regisss/math_qa huggingface dataset:
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 18 - meter platform and caught it after it had traveled 53.4 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 18 + 18 + 9 + 4.5 + 2.25 + 1.125 + 0.5 ans b"
Answer: b
Problem: a certain telescope increases the visual range at a particular location from 90 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 ) 66 2 / 3 %
Rationale: "original visual range = 90 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 90 ) / 90 * 100 % = 2 / 3 * 100 % = 66.67 % answer e"
Answer: e
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 35 more . what was his original selling price ?
Options: a ) $ 180 , b ) $ 280 , c ) $ 420 , d ) $ 550 , e ) $ 700
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 35 0.07 = 35 p = 500 the original selling price was 500 * 1.1 = 550 . the correct answer is d ."
Answer: d
Problem: a car left town a towards town b driving at a speed of v = 32 km / hr . after 3 hours on the road the driver stopped for 15 min in town c . because of a closed road he had to change his route , making the trip 28 km longer . he increased his speed to v = 40 km / hr but still he was 30 min late . find the distance the car has covered .
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: the driver did not plan the stop at c . suppose it took x hours for him to get from c to b . then the distance is s = 40 ⋅ x km . it took x − 3060 − 1560 = x − 4560 = x − 34 h to drive from c to b . the distance from c to b is 32 ( x − 34 ) km , which is 28 km shorter than 40 ⋅ x , i . e . 32 ( x − 34 ) + 28 = 40 x 32 x − 24 + 28 = 40 x 4 = 8 x x = 12 hr ⋅ x = 30 min . then the time of the trip from c to b was 30 min . the distance covered equals 3 ⋅ 32 + 12 ⋅ 40 = 96 + 20 = 116 km . so answer is c .
Answer: c
Problem: total num of pupiles in 3 grades of scholl is 333 . the no of pupiles in grades 1 and 2 are un 3 : 5 ratio and 2 and 3 grades are 7 : 11 ratio . what is the strength of class that has highest no of pupils
Options: a ) 145 , b ) 155 , c ) 165 , d ) 175 , e ) 185
Rationale: ratio g 1 : g 2 = 3 : 5 and g 2 : g 3 = 7 : 11 so g 1 : g 2 : g 3 = 21 : 35 : 55 let the strength of three classes are 21 x , 35 x and 55 x respectively , then 21 x + 35 x + 55 x = 333 = > 111 x = 333 or x = 3 so strength of the class with highest number of pupils = 55 x = 55 * 3 = 165 answer : c
Answer: c
Problem: a train 150 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 20 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 40 sec
Rationale: relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 150 × 2 / 15 ) sec = 20 sec answer : a
Answer: a
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many d women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d
Answer: d
Problem: twenty four meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 2 √ 2 , b ) 2 √ 5 , c ) 6 , d ) 4 √ 2 , e ) none of these
Rationale: "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 24 = > x / 360 * 2 * pi * r + 2 r = 24 = > 2 a / r + 2 r = 24 = > a = r 12 - r ^ 2 = r 12 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 12 - 2 r = 0 r = 6 c"
Answer: c
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 20 % profit ?
Options: a ) 277 , b ) 960 , c ) 277 , d ) 266 , e ) 768
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 120 % of rs . 640 = 120 / 100 * 640 = rs . 768 . answer : e"
Answer: e
Problem: how many positive integers , from 2 to 100 , inclusive , are not divisible by odd integers greater than 1 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 50
Rationale: the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence answer : b
Answer: b
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 6 days . c alone will finish the job in
Options: a ) 10 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 6 = ( 15 * x ) / ( 15 + x ) 90 + 6 x = 15 x 9 x = 90 x = 10 answer : option a"
Answer: a
Problem: in x game of billiards , x can give y 10 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "x scores 60 while y score 50 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 50 = 60 . in x game of 100 points , y gives ( 100 - 60 ) = 40 points to c . d"
Answer: d
Problem: find avrg speed if a man travels at speed of 16 km / hr up and 30 km / hr dawn at an altitude of 200 m .
Options: a ) 22.8 , b ) 21.8 , c ) 20.8 , d ) 28.8 , e ) 29.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 16 * 30 / ( 16 + 30 ) = 20.8 answer : c"
Answer: c
Problem: a can do a work in 16 days and b can do it in 8 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 5 1 / 3 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 16 b ' s 1 day ' s work = 1 / 8 they work together = 1 / 16 + 1 / 8 = 3 / 16 = 16 / 3 = 5 1 / 3 days answer : option b"
Answer: b
Problem: in a forest 100 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,000 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 100 tagged deers comprise 10 % of total # of deers - - > total # of deers = 100 * 10 = 1,000 . answer : d ."
