regisss/math_qa huggingface dataset:
Problem: in a box of 6 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 5 , e ) 1 / 7
Rationale: "first , there are 4 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 6 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 4 c 3 / 6 c 3 = 4 / 20 = 1 / 5 answer is b"
Answer: b
Problem: a candidate appearing for an examination has to secure 52 % marks to pass paper i . but he secured only 45 marks and failed by 35 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 154 , c ) 130 , d ) 140 , e ) 150
Rationale: "he secured 45 marks nd fail by 35 marks so total marks for pass the examinatn = 80 let toal marks x x * 52 / 100 = 80 x = 154 answer : b"
Answer: b
Problem: jim drove 768 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 432 miles , b ) 651 miles , c ) 387 miles , d ) 954 miles , e ) 556 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer a"
Answer: a
Problem: if | 20 x - 10 | = 110 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 30
Rationale: | 20 x - 10 | = 110 20 x - 10 = 110 or 20 x - 10 = - 110 20 x = 120 or 20 x = - 100 x = 6 or x = - 5 product = - 5 * 6 = - 30 answer is e
Answer: e
Problem: when positive integer n is divided by positive integer j , the remainder is 10 . if n / j = 205.08 , what is value of j ?
Options: a ) 125 , b ) 100 , c ) 75 , d ) 150 , e ) 50
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 205.08 here 205 is the quotient . given that remainder = 10 so , 205.08 = 205 + 10 / j so , j = 125 answer : a"
Answer: a
Problem: in a certain kindergarten , half of the children are allergic to peanuts , 10 children are not allergic to cashew nuts , 10 children are allergic to both peanuts and cashew nuts , and 18 children are allergic to cashew nuts . how many of the kindergarten ' s children are not allergic to peanuts and are not allergic to cashew nuts ?
Options: a ) 14 , b ) 10 , c ) 8 , d ) 6 , e ) 4
Rationale: we are given children allergic to cashew nuts as 18 and not allergic to cashew nuts as 10 , so total = 10 + 18 = 28 . . . children allergic to both are 10 . . . 18 are allergic to cashew nuts , so and half or 28 / 2 = 14 are allergic to peanuts . . so children allergic to at least one of the two are 18 + 14 - 10 = 22 . . therefore children not allergic to any of the two are 28 - 22 = 6 answer : d
Answer: d
Problem: a train 1100 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 m , b ) 256 m , c ) 200 m , d ) 278 m , e ) 287 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1100 + x ) / 60 = 65 / 3 x = 200 m . answer : c"
Answer: c
Problem: the sum of number of boys and girls in a school is 300 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 75
Rationale: "we have x + x % of 300 = 300 x + x / 100 * 300 = 300 4 * x = 300 x = 75 answer is e"
Answer: e
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.82 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.55
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.82 = 3 * x - - > x = $ 0.55 . answer : e ."
Answer: e
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 162 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 45 % , e ) 72 %
Rationale: answer : d 162 ° divided by 360 ° equals 0.45 , therefore the sector is equal to 45 % of the total
Answer: d
Problem: 1100 boys and 700 girls are examined in a test ; 42 % of the boys and 30 % of the girls pass . the percentage of the total who failed is ?
Options: a ) 63.3 % , b ) 52.4 % , c ) 81.2 % , d ) 75.4 % , e ) 69.1 %
Rationale: total number of students = 1100 + 700 = 1800 number of students passed = ( 42 % of 1100 + 30 % of 700 ) = 462 + 210 = 672 number of failures = 1128 * 100 / 1800 = 190 / 3 % = 63.3 % answer is a
Answer: a
Problem: john makes $ 60 a week from his job . he earns a raise and nowmakes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17 % , d ) 17.2 % , e ) 18 %
Rationale: "increase = ( 10 / 60 ) * 100 = ( 1 / 6 ) * 100 = 16.66 % . b"
Answer: b
Problem: two heavily loaded sixteen - wheeler transport trucks are 690 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 120 , b ) 130 , c ) 150 , d ) 320 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 690 - 90 = 600 k ratio of speeds 9 : 8 - > 510 / 17 = 30 truck a = 90 + 30 * 9 = 360 truck b = 30 * 8 = 240 delta = 120 km answer a"
Answer: a
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 42 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.8 , d ) 14.82 , e ) 18.3
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 42 inch = ( 136 ã — 42 ) / 312 = 18.3 km answer : e"
Answer: e
Problem: on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 15 , c ) $ 23 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 105 dollars , while lana earned 82 dollars the difference is $ 23 and the answer is c ."
