regisss/math_qa huggingface dataset:
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 2 ) , which indeed is 2 / 45 . c"
Answer: c
Problem: there are 2 friends peter and paul . peter age is twice as old as paul when peter was as old as paul is now . sum of the present ages of peter and paul is 35 . what is the present age of peter ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: let pauls age be ' a ' and peters be ' e ' e + a = 35 ( given ) e = 35 - a - - - - - - eq 1 when peter was as old as paul that is when peter ' s age was ' a ' pauls age was a - ( e - a ) = 2 a - e now peters age is e = 2 ( 2 a - e ) e = 4 a - 2 e 3 e = 4 a 3 ( 35 - a ) = 4 a 105 - 3 a = 4 a a = 15 hence e = 20 answer : c
Answer: c
Problem: the area of a parallelogram is 162 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 62 , e ) 2
Rationale: "2 x * x = 162 = > x = 9 answer : b"
Answer: b
Problem: 34 . the side surface of a cylinder is rolled with a rectangular plate . if the height of a cylinder tank is 10 feet and the perimeter of the circular base is 4 feet , what is the area of the rectangular plate ?
Options: a ) 24 , b ) 34 , c ) 28 , d ) 40 , e ) 14
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both you can multiply them together to find the area , 40 . ( correct answer d )
Answer: d
Problem: 8 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 4543 , c ) 4400 , d ) 2871 , e ) 881
Rationale: "x * ( 92 / 100 ) * ( 85 / 100 ) = 3553 x = 4543 answer : b"
Answer: b
Problem: 57 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 19
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 57 x 12 x 5 = 30 x 6 x x x = 19 hence , the number of days = 19 . answer : e"
Answer: e
Problem: how many plants will be there in a circular bed whose outer edge measure 30 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 30 cm area of circular bed = ( 30 ) 2 ⁄ 4 π space for each plant = 4 cm 2 ∴ required number of plants = ( 30 ) 2 ⁄ 4 π ÷ 4 = 17.89 = 18 ( approx ) answer a"
Answer: a
Problem: the product z of two prime numbers is between 20 and 60 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 18 but less than 36 then what is z ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 51 , e ) 57
Rationale: "the smallest possible product is 57 which is 3 * 19 . all other products are too big . the answer is e ."
Answer: e
Problem: a boat goes 100 km downstream in 10 hours , and 60 m upstream in 15 hours . the speed of the stream is ?
Options: a ) 3 , b ) 22 1 / 4 , c ) 22 1 / 2 , d ) 22 1 / 1 , e ) 22 1 / 3
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 60 - - - - 15 us = 4 ? - - - - - 1 s = ( 10 - 4 ) / 2 = 3 kmp answer : a"
Answer: a
Problem: in how many ways can 16 different gifts be divided among 4 children such that each child receives exactly two gifts ?
Options: a ) 16 ^ 4 , b ) ( 4 ! ) ^ 4 , c ) 16 ! / ( 2 ! ) ^ 4 , d ) 16 ! / 2 ! , e ) 4 ^ 16
Rationale: total 16 different gifts , and 4 children . thus any one child gets 16 c 2 gifts , then the other child gets 14 c 2 gifts ( 16 total - 2 already given ) , then the third one gets 12 c 2 gifts , and the last child gets 10 c 2 gifts . since order in which each child gets the gift is not imp , thus , ans : 16 c 2 * 14 c 2 * 12 c 2 * 10 c 2 = 16 ! / ( 2 ! ) ^ 4 c
Answer: c
Problem: how many different values of positive integer x , for which | x + 4 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: answer d i opted to put the random value option . i used 0 , 4 , - 4 and the the extreme of 60 and - 60 . . i was able to solve it in 1 : 09 d
Answer: d
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 15 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: "39 = 15 + 18 + 12 - 4 - 2 x 2 x = 15 + 18 + 12 - 4 - 39 = 41 - 39 = 2 x = 1 e"
Answer: e
Problem: the edges of a cuboid are 2 cm , 5 cm and 3 cm . find the volume of the cuboid ?