Answer: d
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 20 of money ?
Options: a ) 1500 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2000
Rationale: "p = 20 ( 100 / 10 ) 2 = > p = 2000 answer : e"
Answer: e
Problem: a man sold 20 articles for $ 50 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 54 , e ) 48
Rationale: "production cost per article : $ 50 * ( 100 % - 20 % ) / 20 = $ 2.0 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.0 = 54 thus , solution d is correct ."
Answer: d
Problem: find the least number must be added to 433124 so that remaining no . is divisible by 17 ?
Options: a ) 3 , b ) 2 , c ) 5 , d ) 6 , e ) 1
Rationale: "on dividing 433124 by 17 we get the remainder 15 , so 2 should be added b"
Answer: b
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1554 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 100 , d ) s . 103 , e ) s . 105
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1554 74 x = 1554 = > x = 21 5 x = 105 rs . answer : e"
Answer: e
Problem: the average weight of 25 girls increases by 1 kg when a new girl comes in place of one of them weighing 55 kg . what might be the weight of the new girl ?
Options: a ) 85 kg , b ) 90 kg , c ) 83 kg , d ) 80 kg , e ) 82 kg
Rationale: "total weight increased = 25 x 1 kg = 25 kg . weight of new person = 55 + 25 kg = 80 kg answer : d"
Answer: d
Problem: everyone shakes hands with everyone else in a room . total number of handshakes is 120 . number of persons = ?
Options: a ) a . 14 , b ) b . 12 , c ) c . 11 , d ) d . 15 , e ) e . 16
Rationale: "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 120 or n ( n - 1 ) = 240 or n = 16 answer is ( e )"
Answer: e
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 470 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 525
Rationale: "let no . of non - officers be x 15 * 470 + x * 110 = ( x + 15 ) 120 x = 525 e"
Answer: e
Problem: find the least number which when divided by 31 and 9 leaves a remainder of 3 in each case .
Options: a ) 280 , b ) 282 , c ) 284 , d ) 286 , e ) 288
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 31 , 9 ) + 3 = 282 . answer : b"
Answer: b
Problem: two train each 500 m long , are running in opposite directions on parallel tracks . if their speeds are 45 km / hr and 30 km / hr respectively , the time taken by the slower train to pass the driver of the faster one is ?
Options: a ) 20 s , b ) 24 s , c ) 22 s , d ) 23 s , e ) 21 s
Rationale: relative speed = 45 + 30 = 75 km / hr = 750 / 36 m / s = 125 / 6 m / s we are calculating the time taken by the slower train to pass the driver of the faster one . hence the distance = length of the smaller train = 500 m time = distance / speed = 500 / ( 125 / 6 ) = 24 s answer is b .
Answer: b
Problem: the average age of 32 students in a group is 10 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 45 , b ) 43 , c ) 51 , d ) 53 , e ) 57
Rationale: "age of the teacher = ( 33 * 11 - 32 * 10 ) = 43 years . answer : b"
Answer: b
Problem: mohit sold an article for $ 21000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 25000 , c ) 15000 , d ) 18000 , e ) 17500
Rationale: "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 21000 - 10 / 100 ( 21000 ) = 21000 - 2100 = $ 18900 = > 1.08 x = 18900 = > x = 17500 e"
Answer: e
Problem: a marketing firm determined that , of 200 households surveyed , 80 used neither brand k nor brand b soap , 60 used only brand k soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap k and soap b ( d ) 40
Answer: d
Problem: a shopkeeper cheats to the extent of 10 % while buying and selling , by using false weights . his total gain is .
