 20 x 20 x 9 y = ( 20 x 3 ) = 60 the answer is c ."
Answer: c
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 18 kmph ?
Options: a ) 80 sec , b ) 20 sec , c ) 40 sec , d ) 50 sec , e ) 60 sec
Rationale: "d = 100 + 150 = 250 s = 18 * 5 / 18 = 5 mps t = 250 / 5 = 50 sec d ) 50 sec"
Answer: d
Problem: what is the sum of all even numbers from 1 to 701 ?
Options: a ) 122821 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 700 / 2 = 350 350 * 351 = 122850 answer : d"
Answer: d
Problem: two numbers have a h . c . f of 11 and a product of two numbers is 1991 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 181 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 1991 / 11 = 181 . answer : b"
Answer: b
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 15 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.85 , b ) 69.85 , c ) 62.85 , d ) 82.85 , e ) 60.85
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 85 / 100 ) = 59.375 mp = 69.85 b"
Answer: b
Problem: 16.02 × 0.001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 × 0.001 = ? or , ? = 0.01602 answer d"
Answer: d
Problem: find the numbers which are in the ratio 3 : 2 : 3 such that the sum of the first and the second added to the difference of the third and the second is 24 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 18 , 12,18
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 3 given , ( a + b ) + ( c - b ) = 24 = > a + c = 24 = > 3 x + 3 x = 24 = > x = 6 a , b , c are 3 x , 2 x , 3 x a , b , c are 18 , 12 , 18 . answer : e"
Answer: e
Problem: in one hour , a boat goes 13 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 9 , d ) 12 , e ) 15
Rationale: "sol . speed in still water = 1 / 2 ( 13 + 5 ) kmph = 9 kmph . answer c"
Answer: c
Problem: a library has an average of 510 visitors on sundays and 240 on other days . what is the average number of visitors per day in a month of 30 days beginning with a sunday ?
Options: a ) 290 , b ) 304 , c ) 285 , d ) 270 , e ) 275
Rationale: "in a month of 30 days beginning with a sunday , there will be 4 complete weeks and another two days which will be sunday and monday . hence there will be 5 sundays and 25 other days in a month of 30 days beginning with a sunday average visitors on sundays = 510 total visitors of 5 sundays = 510 × 5 average visitors on other days = 240 total visitors of other 25 days = 240 × 25 total visitors = ( 510 × 5 ) + ( 240 × 25 ) total days = 30 average number of visitors per day = ( ( 510 × 5 ) + ( 240 × 25 ) ) / 30 = ( ( 51 × 5 ) + ( 24 × 25 ) ) / 3 = ( 17 × 5 ) + ( 8 × 25 ) = 85 + 200 = 285 answer is c ."
Answer: c
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 231 games will be played during the tournament . what is the number of participants ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 231 n * ( n - 1 ) = 462 = 22 * 21 ( trial and error ) the answer is d ."
Answer: d
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 15400 . how many times did he participate in the competition ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "15400 = 2 * 2 * 2 * 5 * 5 * 7 * 11 john participated 7 times . the answer is c ."
Answer: c
Problem: the owner of a furniture shop charges his customer 30 % more than the cost price . if a customer paid rs . 8450 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5725 , b ) rs . 5275 , c ) rs . 6275 , d ) rs . 6500 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8450 ( 100 / 130 ) = rs . 6500 . answer : d"
Answer: d
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 6 cups of tea . last week mo drank a total of 22 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 22 t - c = 14 - > t = 18 . c = 2 . mo drinks 6 cups of tea a day then number of days that are not rainy = 18 / 6 = 3 so number of rainy days = 7 - 3 = 4 c is the answer ."
Answer: c
Problem: find the value of 85 p 3 .
Options: a ) 565350 , b ) 595650 , c ) 535950 , d ) 565350 , e ) 575350
Rationale: "85 p 3 = 85 ! / ( 85 - 3 ) ! = 85 ! / 82 ! = 85 * 84 * 83 * 82 ! / 82 ! = 85 * 84 * 83 = 595650 answer : b"
Answer: b
Problem: a certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 12,000 , e ) e ) 11,100
Rationale: let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 142 k x = 12,000 answer : d
Answer: d
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 171 grams of water ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( 2 / 18 ) * 171 = 19 grams the answer is e ."
Answer: e
Problem: two whole numbers whose sum is 42 can not be in the ratio
Options: a ) 2 : 5 , b ) 1 : 6 , c ) 2 : 4 , d ) 3 : 8 , e ) 2 : 40
Rationale: d ) 3 : 8
Answer: d
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 24
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 24 days to doing 4 w widgets . answer : e"
Answer: e
Problem: the average of first 32 natural numbers is ?