Options: a ) 20
b ) 60
c ) 80
d ) 30
e ) 45
Rationale: 2 * 5 * 3 = 30 answer : d
Answer: d
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 60 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 172 , d ) $ 138 , e ) $ 192
Rationale: "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 60 + 150 * 2 . = 16500 + 9000 + 300 = p = $ 172 . c"
Answer: c
Problem: a beaker contains 180 liters of alcohol . on 1 st day , 60 l of alcohol is taken out and replaced by water . 2 nd day , 60 l of mixture iss taken out and replaced by water and the process continues day after day . what will be the quantity of alcohol in beaker after 3 days
Options: a ) 53.3 , b ) 53.8 , c ) 53.7 , d ) 53.5 , e ) 353.3
Rationale: use the formula , final alcohol = initial alcohol × ( 1 − replacementquantityfinalvolume ) n × ( 1 − replacementquantityfinalvolume ) n final alcohol = 180 ( 1 − 60180 ) 3180 ( 1 − 60180 ) 3 = 180 × ( 23 ) 3 = 53.3 ans : a
Answer: a
Problem: how many two - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 answer : 3 such 2 digit number . answer : d
Answer: d
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 110 + 150 = 260 m s = 60 * 5 / 18 = 50 / 3 t = 260 * 3 / 50 = 15.6 sec answer : d"
Answer: d
Problem: a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph
Rationale: avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 7 ; avg speed = 150 / ( 10 / 3 + 5 / 7 ) = 37 kmph answer : e
Answer: e
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 75 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 687 . , e ) 666 .
Rationale: "answer is d : 687 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 75 % of total is 515 , so 100 % is approx . 687 ."
Answer: d
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 77 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 550 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 77 , so 0.14 * { total } = 77 - - > { total } = 550 . answer : a ."
Answer: a
Problem: if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 1 ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 1 = x 2 ( x - 2 ) 2 + 1 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 1 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 1 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 1 = ( 2 - 1 ) 2 = 1 + 1 = 2 correct option : d"
Answer: d
Problem: vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?
Options: a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432
Rationale: vlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a .
Answer: a
Problem: how many odd integers from 1 to 100 ( both inclusive ) have odd number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1 , 9,25 , 49,81 and the corresponding integers are 1 , 3,5 , 7,9 ( more than 4 ) . thus c is the correct answer .
Answer: c
Problem: how many litres of pure acid are there in 10 litres of a 25 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 2.5 , d ) 1.8 , e ) 1.9
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 10 * 25 / 100 = 2.5 answer : option c
Answer: c
Problem: there are 15 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 105 , b ) 110 , c ) 115 , d ) 120 , e ) 125
Rationale: "15 c 2 = 105 the answer is a ."
Answer: a
Problem: rahim bought 65 books for rs . 6500 from one shop and 35 books for rs . 2000 from another . what is the average price he paid per book ?
Options: a ) 80 , b ) 138 , c ) 100 , d ) 129 , e ) 85
Rationale: "average price per book = ( 6500 + 2000 ) / ( 65 + 35 ) = 8500 / 100 = rs . 85 answer : e"
Answer: e
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 13 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 10 k waiters . 13 k = 10 k + 12 k = 4 there are 12 cooks . the answer is d ."
Answer: d
Problem: a man engaged a servant on the condition that he would pay him rs . 800 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?
Options: a ) s . 800 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 800 = 600 400 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : a"
Answer: a
Problem: a customer purchased a package of ground beef at a cost of $ 1.96 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 30 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 4.65 , b ) $ 4.10 , c ) $ 3.60 , d ) $ 3.20 , e ) $ 2.80
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.96 . let x be the price per pound for the steak . then 0.7 x = 196 x = 196 / 0.7 = $ 2.80 the answer is e ."
Answer: e
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 7 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 197
Rationale: "by the question , the equation would be 150 p - 87 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 197 . answer e for me ."
Answer: e
Problem: what is the sum of the greatest common factor and the lowest common multiple of 24 and 36 ?
Options: a ) 92 , b ) 84 , c ) 24 , d ) 60 , e ) 184
Rationale: "prime factorization of 24 = 2 x 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 72 sum = 84 answer b ."
