regisss/math_qa huggingface dataset:
Problem: the sides of a triangle are in the ratio 3 : 5 : 7 . if the pereimeter is 60 cms , the longest side is
Options: a ) 7 , b ) 30 , c ) 28 , d ) 25 , e ) 16
Rationale: "3 x + 5 x + 7 x = 60 15 x = 60 x = 4 longest side = 7 * 4 = 28 answer : c"
Answer: c
Problem: how many positive integers between 5 and 5000 ( both are inclusive ) are there such that they are multiples of 5 ?
Options: a ) 1500 , b ) 1000 , c ) 999 , d ) 1001 , e ) 1005
Rationale: "multiples of 5 = 5 , 10,15 - - - - - , 5000 number of multiples of 5 = > 5000 - 5 / 5 + 1 = 1000 answer is b"
Answer: b
Problem: the sale price sarees listed for rs . 528 after successive discount is 20 % and 10 % is ?
Options: a ) 288 , b ) 277 , c ) 380 , d ) 290 , e ) 262
Rationale: "528 * ( 80 / 100 ) * ( 90 / 100 ) = 380 answer : c"
Answer: c
Problem: a train covers a distance of 9 km in 6 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 100 , b ) 105 , c ) 110 , d ) 120 , e ) 125
Rationale: "speed = ( 9 / 6 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 5 = 125 m . answer : option e"
Answer: e
Problem: the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 52 black cars in the lot , how many red cars are there in the lot ?
Options: a ) 11 , b ) 20 , c ) 24 , d ) 27 , e ) 32
Rationale: "b is correct r / b = 3 / 8 and b = 52 r = 52 * 3 / 8 = 20"
Answer: b
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 5 : 9 . if the shop carries 204 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 51 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: let us assume the number of dogs , cats and bunnies to be 3 x , 5 x and 9 x total dogs and bunnies = 12 x . and we are given that 12 x = 204 . hence x = 17 . dogs = 3 x = 3 * 17 = 51 ( option a )
Answer: a
Problem: a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 900 . how many workers were part of the latter production run ?
Options: a ) a ) 6 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 34
Rationale: "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 900 . . thus for the current period = 900 - 500 = 400 ( 5 n + 45 ) k = 400 k = 400 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 400 / 5 n + 45 500 ( 5 n + 45 ) = 400 ( 5 n + 20 ) 25 n + 225 = 20 n + 80 5 n = 145 n = 29 thus n + 5 = 34 hence e"
Answer: e
Problem: there are 5 guys who have equal number of bullets . all of them shoot 4 bullets . the remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division . what was the original number of bullets each one had ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 25
Rationale: let initially each was having x bullets they shot 4 bullets so 5 x - 20 = x x = 5 so each was having 5 bullets . total was 25 . answer : e
Answer: e
Problem: the cost price of an article is 55 % of the marked price . calculate the gain percent after allowing a discount of 15 % .
Options: a ) 40.5 % , b ) 48.7 % , c ) 54.5 % , d ) 55.6 % % , e ) none
Rationale: sol . let marked price = rs . 100 . then , c . p . = rs . 55 . s . p = rs . 85 . â ˆ ´ gain % = [ 30 / 55 * 100 ] % = 54.5 % . answer c
Answer: c
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 4 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 1.6 , b ) 1 , c ) 0.4 , d ) 0.16 , e ) 0.016
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 16 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 160 / 10,000 = 16 / 1000 = 0.016 ft the answer is e ."
Answer: e
Problem: peter and tom shared the driving on a certain trip . if peter and tom both drove for the same amount of time , but peter only drove 2 / 5 of the total distance , what was the ratio of tom ' s average speed to peter ' s average speed ?
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 1 : 2 , d ) 3 : 2 , e ) 2 : 3
Rationale: the answer is suppose to be d . 3 : 2 . it ' s from the gmatprep option d is answer
Answer: d
Problem: a grocery shop has a sale of rs . 6735 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4691 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6735 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6735 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34309 + x = 39000 = > x = 39000 − 34309 = 4691 answer : d"
Answer: d
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 6
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 12 t = 12 / 2 = 6 answer : e"
Answer: e
Problem: 1 / 4 of all the juniors and 2 / 3 of all the seniors are going on a trip . if there are 2 / 3 as many juniors as seniors , what fraction of the students are not going on the trip ?