Answer: c
Problem: the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is :
Options: a ) 279 , b ) 283 , c ) 308 , d ) 318 , e ) 328
Rationale: "other number = ( 11 * 7700 ) / 275 = 308 . answer : c"
Answer: c
Problem: in measuring the sides of a rectangle , one side is taken 8 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %
Rationale: "let the sides of the rectangle be a and b . actual area of the rectangle without error = ab new side a ( 8 % in excess ) = a + 0.08 a = 1.08 a new side b ( 5 % in deficit ) = b - 0.05 b = 0.95 b area of the new rectangle = ( 1.08 a ) ( 0.95 b ) = ( 1.0260 ) ab say a = 1 and b = 1 area of the original rectangle = 1 area of the new rectangle = 1.026 change in the area calculation = . 026 error percentage in the area calculated = 2.6 % answer : e"
Answer: e
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 3200 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 4050 , e ) 2288
Rationale: "3200 * 9 / 8 * 9 / 8 = 4050 answer : d"
Answer: d
Problem: on a certain test , bill scored 20 more points than john , but half as many points as sue . if the sum of the scores of the 3 students was 160 points , how many points did bill receive ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 80 , e ) 100
Rationale: consider john ' s points as x so bill ' s points are x + 20 so sue ' s points are 2 x + 40 total of all three students is 4 x + 60 , but this total is given as 160 x = 25 so bill ' s points = 25 + 20 = 45 correct answer option b
Answer: b
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 2 : 3 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 99 : 61 , b ) 99 : 160 , c ) 61 : 160 , d ) 61 : 99 , e ) 99 : 160
Rationale: "vessel a = 300 gallons - - > milk = 120 , water = 180 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 495 , water 305 . the ratio = 495 / 305 - - > reduce by 5 = 99 / 61 . answer : a ."
Answer: a
Problem: a man swims downstream 45 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 10 , e ) 10.5
Rationale: "45 - - - 3 ds = 15 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 15 + 6 ) / 2 = 10.5 answer : e"
Answer: e
Problem: the product of two successive numbers is 1122 . which is the smaller of the two numbers ?
Options: a ) 34 , b ) 36 , c ) 33 , d ) 38 , e ) 31
Rationale: "c 33 from the given alternatives , 33 × 34 = 1122 ∴ smaller number = 33"
Answer: c
Problem: a library has an average of 630 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 305 , c ) 280 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 630 x 5 + 240 x 25 / 30 ) = 305 answer : option b"
Answer: b
Problem: the sale price of a trolley bag including the sale tax is rs . 1232 . the rate of sale tax is 10 % . if the shopkeeper has made a profit of 12 % , the cost price of the trolley bag is :
Options: a ) rs 1000 , b ) rs 1515 , c ) rs 1525 , d ) rs 1250 , e ) none of these
Rationale: "explanation : 110 % of s . p . = 1232 s . p . = rs . ( 1232 x 100 / 110 ) = rs . 1120 . c . p . = rs ( 100 / 112 x 1120 ) = rs 1000 answer : a"
Answer: a
Problem: rs 4000 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) rs 4000 , b ) rs 2800 , c ) rs 3800 , d ) rs 3500 , e ) rs 3100
Rationale: "explanation : average rate = ( 144 / 4000 ) * 100 = 3.6 ratio = 14 : 6 = 7 : 3 so , first part = ( 7 / 10 ) * 4000 = rs 2800 . answer : b"
Answer: b
Problem: a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 4.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "d = 25 * 60 + 4500 = 6000 m t = 6000 / 60 * 18 / 5 = 360 sec = 6 mins answer : d"
Answer: d
Problem: the only items of clothing at michelle ’ s boutique are 4 shirts , 8 pairs of pants and 18 ties . what is the probability of randomly selecting 2 ties out of all the items in michelle ’ s boutique ?