Options: a ) 22 , b ) 21 , c ) 8 , d ) 9 , e ) 81
Rationale: answer : b ) 21 %
Answer: b
Problem: the number of singles that a baseball player hit increased 15 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 5 percent . if the total number of singles and doubles that she hit increased 4 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 3 : 5 , b ) 5 : 7 , c ) 7 : 11 , d ) 9 : 11 , e ) 11 : 15
Rationale: soln : - 1.15 s + 0.95 d = 1.04 [ s + d ] 0.11 s = 0.09 d s / d = 9 / 11 answer : d
Answer: d
Problem: the product x of two prime numbers is between 17 and 55 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 51
Rationale: "option b & c can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 51 = 3 * 17 > > answer answer e"
Answer: e
Problem: the average of first 6 prime numbers which are between 60 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 72.33
Rationale: explanation : first six prime numbers which are between 60 and 90 = 61 , 67 , 71 , 73 , 79 , 83 average = ( 61 + 67 + 71 + 73 + 79 + 83 ) / 6 = 72.33 answer : e
Answer: e
Problem: a rectangular grass field is 95 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1550 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 95 + 55 + 2.5 * 2 ) 2 * 2.5 = > 775 775 * 2 = rs . 1550 answer : b"
Answer: b
Problem: the sale price sarees listed for rs . 350 after successive discount is 20 % and 5 % is ?
Options: a ) 266 , b ) 278 , c ) 342 , d ) 787 , e ) 191
Rationale: "350 * ( 80 / 100 ) * ( 95 / 100 ) = 266 answer : a"
Answer: a
Problem: a train is 360 meter long is running at a speed of 56 km / hour . in what time will it pass a bridge of 140 meter length .
Options: a ) 20.14 seconds , b ) 12.14 seconds , c ) 22.14 seconds , d ) 32.14 seconds , e ) none of these
Rationale: "explanation : speed = 56 km / hr = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 140 / 9 = 32.14 seconds answer : d"
Answer: d
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1100 , what is the reduced price for kg ?
Options: a ) s . 40 , b ) s . 46 , c ) s . 55 , d ) s . 41 , e ) s . 42
Rationale: "800 * ( 25 / 100 ) = 275 - - - - 5 ? - - - - 1 = > rs . 55 answer : c"
Answer: c
Problem: in a college , 280 students study hindi , 254 students study sanskrit and 280 students study english . 97 students study hindi as well as physics , 138 students study sanskrit as well as english and 152 students study hindi as well as english . 73 students study all the 3 languages . how many total number of students are there in that college ?
Options: a ) 350 , b ) 500 , c ) 650 , d ) 235 , e ) 450
Rationale: b
Answer: b
Problem: 20 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 230
Rationale: "1 st person will shake hand with 19 people 2 nd person will shake hand with 18 people 3 rd person will shake hand with 17 people . . . . . . total no . of handshakes = 19 + 18 + 17 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 190 or , if there are n persons then no . of shakehands = nc 2 = 20 c 2 = 190 answer : a"
Answer: a
Problem: a and b complete a work in 8 days . a alone can do it in 16 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.78 days , c ) 5.3 days , d ) 3.15 days , e ) 2.75 days
Rationale: "1 / 8 + 1 / 16 = 3 / 16 16 / 3 = 5.3 days answer : c"
Answer: c
Problem: suppose 8 monkeys take 8 minutes to eat 8 bananas . how many monkeys would it take to eat 48 bananas in 48 minutes
Options: a ) 5 monkeys , b ) 6 monkeys , c ) 7 monkeys , d ) 8 monkeys , e ) 9 monkeys
Rationale: "8 monkeys take 8 minutes to eat 8 bananas means each monkey takes 8 min for 1 banana in 48 mins one monkey can eat 6 bananas . . . . which means that 8 monkeys can eat 48 bananas in 48 minutes so answer is 8 monkeys answer : d"
Answer: d
Problem: a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.2 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 120 , e ) e . 200
Rationale: volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.2 = 120 answer : d
Answer: d
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.3 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 13 / 33 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.3 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 26 hours . total hours = 66 . then the fraction would be 26 / 66 = 13 / 33 . therefore answer b b ."
Answer: b
Problem: two employees x and y are paid a total of rs . 528 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 240
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 528 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 528 ⇒ y [ 12 / 10 + 1 ] = 528 ⇒ 22 y / 10 = 528 ⇒ 22 y = 5280 ⇒ y = 5280 / 22 = 480 / 2 = rs . 240 e"
Answer: e
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 2 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 24 hours , e ) 16 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 2 machines 2 units of work ( 2 machines ) - - - > 1 hour for 48 units of work 2 * 24 - - - > 1 * 24 hours d 24 hours"
Answer: d
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 50 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 49 , e ) 47
Rationale: "working backward from the day it ' s covered : day 50 : fully covered day 49 : half covered so 49 days answer : d"
Answer: d
Problem: a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2200
Options: a ) 17 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "explanation : gain % = ( 364.36 * 100 / 2200 ) = 16.56 % = 17 % approx option a"
Answer: a
Problem: if a ( a - 6 ) = 27 and b ( b - 6 ) = 27 , where a ≠ b , then a + b = ?