Options: a ) 4 / 9 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 3 , e ) 5 / 6
Rationale: j be the number of juniors and s be the number of seniors . there are 2 / 3 as many juniors as seniors 23 ∗ s = j j / s = 23 going on trip = j 4 + 23 ∗ s fraction = ( j 4 + 23 s ) / ( j + s ) = ( 2 / 3 * 1 / 4 + 2 / 3 ) / ( 2 / 3 + 1 ) = 1 / 2 fraction not on trip = 1 / 2 answer : b
Answer: b
Problem: sonika deposited rs . 4500 which amounted to rs . 8400 after 2 years at simple interest . had the interest been 4 % more . she would get how much ?
Options: a ) 9680 , b ) 8790 , c ) 8760 , d ) 9020 , e ) 5000
Rationale: "( 4500 * 2 * 4 ) / 100 = 360 8400 - - - - - - - - 8760 answer : c"
Answer: c
Problem: a grocer has a sale of rs . 4000 , rs . 6524 , rs . 5689 , rs . 7230 and rs . 6000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?
Options: a ) s . 12557 , b ) s . 14993 , c ) s . 15560 , d ) s . 12589 , e ) s . 12500
Rationale: "total sale for 5 months = rs . ( 4000 + 6524 + 5689 + 7230 + 6000 ) = rs . 29443 required sale = rs . [ ( 7000 x 6 ) - 29443 ] = rs . ( 42000 - 29443 ) = rs . 12557 . option a"
Answer: a
Problem: in one hour , a boat goes 14 km / hr along the stream and 8 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 14 km / hr , b ) 13 km / hr , c ) 12 km / hr , d ) 11 km / hr , e ) 10 km / hr
Rationale: "let speed of the boat in still water = a and speed of the stream = b then a + b = 14 a - b = 8 adding these two equations , we get 2 a = 22 = > a = 11 ie , speed of boat in still water = 11 km / hr answer : d"
Answer: d
Problem: at a contest with 2000 participants , 1 / 2 of the people are aged 16 to 18 . next year , the number of people aged 16 to 18 will increase by 1 / 4 . after this change , what percentage of the total 2000 people will the 16 - to 18 - year - olds represent ?
Options: a ) 62.50 % , b ) 60 % , c ) 70 % , d ) 65 % , e ) 66 / 3 %
Rationale: i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 4 , we are multiplying it by 1 + 1 / 4 = 5 / 4 , so the answer here must be ( 1 / 2 ) * ( 5 / 4 ) = 5 / 8 = 62.50 % . answer : a
Answer: a
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 26 sec , b ) 28 sec , c ) 12 sec , d ) 77 sec , e ) 66 sec
Rationale: "d = 250 m + 250 m = 500 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 500 * 3 / 125 = 12 sec answer : c"
Answer: c
Problem: the closest approximation of f ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: f ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c
Answer: c
Problem: there are 9 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 97 , b ) 99 , c ) 101 , d ) 103 , e ) 105
Rationale: the total number of ways to form a team of 4 is 9 c 4 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 2 = 21 . the number of ways to form an acceptable team is 126 - 21 = 105 . the answer is e .
Answer: e
Problem: the average of first 11 prime numbers is ?
Options: a ) 14.55 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11
Rationale: "sum of 11 prime no . = 160 average = 160 / 11 = 14.55 answer : a"
Answer: a
Problem: if 12 men or 20 women can do a piece of work in 108 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "d 80 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 108 days . so , 27 women can do it in ( 20 * 108 ) / 27 = 80 days ."
Answer: d
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 7500 , brokerage being 1 / 4 % , is :
Options: a ) 103.92 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 7500 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 7500 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 104.17 = market value of rs . 100 stock = rs . 104.17 - re . 0.25 . = market value of rs . 100 stock = rs . 103.92 . answer : a"
Answer: a
Problem: a bag contains 6 black and 5 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 5 / 11 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 5 ) = 11 . number of white balls = 5 p ( drawing a white ball ) = 5 / 11 option b ."
Answer: b
Problem: in what ratio water be mixed with milk costing rs . 12 per liter to obtain a mixture worth of rs . 8 per litre ?