Options: a ) 16.5 , b ) 17.5 , c ) 18.4 , d ) 15.4 , e ) 15.1
Rationale: "sum of 32 natural no . = 1056 / 2 = 55 average = 528 / 32 = 16.5 answer : a"
Answer: a
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 4680 , what will be a ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 2080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 4680 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 4680 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 4680 / 9 = 2080 . correct choice is ( c )"
Answer: c
Problem: by selling an article at rs . 600 , a profit of 25 % is made . find its cost price ?
Options: a ) 322 , b ) 480 , c ) 287 , d ) 192 , e ) 107
Rationale: "explanation : sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 25 ) ] = 600 * [ 100 / 125 ] = rs . 480 answer : b"
Answer: b
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1200 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 1080 , d ) 900 , e ) 1000
Rationale: let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1200 , loss of pyarelal = 1200 * 9 x / 10 x = 1080 answer : c
Answer: c
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 20 m wide at the top and 12 m wide at the bottom and the area of cross - section is 800 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 50 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 20 + 12 ) = 800 d = 50 answer : b"
Answer: b
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 95 per day . what was his wage on the 8 th day ?
Options: a ) $ 76 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 95 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 95 * 7 ) = 1350 - ( 609 + 665 ) = 1350 - 1274 = 76 answer a
Answer: a
Problem: what is the rate percent when the simple interest on rs . 1500 amount to rs . 250 in 5 years ?
Options: a ) 3.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %
Rationale: "interest for 5 yrs = 250 interest for 1 yr = 50 interest rate = 50 / 1500 x 100 = 3.33 % answer : a"
Answer: a
Problem: nd the area of trapezium whose parallel sides are 20 cm and 15 cm long , and the distance between them is 14 cm ?
Options: a ) 230 cm 2 , b ) 245 cm 2 , c ) 255 cm 2 , d ) 260 cm 2 , e ) 280 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 15 ) * ( 14 ) = 245 cm 2 answer : b"
Answer: b
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 7 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 17 / 140 , b ) 29 / 180 , c ) 26 / 143 , d ) 1 / 5 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 7 * 2 = 14 hours ; in 1 hour 15 journeymen can finish 1 / 14 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 14 = 17 / 140 of the job . answer : a"
Answer: a
Problem: a sum of money lent out at s . i . amounts to a total of $ 420 after 2 years and to $ 595 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 310 , b ) $ 320 , c ) $ 330 , d ) $ 340 , e ) $ 350
Rationale: "s . i for 5 years = $ 595 - $ 420 = $ 175 the s . i . is $ 35 / year s . i . for 2 years = $ 70 principal = $ 420 - $ 70 = $ 350 the answer is e ."
Answer: e
Problem: donovan and michael are racing around a circular 300 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 6 , b ) 9 , c ) 8 , d ) 7 , e ) 10
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 300 / 45 = > 60 / 9 2 . speed / rate of michael = distance / time = > 300 / 40 = > 30 / 4 relative speed between them = 30 / 4 - 60 / 9 = > 270 - 240 / 36 = 30 / 36 = 5 / 6 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 300 , relative rate = 5 / 6 total time taken by micheal to surpass donovan = distance / rate = > 300 * 6 / 5 = > 1800 / 5 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . b"
Answer: b
Problem: the average age of a group of persons going for picnic is years . fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is
Options: a ) 5 , b ) 10 , c ) 15 , d ) 40 , e ) 50
Rationale: solution let the initial number of persons be x . then 16 x + 15 x 15 = 15.5 ( x + 20 ) = 0.5 x = 7.5 x = 15 . answer c
Answer: c
Problem: the average of 10 numbers was calculated as 19 . it is discovered later on that while calculating the average , one number , namely 76 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "10 * 19 - 26 + 76 = 240 240 / 10 = 24 the answer is d ."