Options: a ) − 48 , b ) − 2 , c ) 46 , d ) 6 , e ) 48
Rationale: "i . e . if a = - 3 then b = 9 or if a = 9 then b = - 3 but in each case a + b = - 3 + 9 = 6 answer : option d"
Answer: d
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.64 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 14 %
Rationale: let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.64 9.9 - 45 x + 36 x = 8.64 9 x = 1.26 x = 0.14 the answer is e .
Answer: e
Problem: a cylindrical can has a radius of 4 centimeters and a height of 18 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 144 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 18 = 144 pi answer is d ."
Answer: d
Problem: what is 5 2 / 3 - 3 5 / 4 divided by 5 / 2 - 7 / 6 ?
Options: a ) 2 , b ) 6 , c ) 4 , d ) 5 , e ) 1
Rationale: "5 2 / 3 - 3 5 / 4 = 17 / 3 - 20 / 4 = ( 68 - 60 ) / 12 = 8 / 12 = 4 / 3 5 / 2 - 7 / 6 = ( 15 - 7 ) / 6 = 8 / 6 = 4 / 3 so 4 / 3 / 4 / 3 = 1 answer - e"
Answer: e
Problem: the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 38 cm 2 , b ) 27 cm 2 , c ) 45 cm 2 , d ) 25 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : c"
Answer: c
Problem: sum of the squares of 3 no . ' s is 222 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = √ 484 = 22 a"
Answer: a
Problem: a salesman ' s income consists of a commission and a base salary of $ 450 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 265
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 450 * 2 = $ 900 therefore , commission = $ 1430 - $ 900 = $ 530 for 2 weeks avg weekly commission = $ 265 answer e"
Answer: e
Problem: an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 400 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 900 , c ) 540 , d ) 640 , e ) 720
Rationale: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 400 - - > { not on display } = 600 . according to ( i ) 2 / 3 * { total } = 600 - - > { total } = 900 . answer : b ."
Answer: b
Problem: what is ( 25 ^ 7 + 25 ) / 25 ?
Options: a ) 244140626 , b ) 243120617 , c ) 242580531 , d ) 241230438 , e ) 240760355
Rationale: "( 25 ^ 7 + 25 ) / 25 = 25 * ( 25 ^ 6 + 1 ) / 25 = 25 ^ 6 + 1 clearly this is a number which ends with a 6 in the units place . the answer is a ."
Answer: a
Problem: chris mixed 5 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 5 / 17 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 5 lbs of raisin = $ 5 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 5 = 17 fraction of the value of raisin = 5 / 17 = 1 / 5 ans : a"
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 18 sec . what is the length of the train ?
Options: a ) 118 , b ) 150 , c ) 300 , d ) 258 , e ) 191
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 18 = 300 m answer : c"
Answer: c
Problem: find the value for x from below equation : x / 3 = - 5 ?
Options: a ) - 66 , b ) 13 , c ) - 15 , d ) - 31 , e ) 40
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 5 / 3 simplify both sides : x = - 15 c"
Answer: c
Problem: if an average hard drive had a capacity of 0.7 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 7168
Rationale: 0.7 * 2 ^ 10 = 0.7 * 1024 = 716.8 the answer is e .
Answer: e
Problem: 9 men went to a hotel . 8 of them spent rs . 3 each over their meals and the ninth spent rs . 2 more than the average expenditure of all the 9 . determine the total money spent by them ? a . rs . 29.25
Options: a ) 29.25 , b ) 29.28 , c ) 29.27 , d ) 29.22 , e ) 29.21
Rationale: average of 9 = x 9 x = 8 * 3 + x * 2 x = 3.25 total = 9 * 3.25 = 29.25 . answer : a
Answer: a
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 315
Rationale: "1 c 7 * 2 c 10 = 7 * 45 = 315 the answer is ( e )"
Answer: e
Problem: find the average of all the numbers between 6 and 34 which are divisible by 5
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 40
Rationale: "exp . multiples of 5 between 6 and 34 are 10 , 15,20 , 25,30 average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 5 ( 10 + 30 ) / 2 * 5 = 40 / 2 = 20 answer : b"
Answer: b
Problem: how much time will a train of length 420 m moving at a speed of 72 kmph take to cross another train of length 640 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 76 , e ) 106
Rationale: "the distance to be covered = sum of their lengths = 420 + 640 = 1060 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 1060 / 10 = 106 sec . answer : e"
Answer: e
Problem: machine p and machine q are each used to manufacture 110 sprockets . it takes machine p 10 hours longer to produce 110 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 1
Rationale: p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 10 / x = 110 / 1.1 x + 10 1.1 ( 110 ) = 110 + 11 x 11 x = 11 x = 1 the answer is e
Answer: e
Problem: a spider web consists of 3 concurrent lines forming radial support for 20 concentric regular hexagon . the hexagon vertices are 5 mm from their immidiate neighbour . if the innermost hexagon has a side length 3 mm how many meters is the length of the entire web including the 3 diagonals ?