Options: a ) 2 : 7 , b ) 1 : 2 , c ) 2 : 9 , d ) 2 : 2 , e ) 2 : 6
Rationale: answer with explanation : by the rule of allegation , i . c . p of 1 liter of water = 0 ii . c . p of 1 liter of milk = 12 iii . mean price ( p ) = 8 iv . d – m = 12 - 8 = 4 v . m – c = 8 - 0 = 8  ratio of water and milk = 4 : 8 = 1 : 2 answer : b
Answer: b
Problem: find the largest number of 4 digits which is exactly divisible by 2718 , 1615
Options: a ) 8600 , b ) 8610 , c ) 8620 , d ) 8630 , e ) 8640
Rationale: explanation : lcm of 27 - 18 - 16 - 15 is 2160 . after dividing 9999 by 2160 we get 1359 remainder . so answer will be 9999 - 1359 = 8640 option e
Answer: e
Problem: a reindeer chased by a cheetah passed a certain tree at a constant speed of 50 miles per hour while being chased by a cheetah . then , 2 minutes later , the cheetah passed the same tree at a constant speed of 60 miles per hour . if both animals maintained their speeds , how long after the cheetah passed the tree did the cheetah catch up with the reindeer ?
Options: a ) 30 min , b ) 45 min , c ) 1 hr , d ) 3 min , e ) 1 min
Rationale: when the cheetah is at the tree , the reindeer is 50 / 30 miles ahead on the highway . ( the distance covered in 2 min ) every hour , cheetah runs 10 miles more than the deer . how many hours will it takes it to cover 50 / 30 miles more ? the answer is ( 50 / 30 ) / 10 = 1 / 60 = 1 min answer e
Answer: d
Problem: if the numbers 1 to 100 are written on 100 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 100 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 74 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 100 . answer : c"
Answer: c
Problem: a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . find out the number of days for which the remaining food will last
Options: a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36
Rationale: "explanation : given that fort had provision of food for 150 men for 45 days hence , after 10 days , the remaining food is sufficient for 150 men for 35 days remaining men after 10 days = 150 - 25 = 125 assume that after 10 days , the remaining food is sufficient for 125 men for x days more men , less days ( indirect proportion ) ⇒ men 150 : 125 } : : x : 35 ⇒ 150 × 35 = 125 x ⇒ 6 × 35 = 5 x ⇒ x = 6 × 7 = 42 ⇒ the remaining food is sufficient for 125 men for 42 days . answer : option b"
Answer: b
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 2 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 3 , d ) 4 / 3 , e ) 5 / 2
Rationale: "b work 1 / 8 * 2 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 3 / 4 * remaining work = 4 / 3 * 1 / 4 = 1 / 3 answer : c"
Answer: c
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and sandy will make a basket but jill will miss ?
Options: a ) 1 / 8 , b ) 3 / 8 , c ) 3 / 28 , d ) 5 / 28 , e ) 1 / 56
Rationale: "the probability that jack and sandy will make a basket but jill will miss is 1 / 6 * 6 / 7 * 1 / 8 = 1 / 56 . the answer is e ."
Answer: e
Problem: a mixture contains milk and water in the ratio 7 : 3 . on adding 20 liters of water , the ratio of milk to water becomes 7 : 5 . total quantity of milk & water before adding water to it ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 140
Rationale: "milk : water = 7 : 3 7 x : 3 x + 20 = 7 : 5 5 [ 7 x ] = 7 [ 3 x + 20 ] 35 x = 21 x + 140 35 x - 21 x = 140 14 x = 140 x = 10 the quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10 10 x = 100 option ' b '"
Answer: b
Problem: the average age of a class of 20 students is 14 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 36 years
Rationale: "if age of the teacher was 14 , average would not have changed . since average increased by 2 , age of the teacher = 14 + 22 × 1 = 36 answer : e"
Answer: e
Problem: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points w that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points w for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Problem: the average length of 6 strings is 80 cm . if the average length of one third of the strings is 70 cm , what is the average of the other strings ?
Options: a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .
Rationale: edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third strings is 70 . that means out 6 / 3 = 2 strings . let the avg length of two strings be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining strings . imo correct option is b .