Options: a ) 51 / 145 , b ) 9 / 25 , c ) 3 / 5 , d ) 94 / 145 , e ) 5 / 6
Rationale: we have 4 shirts , 8 pairs of pants and 18 ties . i . e 30 items total ways of picking two items out of all = 30 c 2 = 435 total ways of picking two items out of all ties = 18 c 2 = 153 required probability = 153 / 435 = 51 / 145 answer : option a
Answer: a
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 26 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.26 ( 800 ) = 232 the answer is a ."
Answer: a
Problem: mary and mike enter into a partnership by investing $ 900 and $ 100 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1600 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3500 , b ) $ 3400 , c ) $ 3300 , d ) $ 3200 , e ) $ 3000
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 9 : 1 . i . e . , 90 % of 2 x would go to mary and 10 % of 2 x would go to mike . hence , mary would get ( 90 - 10 ) % of 2 x more than mike or 80 % of 2 x = $ 1600 i . e . , ( 60 / 100 ) * 2 x = 1600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : e"
Answer: e
Problem: if 63 percent of a class answered the first question on a certain test correctly , 49 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 22 % , b ) 24 % , c ) 26 % , d ) 28 % , e ) 32 %
Rationale: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 49 % - 17 % = 32 % . the answer is e ."
Answer: e
Problem: the speed of a boat in still water is 12 kmph . what is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 10 kmph
Rationale: "x = the speed of the stream ( 12 + x ) / ( 12 - x ) = 2 / 1 12 + x = 24 - 2 x 3 x = 12 x = 4 km / hour if the speed of the stream is 4 km / hour , then the ' downstream ' speed of the boat is 12 + 4 = 16 km / hour and the ' upstream ' speed of the boat is 12 - 4 = 8 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 8 = 16 km downstream and 2 x 16 = 32 km / hour upstream . answer : d"
Answer: d
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 2 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 9 , e ) 2 : 2
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : option b explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Problem: a birthday child reaches into a bag filled with toys ( 1 yo - yo , 1 ball , 1 whistle , and 1 box crayons ) . if the child randomly picks 3 toys , what is the probability the child will pick the yo - yo and a ball as two of the 3 toys ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 2 / 5
Rationale: combination formula : ncr = n ! / ( r ! ( n - r ) ! ) , where n is the population / set , and r is the sample / subset . total number possible = 4 c 3 - 4 ! / ( 3 ! ( 4 - 3 ) ! ) = 4 number yo - yo possible = 1 c 1 = 1 number ball possible = 1 c 1 = 1 number other possible = 2 c 1 = 2 probability formula : p ( a ) = ( number favorable outcomes ) / ( total number possible outcomes ) p ( yb ) = ( 1 c 1 ) ( 1 c 1 ) ( 2 c 1 ) / 4 c 3 = 2 / 4 = 1 / 2 answer : b
Answer: b
Problem: 3 investors , a , b , and c , divide the profits from a business enterprise in the ratio of 5 : 7 : 8 , respectively . if investor a earned $ 2500 , how much money did investors b and c earn in total ?
Options: a ) $ 4,000 , b ) $ 4,900 , c ) $ 7,500 , d ) $ 9,500 , e ) $ 10,500
Rationale: let profit for a = 5 x profit for b = 7 x profit for c = 8 x investor a earned = 2500 5 x = 2500 = > x = 500 total profit for b and c = 7 x + 8 x = 15 x therefore , 15 x = 15 * 500 = 7,500 answer c
Answer: c
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 580 ( before payroll deductions ) ?
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 580 x = 80 / 0.16 = 500 the answer is b ."
Answer: b
Problem: find the least number of complete years in which a sum of money put out at 15 % compound interest will be more than double of itself ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "5 years answer : a"
Answer: a
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.3 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.95 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: let the fixed charge of jim â € ™ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 3 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 3 = 2.25 + 9 * . 3 = 4.95 $ answer b
Answer: b
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 15 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 10 % . if ron imported a $ 15,000 imported car and ended up paying $ 1800 in taxes , what is the first tier ' s price level ?