Options: a ) 7.354 m
b ) 8.354 m
c ) 6.354 m
d ) 9.354 m
e ) 5.354 m
Rationale: for perimeter of all hexagon = 6 * ( 3 + 8 + 13 + . . . . . . . . . . . 20 th term . ) sum will be 6060 mm and for length of one diagonal find 20 th term = 98 so total length = 6060 + 294 = 6354 mm = 6.354 m answer : c
Answer: c
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 25 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 75 % ( 100 - 25 ) . therefore 0.5 x amount of flower - nectar = 0.75 x amount of honey = 0.75 x 1 kg therefore amount of flower - nectar needed = ( 0.75 / 0.51 ) kg = 1.5 kgs answer : b"
Answer: b
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 30 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 37.5 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 30 % impurities to the product . it means that he is selling $ 5 worth of product for $ 5.5 . so his profit is $ 5.5 - $ 4 = $ 1.5 and his profit percent is ( 1.5 / 4 ) * 100 = 37.5 % answer : - e"
Answer: e
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 144 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 126
Rationale: "set up equation : x = total number of workers 144 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 144 = 16 / 30 x x = 270 270 - 144 = 126 answer e"
Answer: e
Problem: 95 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: answer = c please refer diagram below 95 - 10 = 85
Answer: c
Problem: in what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 6 sec , b ) 7 sec , c ) 8 sec , d ) 9 sec , e ) 2 sec
Rationale: "t = 60 / 36 * 18 / 5 = 2 sec answer : e"
Answer: e
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 400 in 2 years ?
Options: a ) 5 % , b ) 6 % , c ) 2 % , d ) 25 % , e ) 1 %
Rationale: interest for 2 yrs = 400 interest for 1 yr = 200 interest rate = 200 / 800 x 100 = 25 % answer : d
Answer: d
Problem: if the area of a square with sides of length 9 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4
b ) 27
c ) 12
d ) 16
e ) 18
Rationale: let length of rectangle = l 9 ^ 2 = l * 3 = > l = 81 / 3 = 27 answer b
Answer: b
Problem: taequan is playing a dice game where he rolls two , fair , 6 - sided dice twice . if he gets the same roll on his second try as his first , he wins . if he rolled an 8 on his first try , what is the probability that he will win with his second roll ?
Options: a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 5 / 36
Rationale: there are 5 ways to roll an 8 : 2 and 6 , 6 and 2 , 3 and 5 , 5 and 3 , 4 and 4 ( 4 and 4 is counted just once ) . there are 6 * 6 = 36 ways to roll two six - sided dice . the dice are fair , so the probability of rolling an 8 is 5 / 36 . e
Answer: e
Problem: car a runs at the speed of 100 km / hr & reaches its destination in 5 hr . car b runs at the speed of 80 km / h & reaches its destination in 6 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 13 : 7 , d ) 25 : 24 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 100 × 5 = 500 km distance travelled by car b = 80 × 6 = 480 km ratio = 500 / 480 = 25 : 24 answer : d"
Answer: d
Problem: george baked a total of 100 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 / 5 of the 100 pizzas cooked on saturday = 60 pizzas 3 / 5 of the remaining pizzas on sunday = 24 pizzas we ' re left with ( 100 - 60 - 24 ) = 16 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 6 4 3 2 1 = 16 w = 3 a"
Answer: a
Problem: pipe a usually fills a tank in 2 hours . on account of a leak at the bottom of the tank , it takes pipe a 30 more minutes to fill the tank . how long will the leak take to empty a full tank if pipe a is shut ?