Answer: b
Problem: a can do a piece of work in 24 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 11 , e ) 15
Rationale: "2 / 24 + 4 / 15 + x / 20 = 1 x = 13 answer : c"
Answer: c
Problem: a palindrome is a number that reads the same forward and backward , such as 242 . how many even 9 - digit numbers are palindromes ?
Options: a ) 40 , b ) 40000 , c ) 500 , d ) 5,000 , e ) 100,000
Rationale: if the palindrome must be even , it must begin and end in 2,4 6 and 8 ( 4 ways ) e . g 222212222,444414444 . the middle number in the nine - digit could be 0 - 9 ( 10 ways ) , e . g 22522 , 22822 the 2 nd and fourth numbers , the 3 rd and 5 th and 4 th and 6 th could must also be same i . e 0 - 9 ( 10 ways ) e . g 242343242 , 648565846 we thus have , 4 * 10 * 10 * 10 * 10 = 40000 b
Answer: b
Problem: a cube is divided into 64 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30
Rationale: "each side of the cube has 4 x 4 = 16 cubelets . only the interior cubelets are painted one colour . on each side , 2 x 2 = 4 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 4 = 24 the answer is d ."
Answer: d
Problem: what is the probability of getting a sum of 12 when rolling 3 dice simultaneously ?
Options: a ) 10 / 216 , b ) 12 / 216 , c ) 21 / 216 , d ) 23 / 216 , e ) 25 / 216
Rationale: "sum of 12 can be achieved in following ways 6 , 5,1 - - - total cases = 3 ! = 6 6 , 4,2 - - - total cases = 3 ! = 6 6 , 3,3 - - - total cases = 3 ! / 2 ! = 3 5 , 5,2 - - - total cases = 3 ! / 2 ! = 3 5 , 4,3 - - - total cases = 3 ! = 6 4 , 4,4 - - - total cases = 3 ! / 3 ! = 1 total cases = 25 probability = 25 * ( 1 / 6 * 1 / 6 * 1 / 6 ) = 25 / 216 answer : e"
Answer: e
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 110 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 1 , b ) $ 27 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 110 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 54.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 11 . in any case , there is no necessity to know each item ' s price , just the sum . answer : a
Answer: a
Problem: find the cost of fencing around a circular field of diameter 30 m at the rate of rs . 2 a meter ?
Options: a ) 100.5 , b ) 188.5 , c ) 190.5 , d ) 168.5 , e ) 175.5
Rationale: "2 * 22 / 7 * 15 = 94.25 94.25 * 2 = rs . 188.5 answer : b"
Answer: b
Problem: what is the ratio whose term differ by 40 and the measure of which is 2 / 7 ?
Options: a ) 32 : 23 , b ) 16 : 56 , c ) 71 : 85 , d ) 32 : 39 , e ) 41 : 52
Rationale: let the ratio be x : ( x + 40 ) then , x / ( x + 40 ) = 2 / 7 x = 16 required ratio = 16 : 56 answer is b
Answer: b
Problem: in how many ways 4 boys and 2 girls can be seated in a row so that they are alternate .
Options: a ) 48 , b ) 288 , c ) 12 , d ) 256 , e ) none
Rationale: "solution : let the arrangement be , b g b g b b 4 boys can be seated in 4 ! ways . girl can be seated in 2 ! ways . required number of ways , = 4 ! * 2 ! = 48 answer : option a"
Answer: a
Problem: find the ones digit of 73 ^ 352
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 352 will be the same as the units digit of 3 ^ 352 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 352 = ( multiple of 4 ) + 0 , since 3 is an odd number , the units digit of 3 ^ 352 will be 1 . answer : a ."
Answer: a
Problem: the difference between the compound interest and simple interest on a certain sum of money at 5 % per annum for 2 years is 45 . then the original sum is ?