Answer: b
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 5 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 325 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 65 + 65 + 65 + 65 + 65 = 5 × 65 = 325 miles correct answer is c ) 325 miles"
Answer: c
Problem: in a race where 12 cars are running , the chance that car x will win is 1 / 6 , that y will win is 1 / 10 and that z will win is 1 / 8 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 27 / 410 , d ) 47 / 120 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 6 + 1 / 10 + 1 / 8 = 47 / 120 answer : d"
Answer: d
Problem: in a box of 12 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that both pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 3 defective in a lot of 12 pens i . e . probability of first pen being defective = ( 1 / 3 ) i . e . probability of second pen being defective = ( 1 / 2 ) probability of both pen being defective = ( 1 / 2 ) * ( 1 / 3 ) = 1 / 6 answer : option a"
Answer: a
Problem: the timing of a college is from 12 p . m to 4.20 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 260 – 20 ) / 5 = 48 minutes answer d
Answer: d
Problem: after decreasing 50 % in the price of an article costs rs . 1200 . find the actual cost of an article ?
Options: a ) 1200 , b ) 50 , c ) 2400 , d ) 100 , e ) 600
Rationale: "cp * ( 50 / 100 ) = 1200 cp = 24 * 100 = > cp = 2400 answer : c"
Answer: c
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 30 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 112 % , b ) b . 100 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a"
Answer: a
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 30
Rationale: we have 3 places ( - - - ) to fill & we can use only digits 2 , 4 , 5 first place can be filled in 3 ways 2 nd place can be filled in 3 ways because we can repeat the digits 3 rd place can be filled in 3 ways because we can repeat the digits total no of codes = 3 x 3 x 3 = 27 but one combination ( 555 ) will not be even so total no of even codes = 27 - 1 = 26 answer d
Answer: d
Problem: which no . need to add to 859622 to get a number exactly divisible by 456 ?
Options: a ) 345652 , b ) 547678 , c ) 356789 , d ) 778990 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Problem: a 250 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 1266 , d ) 75 , e ) 211
Rationale: "s = 250 / 12 * 18 / 5 = 75 kmph answer : d"
Answer: d
Problem: in what time will a train 120 m long cross an electric pole , it its speed be 185 km / hr ?
Options: a ) 2.3 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 185 * 5 / 18 = 51 m / sec time taken = 120 / 51 = 2.3 sec . answer : a"
Answer: a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 750 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 33 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "750 - - - 250 100 - - - ? = > 33.33 % answer : b"
Answer: b
Problem: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 4 : 5 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 4 : 5"
Answer: c
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent e should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked e will be 25 % greater than the original number . the answer is c ."
Answer: c
Problem: the side of a cube is 8 m , find the voiume ?
Options: a ) 515 , b ) 509 , c ) 502 , d ) 508 , e ) 512
Rationale: "cube volume = a ( power ) 3 a ( power ) 3 = 8 ( power ) 3 = 512 m ( power ) 3 . answer is e ."
Answer: e
Problem: a rectangle has 20 meter length and 15 meter breadth . find ratio between area of rectangle and square whose side is same with rectangle ' s length .
Options: a ) 3 : 2
b ) 3 : 4
c ) 4 : 5
d ) 2 : 3
e ) 2 : 5
Rationale: area of rectangle = 20 * 15 = 300 area of square = 20 ^ 2 = 400 ratio of rectangle ' area and square ' s area = 300 : 400 = 3 : 4 answer : b
Answer: b
Problem: a number when divided by 221 gives a remainder 43 , what remainder will be obtained by dividing the same number 17 ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 5 , e ) 20
Rationale: 221 + 43 = 264 / 17 = 9 answer a
Answer: a
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 8 % of the money for taxi fare and buys 20 mangoes . how many oranges can he buy ?
Options: a ) 21 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 8 % of 200 = 16 for taxi fare , so he is left with 184 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 84 ( 184 - 100 ) no of oranges he can buy = 84 / 4 = > 21 so , george can buy 21 oranges . a"
Answer: a
Problem: a sum of 14,400 amounts to 16,600 in 3 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 5 % , e ) 8 %
Rationale: "d 5 % s . i . = ( 16600 - 14400 ) = 2200 . rate = ( 100 x 2200 ) / ( 14400 x 3 ) % = 5 %"
Answer: d
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 66 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 30 . answer : b .