Answer: d
Problem: anand and deepak started a business investing rs . 22,500 and rs . 35,000 respectively . out of a total profit of rs . 13,800 , deepak ’ s share is _____
Options: a ) 5400 , b ) 3797 , c ) 27877 , d ) 2772 , e ) 9911
Rationale: explanation : ratio of their investments = 22500 : 35000 = 9 : 14 so deepak ' s share = 923923 × 13800 = rs . 5,400 answer : a
Answer: a
Problem: of the 3,600 employees of company x , 3 / 4 are clerical . if the clerical staff were to be reduced by 4 / 5 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 37 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 3 / 4 are clerical out of 3600 so 2700 are clerical 2700 reduced by 4 / 5 is 2700 * 4 / 5 so it reduced 2160 people , so there is 540 clerical people left but since 2160 people left , it also reduced from the total of 3600 so there are 1440 people total since 540 clerical left / 1440 people total you get ( a ) 37 %"
Answer: a
Problem: the sum of the squares of three numbers is 41 , while the sum of their products taken two at a time is 20 . their sum is :
Options: a ) 10 , b ) 5 , c ) 9 , d ) 15 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 138 xy + yz + zx = 131 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 41 + ( 2 * 20 ) ( x + y + z ) ^ 2 = 81 so x + y + z = 9 answer : c"
Answer: c
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?
Options: a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780
Rationale: let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d .
Answer: d
Problem: a cyclist rides a bicycle 9 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.5 , b ) 9.8 , c ) 10.1 , d ) 10.6 , e ) 11.2
Rationale: "distance = 21 km time = 9 / 12 + 12 / 9 = ( 81 + 144 ) / 108 = 225 / 108 = 25 / 12 hours average speed = ( 21 * 12 ) / 25 = 10.1 km / h the answer is c ."
Answer: c
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 173 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 195.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 173 / 22.50 = 1 = â € º x - 173 = 22.50 = â € º x = 195.50 . hence , price of the third variety = rs . 195.50 per kg . answer c"
Answer: c
Problem: 110 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 165
Rationale: "final number = initial number + 50 % ( original number ) = 110 + 50 % ( 110 ) = 110 + 55 = 165 . answer e"
Answer: e
Problem: in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 24 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 24 / 8 = 6 ans b"
Answer: b
Problem: a textile manufacturing firm employees 50 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 50 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 − ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 × ( 49 / 50 ) − 150000 × ( 49 / 50 ) − 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 − 2 , 68,000 = > rs . 7,000 . answer : b"
Answer: b
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 4 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1815
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 4 x + 15 3 x = 1350 x = 450 large number = 450 + 1365 = 1815 e"
Answer: e
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 216 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 6
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 216 per week 36 x = 216 x = 6 correct option : e"
Answer: e
Problem: by selling 15 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 2.15 , b ) 4.2 , c ) 5.18 , d ) 3.75 , e ) 4.2
Rationale: "40 % - - - 15 160 % - - - ? 40 / 160 * 15 = 3.75 answer : d"
Answer: d
Problem: find the area of a cuboid of length 10 cm , breadth 8 cm . and height 6 cm .
Options: a ) 400 cm cube , b ) 410 cm cube , c ) 420 cm cube , d ) 430 cm cube , e ) 480 cm cube
Rationale: "area of a cuboid = lxbxh = 10 cm x 8 cm x 6 cm = 480 cm cube answer : e"
Answer: e
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 8 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 87.8 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 8 % of 400 = 8 / 100 × 400 = 3200 / 100 = 32 therefore , total number of rotten fruits = 90 + 32 = 122 therefore number of fruits in good condition = 1000 - 122 = 878 therefore percentage of fruits in good condition = ( 878 / 1000 × 100 ) % = ( 87800 / 1000 ) % = 87.8 % answer : b"
Answer: b
Problem: in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate
Options: a ) 356000 , b ) 356500 , c ) 357000 , d ) 400000 , e ) none of these
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 c )"
Answer: c
Problem: of 30 applicants for a job , 12 had at least 4 years ' experience , 19 had degrees , and 6 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 = 30 - 6 = 24 aub = a + b - aib aib = 19 + 12 - 24 = 7 answer d"
Answer: d
Problem: the circumferences of two circles are 264 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29960 sq m , b ) 33880 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 12786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 704 s = 264 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 132 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 132 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 132 - 352 ) ( 132 + 352 ) / ∏ = ( 220 ) ( 484 ) / ( 22 / 7 ) = 33880 sq m answer : b"
Answer: b
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.25 km and 1.00 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 67 , e ) 54
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.25 + 1.0 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : e"
Answer: e
Problem: a reduction of 25 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 2.5 , d ) 3.3 , e ) 2.9
Rationale: "100 * ( 25 / 100 ) = 25 - - - 10 ? - - - 1 = > rs . 2.5 100 - - - 75 ? - - - 2.5 = > rs . 3.3 answer : d"
Answer: d
Problem: if 15 % of 30 % of 50 % of a number is 90 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 4000 . answer : a"
Answer: a
Problem: a certain box has 9 cards and each card has one of the integers from 1 to 9 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 9 cards ?