Options: a ) rs . 16500 / - , b ) rs . 17000 / - , c ) rs . 18000 / - , d ) rs . 19000 / - , e ) rs . 20000 / -
Rationale: "for 2 years = ( 1002 d ) / r 2 = ( 1002 × 45 ) / ( 5 × 5 ) = ( 10000 × 45 ) / 25 = rs . 18000 / - c"
Answer: c
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 13 is :
Options: a ) 448 , b ) 553 , c ) 542 , d ) 548 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 13 = 540 + 13 = 553 . answer : b"
Answer: b
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 4 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 7 / 12 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 4 x = 3 / 4 x so if gold card balance is transferred then the rest unspent will be 3 / 4 x - x / 6 = 7 / 12 x so the ans is a"
Answer: a
Problem: at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 30 of which were white and 5 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 30 short - stemmed pink = 5 = > short - stemmed red = 5 5 / p = 5 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 30 ( as no long stemmed white ) = > r + r + 30 = 120 = > 2 r = 90 and r = 45 long stemmed r = 45 - 5 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - e"
Answer: e
Problem: a car is running at a speed of 108 kmph . what distance will it cover in 15 sec ?
Options: a ) 300 m , b ) 150 m , c ) 200 m , d ) 450 m , e ) 500 m
Rationale: "speed = 108 kmph = 108 * 5 / 18 = 30 m / s distance covered in 15 sec = 30 * 15 = 450 m answer is d"
Answer: d
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 60 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 12.9 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 60 = 140 * 5 / 18 = 350 / 9 t = 500 * 9 / 350 = 12.9 sec answer : option d"
Answer: d
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 52 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 44 ¢ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: if the average price is 52 , then mary has 6 oranges and 4 apples ( a ratio of 3 : 2 ) . for the average price to be 44 , the ratio should be 1 : 4 . mary must put back 5 oranges . the answer is e .
Answer: e
Problem: there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ?
Options: a ) rs . 450 , b ) rs . 320 , c ) rs . 550 , d ) rs . 420 , e ) none
Rationale: "solution : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 42 . = > 7 x = 84 = > x = 12 therefore original expenditure , = rs . ( 35 × 12 ) = rs . 420 . answer : option d"
Answer: d
Problem: excluding stoppages , the speed of a bus is 54 km / hr and including stoppages , it is 45 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 10 , c ) 99 , d ) 77 , e ) 29
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 9 km = 9 / 54 * 60 = 10 min . answer : b"
Answer: b
Problem: a man two flats for $ 675958 each . on one he gains 15 % while on the other he loses 15 % . how much does he gain or lose in the whole transaction ?
Options: a ) 2 % , b ) 2.25 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 15 / 10 ) ^ 2 = 9 / 4 = 2.25 % answer is b"
Answer: b
Problem: the product of three consecutive numbers is 990 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 19 , d ) 38 , e ) 56
Rationale: "product of three numbers = 990 990 = 9 * 10 * 11 . so , the three numbers are 9 , 10 and 11 . and sum of smallest of these two = 9 + 10 = 19 . answer : option c"
Answer: c
Problem: 61 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 62 , e ) 21
Rationale: "61 + 5 * 12 / ( 180 / 3 ) = 61 + 5 * 12 / ( 60 ) = 61 + ( 5 * 12 ) / 60 = 61 + 1 = 62 . answer : d"
Answer: d
Problem: the area of a triangle will be when a = 5 m , b = 7 m , c = 8 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 10
Rationale: s = ( 5 + 7 + 8 ) / 2 = e answer : e
Answer: e
Problem: there is enough provisions for 600 men in an army camp for 25 days . if there were 100 men less , how long will the provision last ?
Options: a ) 10 days , b ) 50 days , c ) 100 days , d ) 150 days , e ) 200 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 100 * d 2 d 2 = 600 * 25 / 100 = 150 days . answer : d"
Answer: d
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 34 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 890 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? b"
Answer: b
Problem: veena ranks 79 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 82 , d ) 90 , e ) 93
Rationale: total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 79 + 1 = 82 answer : c
Answer: c
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 4 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 76 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 4 = 72 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 72 + 4 = 76 a"
Answer: a
Problem: a certain telescope increases the visual range at a particular location from 100 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 50 %
Rationale: "original visual range = 100 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 100 ) / 100 * 100 % = 1 / 2 * 100 % = 50 % answer e"
Answer: e
Problem: what is the area of a square field whose diagonal of length 10 m ?
Options: a ) 50 , b ) 70 , c ) 60 , d ) 20 , e ) 25
Rationale: "d 2 / 2 = ( 10 * 10 ) / 2 = 50 answer : a"
Answer: a
Problem: if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 10 : 1 / 11 : 1 / 15 : 1 / 16 , then find the total number of items the wholesaler distributes ?