Options: a ) 7 hours , b ) 8 hours , c ) 9 hours , d ) 10 hours , e ) 11 hours
Rationale: pipe a fills the tank normally in 2 hours . therefore , it will fill ½ of the tank in an hour . let the leak take x hours to empty a full tank when pipe a is shut . therefore , the leak will empty of the tank in an hour . the net amount of water that gets filled in the tank in an hour when pipe a is open and when there is a leak = of the tank . — ( 1 ) when there is a leak , the problem states that pipe a takes two and a half hours to fill the tank . i . e . hours . therefore , in an hour , of the tank gets filled . – ( 2 ) equating ( 1 ) and ( 2 ) , we get = > = > x = 10 hours . the problem can also be mentally done as follows . pipe a takes 2 hours to fill the tank . therefore , it fills half the tank in an hour or 50 % of the tank in an hour . when there is a leak it takes 2 hours 30 minutes for the tank to fill . i . e hours to fill the tank or or 40 % of the tank gets filled . on account of the leak , ( 50 - 40 ) % = 10 % of the water gets wasted every hour . therefore , the leak will take 10 hours to drain a full tank . answer : d
Answer: d
Problem: walking at 5 / 6 th of its usual speed a cab is 5 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 32 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 5 m ut / 5 = 5 m ut = 25 m answer is a"
Answer: a
Problem: what is the 8 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0,7 , thus 8 th digit to the right of the decimal point is 2 . answer : b ."
Answer: b
Problem: find the value of x : 3 x ^ 2 - 6 x + 3 = 0
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 ± √ ( ( - 6 ) 2 - 4 × 3 × 3 ) ) / ( 2 × 3 ) = ( 6 ± √ ( 36 - 36 ) ) / 6 = ( 6 ± 0 ) / 6 x 1 = x 2 = 1 b
Answer: b
Problem: in a kilometer race , a beats b by 50 meters or 5 seconds . what time does a take to complete the race ?
Options: a ) 199 sec , b ) 190 sec , c ) 726 sec , d ) 90 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 5 ) / 50 = 100 sec . time taken by a = 100 - 10 = 90 sec . answer : d"
Answer: d
Problem: what is the smallest number which when increased by 3 is divisible by 27 , 35 , 25 , & 21 ?
Options: a ) 4722 , b ) 4725 , c ) 4728 , d ) 4731 , e ) 4733
Rationale: "here smallest number means lcm hence lcm of 27,35 , 25,21 = 3 ^ 3 x 5 ^ 2 x 7 = 4725 therefore required number is 4725 - 3 = 4722 ans - a"
Answer: a
Problem: a train 150 m long crosses a platform 130 m long in 20 sec ; find the speed of the train ?
Options: a ) 50 , b ) 60 , c ) 55 , d ) 45 , e ) 53
Rationale: "d = 150 + 130 = 280 t = 20 s = 280 / 20 * 18 / 5 = 50 kmph . answer : a"
Answer: a
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 245 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 80 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 245 x = 5 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 5 = 80 answer c"
Answer: c
Problem: when 6 + 2 = 85 , 8 + 3 = 115 , 7 + 5 = 125 , then 5 + 8 = ?
Options: a ) 145 , b ) 185 , c ) 245 , d ) 135 , e ) 140
Rationale: "6 + 2 = > 6 + 2 = 8 = > 8 ã — 10 + 5 = 85 8 + 3 = > 8 + 3 = 11 = > 11 ã — 10 + 5 = 115 7 + 5 = > 7 + 5 = 12 = > 12 ã — 10 + 5 = 125 then 5 + 8 = > 5 + 8 = 13 = > 13 ã — 10 + 5 = 135 answer : d"
Answer: d
Problem: pipe a can fill a tank in 4 hours . due to a leak at the bottom , it takes 8 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 8 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 4 - 1 / x = 1 / 8 = > 1 / x = 1 / 4 - 1 / 8 = ( 2 - 1 ) / 8 = 1 / 8 = > x = 8 . answer : d"
Answer: d
Problem: in how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 50803200 , b ) 50328000 , c ) 50003280 , d ) 50703200 , e ) 50603200
Rationale: "number of ways = 2 * 7 ! * 7 ! = 50803200 answer is a"
Answer: a
Problem: how many two - element subsets of < 1 , 23 , 45 , 67 > are there that do not contain the pair of elements 2 and 4 ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 20
Rationale: 7 c 2 - 1 = 20 answer is e
Answer: e
Problem: a certain junior class has 3000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 1 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 60 / 3000 first then we can only pick 1 other pair from the 800 so total will be 60 / 800 * 3000 simplify and you get 1 / 40000 answer is a"
Answer: a
Problem: there is a sufficient food for 200 men for 20 days after 15 days 100 men leave the place . for how many days will the rest of the food last for the rest of the men ?