Answer: b
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 168 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 168,000 m : c is the circumference c = 3 meters correct answer a"
Answer: a
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 7 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 7 total people can seat = 81 + 7 = 88 answer : d"
Answer: d
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 3
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 2 ( 1 - x ) p 12 xp = 2 p - 2 xp 14 xp = 2 p x = 1 / 7 the answer is a ."
Answer: a
Problem: what is the sum of all remainders obtained when the first 120 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 405 . answer : d ."
Answer: d
Problem: if a certain number of labours can dig earth 100 m deep , 25 m long , and 30 m broad in 12 days , then find the number of days the same number of labours will require to dig earth 75 m deep , 20 m long and 50 m broad .
Options: a ) 12 , b ) 18 , c ) 6 , d ) 1 , e ) 2
Rationale: explanation : more number of days means more length , more depth and more width . hence , its a direct proportion . ( 100 * 25 * 30 ) : ( 75 * 20 * 50 ) : : 12 : x 75000 : 75000 : : 12 : x x = 12 answer : a
Answer: a
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 27.3 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) 34 % , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 27.3 ) / ( 100 â ˆ ’ 5 ) = 100 ã — 127.3 / 95 = 134 hence , required % profit = 134 â € “ 100 = 34 % answer d"
Answer: d
Problem: in town x , 64 percent of the population are employed , and 45 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 45 % , c ) 32 % , d ) 40 % , e ) 28 %
Rationale: "answer b male - employed - 64 % female - employed - 19 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 19 / 64 = 28 e"
Answer: e
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40,000 , the amount invested by y is
Options: a ) 33488 , b ) 63809 , c ) 60000 , d ) 37887 , e ) 77824
Rationale: "explanation : suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c ) 60000"
Answer: c
Problem: 135 kg of an alloy a is mixed with 145 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 5 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 142 kg , c ) 135 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 135 kg of a = 135 * 5 / 8 = 84 kg quantity of tin in 145 kg of b = 145 * 2 / 5 = 58 kg quantity of tin in the new alloy = 84 + 58 = 142 kg answer is b"
Answer: b
Problem: a sum of money lent out at s . i . amounts to a total of $ 520 after 2 years and to $ 820 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 340 , b ) $ 360 , c ) $ 380 , d ) $ 400 , e ) $ 420
Rationale: "s . i for 5 years = $ 820 - $ 520 = $ 300 the s . i . is $ 60 / year s . i . for 2 years = $ 120 principal = $ 520 - $ 120 = $ 400 the answer is d ."
Answer: d
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 61 ⁄ 4 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 6 1 ⁄ 4 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 254 × 21 / 00 = 625 his overall gain in 2 years = rs . 625 - rs . 400 = rs . 225 his overall gain in 1 year = 2252 = rs . 112.5 answer : option d"
Answer: d
Problem: a small water pump would take 4 hours to fill an empty tank . a larger pump would take 1 / 2 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 1 / 6 , b ) 4 / 9 , c ) 1 / 4 , d ) 5 / 9 , e ) 1 / 3
Rationale: "rate of the small pump is 1 / 4 tank / hour rate of the larger pump is 1 / ( 1 / 2 ) or 2 tank / hour ; combined rate of the two pumps is 1 / 4 + 2 = 9 / 4 tank / hour , together they will fill the empty tank in 1 / ( 9 / 4 ) ) = 4 / 9 hours ( time = job / rate ) . answer : b"
Answer: b
Problem: a man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 / 2 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 9 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 9 , d = 9 b - 9 c ; every 3 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 3 , d = 3 b + 3 c ; d = 9 b - 9 c = 3 b + 3 c , - - > b = 2 c , - - > d = 9 b - 9 b / 2 = 9 b / 2 . interval = \ frac { d } { b } = \ frac { 9 / 2 b } { b } = 9 / 2 answer : d ( 9 / 2 minutes ) ."