Options: a ) 945 , b ) 745 , c ) 845 , d ) 145 , e ) 345
Rationale: "here , a : b : c : d = 1 / 10 : 1 / 11 : 1 / 15 : 1 / 16 1 ) l . c . m of 10 , 11 , 15,16 is 2640 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 10 ) x 2640 = 264 b = ( 1 / 11 ) x 2640 = 240 c = ( 1 / 15 ) x 2640 = 176 d = ( 1 / 16 ) x 2640 = 165 3 ) total number of toys = ( 264 x + 240 x + 176 x + 165 x ) = 845 x minimum number of pens ( x ) = 1 therefore , total number of items = 845 items . correct option : c"
Answer: c
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 9 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , and 3 ^ 2 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 = 2520 the answer is d ."
Answer: d
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 36 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 36 kg joins the group , total weight of boys = 20 x + 36 so 20 x + 36 = 21 ( x + 1 ) = > x = 15 answer : b"
Answer: b
Problem: if 2994 ã · 14.5 = 175 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 175 in the place of 2994 / 14.5 ] = 175 / 10 = 17.5 answer is c ."
Answer: c
Problem: what is the remainder when the number y = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus y = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Problem: there are 50 students in a class . if 2 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 49 , e ) 11
Rationale: "number of students absent on a particular day = 1 % of 50 i . e . , 2 / 100 × 50 = 1 therefore , the number of students present = 50 - 1 = 49 students . answer : d"
Answer: d
Problem: if k and w are the dimensions of a rectangle that has area 40 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: "kw = 40 = 40 * 1 = 20 * 2 = 10 * 4 = 8 * 5 = - - > k can take 4 values , namely : 8 , 10,20 and 40 answer : c ."
Answer: c
Problem: jim drove 215 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 432 miles , c ) 456 miles , d ) 887 miles , e ) 985 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 215 = 985 miles correct answer e"
Answer: e
Problem: for a certain alarm system , each code is comprised of 5 digits , but no digit can be used more than twice . how many codes can be made ?
Options: a ) 30240 , b ) 60480 , c ) 91440 , d ) 98240 , e ) 101040
Rationale: case 1 : all digits distinct select 5 digits out of 10 in 10 c 5 ways and arrange them in 5 ! ways which gives us 10 c 5 x 5 ! = 30240 case 2 : two digits are same , other 3 are distinct e . g . 45722 select a digit which is to be repeated in 10 c 1 ways , select other 3 digits in 9 c 3 ways and arrange them in 5 ! / 2 ! ways to get 10 c 1 x 9 c 3 x 5 ! / 2 ! = 50400 ways case 3 : two digits repeated and one other digit e . g . 33448 select 2 digits to be repeated in 10 c 2 ways , select the single digit in 8 c 1 ways and arrange them all in 5 ! / 2 ! . 2 ! ways to get 10 c 2 x 8 c 1 x 5 ! / 2 ! . 2 ! = 10800 sum of all = 30240 + 50400 + 10800 = 91440 ways ans : c
Answer: c
Problem: in the rectangular coordinate system , if the line x = 3 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) - 2 , b ) 0 , c ) 1 / 2 , d ) 1 , e ) 2 / 3
Rationale: x = 3 y + 5 , and thus y = x / 3 - 5 / 3 the slope is 1 / 3 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 3 and thus p = 2 / 3 the answer is e .
Answer: e
Problem: what decimal fraction is 30 ml of a litre ?
Options: a ) . 3 , b ) . 0003 , c ) . 003 , d ) 0.03 , e ) none of these
Rationale: "answer required fraction = 30 / 1000 = 3 / 100 = . 03 correct option : d"
Answer: d
Problem: a can do a piece of work in 12 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 12 ∗ 1 / 2 = 6 days option b"
Answer: b
Problem: the average of 10 numbers was calculated as 20 . it is discovered later on that while calculating the average , one number , namely 86 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "10 * 20 - 26 + 86 = 260 260 / 10 = 26 the answer is e ."