Options: a ) $ 7000 , b ) $ 6500 , c ) $ 6050 , d ) $ 6000 , e ) $ 6100
Rationale: "let t be the tier price , p be total price = 15000 per the given conditions : 0.15 t + 0.10 ( p - t ) = 1800 0.15 t + 0.10 * 15000 - 0.10 t = 1800 0.05 t + 1500 = 1800 0.05 t = 1800 - 1500 = 300 t = 300 / 0.05 = 6000 answer d"
Answer: d
Problem: in what time will a train 90 meters long cross an electric pole , if its speed is 124 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.6 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 124 * ( 5 / 18 ) = 34 m / sec time = distance / speed = 90 / 34 = 2.6 seconds option d"
Answer: d
Problem: what is the rate percent when the simple interest on rs . 600 amount to rs . 160 in 4 years ?
Options: a ) 6.66 % , b ) 7.66 % , c ) 6.06 % , d ) 6.16 % , e ) 8.66 %
Rationale: "160 = ( 600 * 4 * r ) / 100 r = 6.66 % answer : a"
Answer: a
Problem: find two integers , neither of which ends in a zero , and whose product is exactly 10 , 000,000
Options: a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 128 and 78,125
Rationale: "10 , 000,000 = 10 ^ 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 7 ) x ( 5 ^ 7 ) = 128 x 78125 so the numbers are 128 and 78,125 answer : e"
Answer: e
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 3000 as profit , what is their total profit ?
Options: a ) 21000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 3000 = > total profit = 3000 * 7 = 21000 . answer : option a"
Answer: a
Problem: a person crosses a 1080 m long street in 10 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 6.4 , c ) 4.8 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 10 x 60 ) m / sec = 1.8 m / sec . converting m / sec to km / hr = 1.8 x ( 18 / 5 ) km / hr = 6.4 km / hr . answer : b"
Answer: b
Problem: exactly 12 % of the reporters for a certain wire service cover local politics in country x . if 40 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 12 reporters cover local politics . now , as 40 % of the reporters who cover all politics do not cover local politics then the rest 60 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 60 % of them equal to 12 ( # of reporters who cover local politics ) : 0.6 x = 12 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."
Answer: d
Problem: a man can row his boat with the stream at 6 km / h and against the stream in 3 km / h . the man ' s rate is ?
Options: a ) 1.5 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 6 us = 3 s = ? s = ( 6 - 3 ) / 2 = 1.5 kmph answer : a"
Answer: a
Problem: ronald and elan are working on an assignment . ronald takes 6 hours to type 32 pages on a computer , while elan takes 5 hours to type 40 pages . how much time will they take , working together on two different computers to type an assignment of 110 pages ?
Options: a ) 3 hours , b ) 6 hours , c ) 4 hours , d ) 8 hours , e ) 10 hours
Rationale: number of pages typed by ronald in one hour = 32 / 6 = 16 / 3 number of pages typed by elan in one hour = 40 / 5 = 8 number of pages typed by both in one hour = ( ( 16 / 3 ) + 8 ) = 40 / 3 therefore , time taken by both to type 110 pages = 110 x 3 / 40 = 8 hours . answer : d
Answer: d
Problem: an error 2 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is ?
Options: a ) 4.04 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 a )"
Answer: a
Problem: the difference between a number and its two - fifth is 510 . what is 50 % of that number ?
Options: a ) 426 , b ) 425 , c ) 427 , d ) 428 , e ) 429
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 50 % of 850 = 425 . answer : b"
Answer: b
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 46 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 54 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 45 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.46 m = = > revenue = price x quantity = 0.54 ( m + w ) = = > profit = 0.54 ( m + w ) - 0.46 m = 0.2 * ( 0.46 m ) [ 20 % of cost ] = = > 0.54 m + 0.54 w - 0.46 m = 0.092 m = = > 0.012 m = 0.54 w = = > m / w = 0.54 / 0.012 = 45 - - or - - w / m = 1 / 45 d is correct ."