Answer: d
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 2 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 6 hours , b ) 8 hours , c ) 9 hours , d ) 10 hours , e ) 12 hours
Rationale: "explanation : solution 1 the pump can fill the tank in 2 hour . but , because of the leak , it took 2 2 / 3 hours to fill the tank . i . e . , the additional water filled by the pump in 2 / 3 hour is emptied by the leak in 2 2 / 3 = 8 / 3 hours . therefore , the water filled by pump in 2 bour can be emptied by the leak in 8 / 3 x 3 = 8 hours . i . e . , the leak can drain all the water of the tank in 8 hours . answer is b"
Answer: b
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of the above
Rationale: "speed = ( 72 x ( 5 / 18 ) ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , ( ( x + 250 ) / 26 ) = 20 x + 250 = 520 x = 270 . d"
Answer: d
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 22.5 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 120
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 22.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 22.5 miles in 90 mins so answer 30 + 90 = 120 mins . ( answer e )"
Answer: e
Problem: what is the average of first 21 multiples of 5 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 55 , d ) d ) 81 , e ) e ) 82
Rationale: required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 5 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 55 c
Answer: c
Problem: the sale price sarees listed for rs . 560 after successive discount is 20 % and 30 % is ?
Options: a ) 321 , b ) 314 , c ) 316 , d ) 265 , e ) 162
Rationale: "explanation : 560 * ( 80 / 100 ) * ( 70 / 100 ) = 314 answer : b"
Answer: b
Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be a couple ?
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 90 / 2900 , d ) 17 / 2700 , e ) 1 / 20
Rationale: "in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . ans - d"
Answer: d
Problem: a can complete a work in 12 days and b can do the same work in 8 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 1 / 2 days , c ) 6 1 / 2 days , d ) 7 3 / 4 days , e ) 10 days
Rationale: the required answer = ( 12 - 2 ) * 8 / 12 = 80 / 12 = 6 1 / 2 days answer is c
Answer: c
Problem: a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 2 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 1800 , c ) 500 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 2 min = 120 sec . let the length of the train be x meters . then , ( 800 + x ) / 120 = 65 / 3 x = 1800 m . answer : b"
Answer: b
Problem: given that e and f are events such that p ( e ) = 25 , p ( f ) = 75 and p ( e n f ) = 75 , find p ( e | f ) and p ( f | e )
Options: a ) 5 , b ) 46 , c ) 52 , d ) 12 , e ) 3
Rationale: here , e and f are events p ( e | f ) = p ( enf ) / p ( f ) = 75 / 25 = 3 p ( f | e ) = p ( enf ) / p ( e ) = 75 / 75 = 1 . e )
Answer: e
Problem: a train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train ?
Options: a ) 90 , b ) 60 , c ) 120 , d ) 180 , e ) 360
Rationale: "length = speed * time speed = l / t s = 2500 / 100 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a"
Answer: a
Problem: if integer k is equal to the sum of all even multiples of 35 between 280 and 630 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 11 * 455
Rationale: "if we break down what the stem is asking what is the sum of all mult of 30 between 300 and 600 . using arithmetic progression to find n : 630 = 280 + ( n - 1 ) 35 350 + 35 = 35 n 385 = 35 n = > n = 11 the sum would be : 11 * mean mean = [ 630 + 280 ] / 2 = 455 11 * 455 = e"
Answer: e
Problem: if 360 is divided into 4 parts proportional to 5 , 7 , 4 , 8 then the smallest part is :
Options: a ) 50 , b ) 60 , c ) 40 , d ) 18 , e ) 22
Rationale: given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24 : . the smallest part = ( 360 * 4 / 24 ) = 60 answer : b
Answer: b
Problem: 1370 , 1320 , 1070 , - 180 , - 6430 , x
Options: a ) - 37680 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 - 6430 - 50 * ( 5 ^ 4 ) = - 37680 answer : a ."
Answer: a
Problem: a scale 10 ft . 5 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 25 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 10 * 12 ) + 5 = 125 inches length of each of the 5 parts = 125 / 5 = 25 inches answer : a"
Answer: a
Problem: a train 150 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 84 kmph
Rationale: "speed of train relative to man : 150 / 6 * 18 / 5 km / hr = 90 km / hr let speed of train = x therefore x + 6 = 90 x = 90 - 6 x = 84 km / hr answer : e"
Answer: e
Problem: a thief runs away from a with a speed of 20 km / hr . a police from a station 60 km away started chasing him after 1 hr . with a speed of 40 km / hr . time taken by the police to catch the thief is :
Options: a ) 4 hrs , b ) 4.5 hrs , c ) 5.4 hrs , d ) 6 hrs . , e ) none of these
Rationale: explanation : solution : distance traveled by the thief in 1 hr . = 20 km . total distance of them after 1 hr = ( 60 + 20 ) km = 80 km . their relative speed = ( 40 - 20 ) = 20 km / hr . time taken to catch the thief = 80 / 20 = 4 hrs . answer : a
Answer: a
Problem: what is the square root of 16 , divided by 2 ?