Answer: e
Problem: find the compound interest on $ 1200 for 3 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 874 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 3 = $ 2074 ci = $ 874 answer is c"
Answer: c
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross - section is 690 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 27 , d ) 69 , e ) 71
Rationale: "1 / 2 * d ( 12 + 8 ) = 690 d = 69 answer : d"
Answer: d
Problem: a cistern which could be filled in 7 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 70 / 3 hrs , c ) 55 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: 1 / 7 - 1 / x = 1 / 10 = > 70 / 3 hrs answer : b
Answer: b
Problem: pooja travels from a to b a distance of 800 miles in 10 hours . he returns to a in 5 hours . find his average speed ?
Options: a ) 123.07 mph , b ) 100 mph , c ) 150.07 mph , d ) 200 mph , e ) 300 mph
Rationale: speed from a to b = 800 / 8 = 100 mph speed from b to a = 800 / 5 = 160 mph average speed = 2 * 100 * 160 / 260 = 123.07 mph answer is a
Answer: a
Problem: find the simple interest on rs . 68,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8500 , d ) 9500 , e ) none of them
Rationale: "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is c ."
Answer: c
Problem: if y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 4 * 11025 = 44 , 100 , which is a square of 210 b"
Answer: b
Problem: when jessica withdrew $ 400 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 4 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 750
Rationale: as per the question 400 = 2 a / 5 thus - a which is the total amount = 1000 the amount thus left = 600 she then deposited 1 / 4 of 600 = 150 total amount in her account = 750 answer e
Answer: e
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 290 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 52 sec
Rationale: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 290 = 650 meter time taken to cross the platform = 650 / ( 25 / 2 ) = 650 × 2 / 25 = 52 seconds answer : option e"
Answer: e
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 81 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 20 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 81 x < = 8 x > = - 10 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 10 × - 6 = 60 minimum possible value of xy is - 10 × 8 = - 80 - 80 + 60 = - 20 answer : b"
Answer: b
Problem: the simple interest on a sum of money will be rs . 900 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 1800 , b ) 2888 , c ) 1200 , d ) 2699 , e ) 2771
Rationale: "p - - - 10 - - - - 900 p - - - 5 - - - - - 450 3 p - - - 5 - - - - - 1350 - - - - - - = > 1800 answer : a"
Answer: a
Problem: a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is :
Options: a ) 0
b ) 1
c ) 2
d ) 3
e ) 4
Rationale: let x = 6 q + 3 . then , x 2 = ( 6 q + 3 ) 2 = 36 q 2 + 36 q + 9 = 6 ( 6 q 2 + 6 q + 1 ) + 3 . so , when 2 n is divided by 4 , remainder = 3 . answer : d
Answer: d
Problem: the present ratio of students to teachers at a certain school is 40 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 40 to 1 . we can rewrite this using variable multipliers . students : teachers = 40 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 40 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 40 x + 50 25 x + 125 = 40 x + 50 5 = x since x is the present number of teachers , currently there are 5 teachers . answer a ."
Answer: a
Problem: what is the sum of all possible solutions to | x - 6 | ^ 2 + | x - 6 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: denote | x - 6 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 6 | , so it ' s an absolute value and thus can not be negative . y = | x - 6 | = 4 - - > x = 10 or x = - 2 . the sum = 12 . answer : d .
Answer: d
Problem: how many diagonals does a polygon with 15 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 80
b ) 90
c ) 77
d ) 88
e ) 99
Rationale: if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 15 - 1 then 14 * ( 14 - 3 ) / 2 = 77 correct option : c
Answer: c
Problem: a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a
Options: a ) 300 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a"
Answer: a
Problem: a hall is 18 meters long and 9 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 640 , b ) 758 , c ) 862 , d ) 972 , e ) 1024
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 972 the answer is d ."
Answer: d
Problem: truck x is 13 miles ahead of truck y , which is traveling the same direction along the same route as truck x . if truck x is traveling at an average speed of 47 miles per hour and truck y is traveling at an average speed of 53 miles per hour , how long will it take truck y to overtake and drive 5 miles ahead of truck x ?
Options: a ) 2 hours , b ) 2 hours 20 minutes , c ) 2 hours 30 minutes , d ) 2 hours 45 minutes , e ) 3 hours
Rationale: relative speed = 53 - 47 = 6 miles per hour dist required = 13 + 5 = 18 miles time taken to overtake = 18 / 6 = 3 hours . e is the answer .