Options: a ) 10 days , b ) 5 days , c ) 15 days , d ) 12 days , e ) 10 days
Rationale: explanation : after 13 days , 100 men left , therefore 5 days * 200 men = x days * 100 men x = 10 days answer : option a
Answer: a
Problem: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 30 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 90 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 30 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 30 = 180 / 4 t t = 90 b - c = 90 mph answer a"
Answer: a
Problem: how much 60 % of 50 is greater than 30 % of 30 ?
Options: a ) 21 , b ) 91 , c ) 11 , d ) 17 , e ) 12
Rationale: "( 60 / 100 ) * 50 – ( 30 / 100 ) * 30 30 - 9 = 21 answer : a"
Answer: a
Problem: the average of 50 numbers id 50 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22 , b ) 33 , c ) 22 , d ) 41 , e ) 50
Rationale: "explanation : total of 50 numbers = ( 50 × 50 ) = 2500 total of 48 numbers = ( 2500 - ( 45 + 55 ) ] = 2400 required average = 2400 / 48 = 50 answer : e"
Answer: e
Problem: a can do a work in 9 days . b can do the same work in 18 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 9 b rate = 1 / 18 ( a + b ) rate = ( 1 / 9 ) + ( 1 / 18 ) = 1 / 6 a & b finish the work in 6 days correct option is e"
Answer: e
Problem: how many numbers between 100 and 672 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 14 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 672 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 672 : 672 / 42 = 14 hence , 42 * 16 = 672 is the last number divisible by 42 within 672 hence , total numbers divisible by 2 , 3 , 7 together are ( 16 â € “ 2 ) = 14 answer : d"
Answer: d
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 3,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 15,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 3,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 3,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 240 = 0.10 x combine terms and subtract 0.08 x from both sides : 310 = 0.02 x divide both sides by 0.02 : 15,500 = x your answer is b ."
Answer: b
Problem: a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 586.75 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 789
Rationale: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.75 = > x = 789"
Answer: e
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 157 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 450 , e ) 520
Rationale: "10 * 157 = 1570 3 * 100 + 5 * 150 = 1050 1570 – 1050 = 520 answer : e"
Answer: e
Problem: 0.0004 ? = 0.02
Options: a ) 0.02 , b ) 0.2 , c ) 2 , d ) 20 , e ) none of these
Rationale: "explanation : required answer = 0.0004 / 0.02 = 0.04 / 2 = 0.02 . answer : option a"
Answer: a
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability t that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability t = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Problem: the length of a rectangle is reduced by 25 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 33 % , e ) 40 %
Rationale: "sol . required change = ( 25 * 100 ) / ( 100 - 25 ) = 25 % d"
Answer: d
Problem: a survey was sent to 95 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 7 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 95 ) = x / 100 x = 7 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 7 ) % = 7 % answer is c"
Answer: c
Problem: tough and tricky questions : word problems . ak car company wants to manufacture a new car known as model x , and it is trying to determine how many cars it needs to sell in order to make an annual profit of $ 30 , 500000 . the annual fixed costs for model x total $ 50 , 200000 . in addition , each model x car has an average cost of $ 5000 per vehicle to manufacture . if the company forecasts it will sell 20000 model x cars this year , at what price must the company sell the car to achieve the desired annual profit ?
Options: a ) $ 4035 , b ) $ 4036 , c ) $ 9035 , d ) $ 16140 , e ) $ 36140
Rationale: the ak company plans to make a profit of $ 30 , 500000 and it needs to earn the fixed costs of $ 50 , 200000 , so it needs to earn $ 80 , 700000 on top of the costs for the production of the 20000 cars . therefore , price of each car needs to be the unit costs plus $ 80 , 700000 / 20000 . after removing the 0 ' s , we end with the unit costs plus $ 8070 / 2 , which is $ 5000 plus $ 4035 . therefore , answer c is correct .
Answer: c
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 15 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? c"
Answer: c