Options: a ) 9 , b ) 2 , c ) 122 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 16 = 4 , 4 / 2 = 2 ( b ) 2"
Answer: b
Problem: the value of ( 4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31 ) is :
Options: a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none of these
Rationale: solution given expression = 4.7 × ( 13.26 + 9.43 + 77.31 ) = 4.7 × 100 = 470 . answer c
Answer: c
Problem: an ant walks an average of 500 meters in 60 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 1.0 , b ) 0.5 , c ) 0.75 , d ) 0.425 , e ) 0.3
Rationale: "the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425"
Answer: d
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 10 gallons of water and 20 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 20 gallons salt is added and 10 gallons of water is added . so salt now becomes - > ( 0.2 x + 20 ) and water - - > ( 0.6 x + 10 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 20 ) = ( 0.6 x + 10 ) / 2 , solving , x = 150 . answer : d"
Answer: d
Problem: roses can be purchased individually for $ 2.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 325 , d ) 324 , e ) 326
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 2.3 = ~ 13 roses for that amount . total = 312 + 13 = 325 . answer : c ."
Answer: c
Problem: in the land of oz only one or two - letter words are used . the local language has 65 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 130
Rationale: the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 65 letters is 65 ; the number of 2 letter words ( xx ) that can be made from 65 letters is 65 * 65 , since each x can take 65 values . total : 65 + 65 * 65 . similarly : the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . the difference is ( 65 + 65 * 65 ) - ( 64 + 64 * 64 ) = 130 . answer : e .
Answer: e
Problem: baker ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each cake box is 8 inches by 7 inches by 5 inches , then what is the maximum number of cake boxes that can be placed in each carton ?
Options: a ) 330 , b ) 300 , c ) 252 , d ) 225 , e ) 210
Rationale: baker ram is storing cake boxes in cartons the dimensions of the carton are 25 x 42 x 60 and those of each cake box are 8 x 7 x 5 . to maximize number of boxes try and fit maximum into the base of the box . if you take the base as 25 x 42 and fit 5 x 6 boxes of 5 x 7 , then the total number of boxes is 5 x 6 x integer ( 60 / 8 ) = 5 x 6 x 7 = 210 . alternatively you could try taking the base as 60 x 42 and fit 12 x 6 boxes of 5 x 7 , then the total number of boxes is 12 x 6 x integer ( 25 / 8 ) = 12 x 6 x 3 = 216 . but since that is not an answer option , i go with ( e ) 210 .
Answer: e
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 4.5 liters of alcohol and 5.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 7 % , b ) 10 % , c ) 13 % , d ) 16 % , e ) 19 %
Rationale: the percent of alcohol in the solution is ( 0.05 ( 40 ) + 4.5 ) / 50 = 6.5 / 50 = 13 % the answer is c .
Answer: c
Problem: a snail , climbing a 20 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 16 , c ) 17 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 16 days it will climb 16 feet on the 17 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 17 answer : c"
Answer: c
Problem: if n is the smallest integer such that 432 times n is the square of an integer , what is the value of n ?
Options: a ) 2
b ) 3
c ) 6
d ) 12
e ) 24
Rationale: the prime factorization of a square has to have even powers of all its prime factors . if the original number has a factor , say of 7 , then when it ’ s squared , the square will have a factor of 7 ^ 2 . another way to say that is : any positive integer all of whose prime factors have even powers must be a perfect square of some other integer . look at the prime factorization of 432 432 = ( 2 ^ 4 ) * ( 3 ^ 3 ) the factor of 2 already has an even power — - that ’ s all set . the factor of 3 currently has an odd power . if n = 3 , then 432 * n would have an even power of 2 and an even power of 3 ; therefore , it would be a perfect square . thus , n = 3 is a choice that makes 432 * n a perfect square . answer : b .