Answer: e
Problem: how many bricks , each measuring 125 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 1280 , b ) 2400 , c ) 5500 , d ) 7400 , e ) 3400
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 125 x 11.25 x 6 ) = 1280 answer : a"
Answer: a
Problem: the number of boxes in a warehouse can be divided evenly into 5 equal shipments by boat or 24 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 54 , d ) 81 , e ) 120
Rationale: answer is the lcm of 5 and 24 = 120 answer e
Answer: e
Problem: a sum of money amounts to rs . 6690 after 3 years and to rs . 10,035 after 6 years on compound interest . find the sum .
Options: a ) 4360 , b ) 4460 , c ) 4560 , d ) 4660 , e ) 4760
Rationale: "let the sum be rs . p . then p ( 1 + r / 100 ) 3 = 6690 … ( i ) p ( 1 + r / 100 ) 6 = 10035 … ( ii ) on dividing , we get ( 1 + r / 100 ) 3 = 10025 / 6690 = 3 / 2 . substituting this value in ( i ) , we get : p * ( 3 / 2 ) = 6690 or p = ( 6690 * 2 / 3 ) = 4460 hence , the sum is rs . 4460 . answer : b"
Answer: b
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 45 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 175 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 45 35 - - - ? = > 175 answer : c"
Answer: c
Problem: without stoppages , a train travels certain distance with an average speed of 100 km / h , and with stoppages , it covers the same distance with an average speed of 95 km / h . how many minutes per hour the train stops ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: due to stoppages , it covers 5 km less . time taken to cover 5 km = 5 â  „ 100 h = 1 â  „ 20 h = 1 â  „ 20 ã — 60 min = 3 min answer c
Answer: c
Problem: a tank is 25 m long , 12 m wide and 6 m deep . what is the cost of plastering its walls and bottom at the rate of 75 paise per sq . m ?
Options: a ) 558 , b ) 502 , c ) 516 , d ) 612 , e ) 700
Rationale: "total surface s = 2 lw + 2 lh + 2 wh = ( 25 * 12 ) + ( 2 * 25 * 6 ) + ( 2 * 12 * 6 ) = 300 + 300 + 144 = 744 m 2 therefore cost of plastering = 744 * 75 = 5800 paise = 558 answer a"
Answer: a
Problem: a man swims downstream 36 km and upstream 26 km taking 2 hours each time , what is the speed of the man in still water ?
Options: a ) 9 , b ) 18.4 , c ) 15.5 , d ) 16.7 , e ) 13.4
Rationale: "36 - - - 2 ds = 18 ? - - - - 1 26 - - - - 2 us = 13 ? - - - - 1 m = ? m = ( 18 + 13 ) / 2 = 15.5 answer : c"
Answer: c
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 19200 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6400 , d ) 1298 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 19200 = 6400 answer : c"
Answer: c
Problem: a student chose a number , multiplied it by 3 , then subtracted 220 from the result and got 110 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "let x be the number he chose , then 3 ⋅ x − 220 = 110 3 x = 330 x = 110 correct answer c"
Answer: c
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 10
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 11 , d ) 2 ^ 35 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 10 + 2 ^ 10 , which will give you 2 ^ 11 answer c"
Answer: c
Problem: a football field is 7200 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?
Options: a ) 450 , b ) 600 , c ) 750 , d ) 2400 , e ) 3200
Rationale: "answer a ) 9600 yards need 1200 lbs 1 yard will need 1200 / 7200 = 1 / 6 lbs 3600 yards will need 1 / 6 * 3600 yards = 600 lbs b"
Answer: b
Problem: { ( 476 + 424 ) 2 - 4 x 476 x 424 } = ?
Options: a ) 2135 , b ) 6551 , c ) 2704 , d ) 6466 , e ) 1113
Rationale: given exp . = [ ( a + b ) 2 - 4 ab ] , where a = 476 and b = 424 = [ ( 476 + 424 ) 2 - 4 x 476 x 424 ] = [ ( 900 ) 2 - 807296 ] = 810000 - 807296 = 2704 . correct option is c
Answer: c