Answer: d
Problem: a train 441 m long can cross an electric pole in 21 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 76 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: length = speed * time speed = l / t s = 441 / 21 s = 21 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 76 kmph answer : c
Answer: c
Problem: a can run 4 times as fast as b and gives b a start of 75 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 100 m , d ) 65 m , e ) 75 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 75 m he gains 75 * ( 4 / 3 ) i . e 100 m answer : c"
Answer: c
Problem: when the price of an article was reduced by 15 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % increase , b ) 44 % decrease , c ) 53 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: if n items are sold for $ p each , revenue is $ np . if we reduce the price by 15 % , the new price is 0.85 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.85 p ) ( 1.8 n ) = 1.53 np , which is 1.53 times the old revenue , so is 53 % greater . answer : c
Answer: c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 64 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 82 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 64 % is one st . dev , then on either side of m we have 64 / 2 = 32 % . so , 32 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 32 = 82 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 82 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it d"
Answer: d
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 27 sec . the length of each train is ?
Options: a ) 50 , b ) 37.5 , c ) 27 , d ) 28 , e ) 21
Rationale: let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 27 = 25 / 9 = > x = 37.5 . answer : b
Answer: b
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 7 more than 1 / 4 of the fine and peter paid $ 7 less than 1 / 3 of the fine , leaving pay $ 12 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 65 , b ) $ 55 , c ) $ 50 , d ) $ 60 , e ) $ 45
Rationale: call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 7 ] + [ ( 1 / 3 ) f – 7 ] + [ ( 1 / 2 ) f – 12 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 12 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 144 12 f = 13 f – 144 – f = – 144 f = 144 well , if the fine cost $ 144 , then sam paid the part not covered by joe or peter . half the fine is $ 72 , and sam paid $ 12 less than this : $ 60 . answer = d
Answer: d
Problem: if two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "the projectiles travel a total of 999 km per hour . the time to meet is 1998 / 999 = 2 hours = 120 minutes the answer is d ."
Answer: d
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5650 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5650 = 21150 exp in % = 100 - 10 = 90 % , 21150 = 90 % saving = 10 % = 21150 x 10 / 90 = rs . 2350 answer : b
Answer: b
Problem: a large box contains 15 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 375 , d ) d ) 450 , e ) e ) 690
Rationale: "the only thing you have to do is a simple multiply we have : 15 * 25 = 375 correct answer is : c ) 375"
Answer: c
Problem: an assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72
Rationale: "the time to produce the first 60 cogs is 60 / 90 = 2 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 5 / 3 ) hours = 72 cogs per hour . the answer is e ."
Answer: e
Problem: there has been successive increases of 25 % and then 15 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 30 % , b ) 50 % , c ) 66.66 % , d ) 15 % , e ) 75 %
Rationale: let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.15 * 1.25 * p = x * p y = x / ( 1.15 * 1.25 ) which is about 0.7 x which is a decrease of about 30 % . the answer is a .
Answer: a
Problem: a train covers a distance of 12 km in 5 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the train = 40 * 6 = 240 m . answer : c"
Answer: c
Problem: ab + ba ___ 202 in the addition problem above , a and b represent digits in two different two - digit numbers . what is the sum of a and b ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 20 , e ) 14
Rationale: two ways to do it . . 1 ) straight logic . . only 20 fits in . . d
Answer: d
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 29 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 227 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 29 : x = > x = { \ color { blue } \ frac { 29 \ times 1 } { 0.128 } } = > x = 226.56 so time will be approx 227 seconds answer : d"
Answer: d
Problem: the sum of three consecutive even numbers is 36 , find the first number ?
Options: a ) 21 , b ) 18 , c ) 12 , d ) 16 , e ) 10
Rationale: "let the first number be n let the second number be n + 2 let the third number be n + 4 n + n + 2 + n + 4 = 36 combine like terms : 3 n + 6 = 36 3 n = 36 - 6 3 n = 30 3 n = 30 n = 10 n + 2 = 12 n + 4 = 16 the first number is 10 answer : e"
Answer: e
Problem: 30 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 3 : 4 ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 30 + x = ( 4 / 7 ) * ( 30 + x ) 420 + 35 x = 600 + 20 x 15 x = 180 x = 12 the answer is c ."
Answer: c
Problem: . for the fifa world cup , paul the octopus has been predicting the winner of each match with amazing success . it is rumored that in a match between 2 teams a and b , paul picks a with the same probability as a ’ s chances of winning . let ’ s assume such rumors to be true and that in a match between ghana and bolivia ; ghana the stronger team has a probability of 2 / 3 of winning the game . what is the probability that paul will correctly pick the winner of the ghana - bolivia game ?