Answer: b
Problem: the average of the marks of 12 students in a class is 36 . if the marks of each student are doubled , find the new average ?
Options: a ) 72 , b ) 23 , c ) 29 , d ) 26 , e ) 13
Rationale: "sum of the marks for the 12 students = 12 * 36 = 432 . the marks of each student are doubled , the sum also will be doubled . the new sum = 432 * 2 = 864 . so , the new average = 864 / 12 = 72 . answer : a"
Answer: a
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 85 , e ) 11
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 20 = rs . 85 . answer : d"
Answer: d
Problem: if the simple interest on $ 1500 increase by $ 20 , when the time increase by 2 years . find the rate percent per annum .
Options: a ) 0.6 % , b ) 0.5 % , c ) 0.1 % , d ) 0.2 % , e ) 0.7 %
Rationale: applying the above formula , we have 20 = 1500 * r * 2 / 100 r = 20 * 100 / 1500 * 2 = 0.7 % . answer is e
Answer: e
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 8.40 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 8.40 when c . p = ( 100 * 8.40 ) / 21 = 40 answer : b"
Answer: b
Problem: the sum of two numbers is 29 and the difference of their squares is 145 . the difference between the number is
Options: a ) 13 , b ) 5 , c ) 8 , d ) 11 , e ) 12
Rationale: "explanation : let the numbers be x and y . we know that , ( x − y ) = x 2 − y 2 / ( x + y ) = 145 / 29 = 5 correct option : b"
Answer: b
Problem: the cube root of what integer power of 2 is closest to 50 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: integer powers of 2 = 2 , 2 ^ 2 , 2 ^ 3 , 2 ^ 4 , 2 ^ 5 , 2 ^ 6 , 2 ^ 7 etc . let , cube root of x is closest to 50 i . e . x is closest to cube of 50 = 50 * 50 * 50 = 125000 but x must be equivalent to an integer power of 2 2 ^ 10 = 1024 2 ^ 7 = 128 i . e . 2 ^ 17 = 128 * 1024 = 128000 ( approx . ) i . e . 2 ^ 18 = 256 * 1024 = 256000 ( approx . ) i . e . 2 ^ 16 = 64 * 1024 = 64000 ( approx . ) i . e . 2 ^ 17 which is closest to 125000 i . e . integer power of 2 must be 7 answer : option b
Answer: b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 190 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1007 , d ) s . 1357.1 , e ) s . 1002
Rationale: "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 190 100 % - - - - ? = > rs . 1357.1 answer : d"
Answer: d
Problem: if 3 ^ x * 4 ^ y = 19683 and x – y = 9 , then x = ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b .
Answer: b
Problem: in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 1.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
Rationale: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 2 = 8 : 10 - - > qy = 1.6 . answer : a ."
Answer: a
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 210 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 14 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 210 rs . 5 m + 5 m + 5 m - - - - - 210 rs . 15 m - - - - - - 210 rs . = > 1 m = 14 rs . answer : e"
Answer: e
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 62 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 110 / 100 = 66 in june total income = 66 + 40 = 106 % of mrs lee ' s income = 66 / 106 = 62.26 ( a )"
Answer: a
Problem: express a speed of 60 kmph in meters per second ?
Options: a ) 10 mps , b ) 16.67 mps , c ) 97.67 mps , d ) 17.67 mps , e ) 18 mps
Rationale: "60 * 5 / 18 = 16.67 mps answer : b"
Answer: b
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 50 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 50 , d ) 60 , e ) 50
Rationale: 200 men do the rest of the work in 100 - 50 = 50 days 100 men can do the rest of the work in 50 * 200 / 100 = 100 days required number of days = 100 - 50 = 50 days answer is c
Answer: c
Problem: how many multiples of 6 are there between 30 and 140 , 30 and 140 inclusive ?
Options: a ) 18 , b ) 16 , c ) 17 , d ) 19 , e ) 15
Rationale: "6 multiples are . . . 30 , 36,42 , 48,54 , 60,66 , 72,78 , 84,90 , 96,102 , 108,114 , 120,126 , 132,138 , . . . , . . . , the answer is = 19 answer is d"
Answer: d