Options: a ) 1 / 36 , b ) 1 / 15 , c ) 1 / 18 , d ) 1 / 9 , e ) 2 / 9
Rationale: "the average of the numbers is 5 . the total number of ways to choose 2 cards from 9 cards is 9 c 2 = 36 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 36 = 1 / 18 the answer is c ."
Answer: c
Problem: what is the 6 th digit to the right of the decimal point in the decimal equivalent of 16 / 45 ?
Options: a ) 5 , b ) 12 , c ) 2 , d ) 35 , e ) 4
Rationale: "16 / 45 = 0.3555 . . . . 35 is non - terminating repeating decimal . the 22 nd digit to the right of decimal point will be 5 . answer a"
Answer: a
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 13600 after a year ?
Options: a ) 3630 , b ) 9232 , c ) 8828 , d ) 2387 , e ) 4080
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13600 = 4080 answer : e"
Answer: e
Problem: two trains 120 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.07 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 120 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.07 answer : c"
Answer: c
Problem: the average weight of 4 pigs is 15 kg . weight less than 16 kg is considered as under weight . what maximum no . of pig can be under weight .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: sum of all four pigs weigh = 60 kg it is possible that all four pigs are underweight . because the average is 15 kg which itself underweight . answer e
Answer: e
Problem: a can do a job in 30 days and b in 40 days . if they work on it together for 10 days , then the fraction of the work that is left is ?
Options: a ) 2 / 11 , b ) 3 / 13 , c ) 5 / 12 , d ) 7 / 10 , e ) 6 / 15
Rationale: "a ' s 1 day work = 1 / 30 b ' s 1 day work = 1 / 40 a + b 1 day work = 1 / 30 + 1 / 40 = 7 / 120 a + b 4 days work = 7 / 120 * 10 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is c"
Answer: c
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 15 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 204 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 emlpoyee paid = . 85 * 240 = 204 $ answer a"
Answer: a
Problem: the compound ratio of 1 : 4 , 2 : 5 and 1 : 6 ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 10 , d ) 1 : 30 , e ) 1 : 60
Rationale: 1 / 4 * 2 / 5 * 1 / 6 = 1 / 60 1 : 60 answer : e
Answer: e
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 } = 189 or x = 1575 . ∴ p . w . = rs . 1575 . answer b"
Answer: b
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 35 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 25
Rationale: 12 * 35 = 420 420 % 21 = 20 answer : d
Answer: d
Problem: tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?
Options: a ) 3 / 10 , b ) 1 / 2 , c ) 2 / 5 , d ) 3 / 7 , e ) 1 / 6
Rationale: "here , s = { 1 , 2,3 , . . . . . . , 19,20 } e = event getting a multiple of 3 = { 3,6 , 9,12 , 15,18 } probability = 6 / 20 = 3 / 10 correct option is a"
Answer: a
Problem: the sum of the digits of [ ( 10 ^ x ) ^ y ] - 64 = 279 . what is the value of xy ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: 1000 − 64 = 936 . whatever xy is you finish with 36 = = > 3 + 6 = 9 therefore , 279 − 9 = 270 and 270 / 9 = 30 now you add the last two digits ( 3 and 6 ) answer is 30 + 2 = 32 answer : e
Answer: e
Problem: a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 43 %
Rationale: "initial ratio of federal taxes to gross profits : 7 / 50 = 0.14 final ratio : 30 / 150 = 0.2 thus , the percentage change : ( 0.2 - 0.14 ) / 0.14 * 100 = 6 / 14 * 100 = 3 / 7 * 100 = just less than 50 % . answer : e"
Answer: e
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 42 / 55 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / ( 11 / 2 ) = 84 / 11 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 11 ) / 10 = 84 / 110 = 42 / 55 answer d"
Answer: d
Problem: two trains a and b are 100 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 100 + 150 = 250 m . time taken = 250 / 25 = 10 s . correct answer b ."
Answer: b
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 5,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 7,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 5,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 5,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 400 = 0.10 x combine terms and subtract 0.08 x from both sides : 150 = 0.02 x divide both sides by 0.02 : 7,500 = x your answer is a ."
Answer: a
Problem: 15 % people of a village in sri lanka died by bombardment , 25 % of the remainder left the village on account of fear . if now the population is reduced to 4555 , how much was it in the beginning ?
Options: a ) 7400 , b ) 7145 , c ) 7200 , d ) 7323 , e ) 6030
Rationale: "x * ( 85 / 100 ) * ( 75 / 100 ) = 4555 x = 7145 answer : b"
Answer: b