Options: a ) 59 , b ) 88 , c ) 77 , d ) 26 , e ) 18
Rationale: the probability that paul correctly picks the winner = ( a ' s chances of winning ) x ( pauls picking the winner corectly ) + ( a ' s chances of loosing ) x ( paul picks wrongly ) = 23 × 23 + 13 × 13 = 59 answer : a
Answer: a
Problem: john has 10 pairs of matched socks . if he loses 5 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3
Rationale: because we have to maximize the pair of matched socks , we will remove 2 pairs ( 4 socks ) out of 10 pairs 1 sock from the 3 th pair . thus the no of matching socks pair remaining = 10 - 3 = 7 answer b
Answer: b
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 18 } + { 16 } ?
Options: a ) 23 , b ) 20 , c ) 11 , d ) 19 , e ) 2
Rationale: soln : { 18 } + { 16 } = 18 * { 16 } + { 16 } = 19 * { 16 } answer : d
Answer: d
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 125 billion gallons to 150 billion gallons . if the storm increased the amount of water in the reservoirs to 80 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 9 , b ) 14 , c ) 25 , d ) 30 , e ) 44
Rationale: after the reservoir is filled to 150 gallons the amount of water is at 80 % - which means that 20 % of the reservoir is empty . to figure out what that 20 % is approximate : 150 gallons / 80 percent = x gallons / 20 percent , therefore , x = 37.5 gallons , answer choices a , b , c , d are below 37.5 . we know that the reservoir must be short more than 37.5 gallons , therefore , the only possible choice is e .
Answer: e
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 50 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.5 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.5 * 52 = ~ 45 , so percent of people who are less than 25 years old is 100 - 45 = 55 . answer : b ."
Answer: b
Problem: if ( a – b ) is 7 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 7 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 7 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 7 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 7 = ( c – a ) – 3 = > 2 ( a – c ) = 4 = > ( a – c ) = 2 answer : b"
Answer: b
Problem: a person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes . if field has a length that is twice its width , find the area of the field in square meters .
Options: a ) 20,000 square meters
b ) 10,000 square meters
c ) 30,000 square meters
d ) 40,000 square meters
e ) 50,000 square meters
Rationale: let us first find the distance d jogged distance = rate * time = ( 12 km / hr ) * 30 minutes = ( 12 km / hr ) * 0.5 hr = 6 km the distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to 6 km / 10 = 0.6 km = 0.6 * 1000 meters = 600 meters let l and w be the length and width of the field . the length is twice the width . hence l = 2 w the perimeter is 600 meters and is given by 2 ( l + w ) = 600 substitute l by 2 w 2 ( 2 w + w ) = 600 simplify and solve for w 4 w + 2 w = 600 6 w = 600 w = 100 find l l = 2 w = 200 find the area a of the rectangle a = l * w = 200 * 100 = 20,000 square meters correct answer a
Answer: a
Problem: a man is 27 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: let the son ' s present age be x years . then , man ' s present age = ( x + 27 ) years . ( x + 27 ) + 2 = 2 ( x + 2 ) x + 29 = 2 x + 4 = > x = 25 . answer : b
Answer: b
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 65 , b ) 68 , c ) 70 , d ) 77 , e ) 80
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 2 x 60 ) = 30 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 30 x + 20 x + 15 x + 12 x ) = 77 x . for minimum number of pencils x = 1 . the person should have atleast 77 pencils . d )"
Answer: d
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 63 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 63 books , thus 76 - 63 = 12 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 40 . answer : d ."
Answer: d
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have no faces coloured ?
Options: a ) 24 , b ) 8 , c ) 16 , d ) 0 , e ) 4
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having only one faces coloured = ( x - 2 ) ^ 3 here , x = side of big cube / side of small cube x = 4 / 1 x = 4 required number = ( 4 - 2 ) ^ 3 = 8 answer : b"
Answer: b
Problem: [ ( 3.242 x 16 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 0.051872 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 16 = 5.1872 now divide 5.1872 by 100 so , 5.1872 ÷ 100 = 0.051872 ∴ shift the decimal two places to the left as 100 correct option : c"
Answer: c
Problem: sabrina is contemplating a job switch . she is thinking of leaving her job paying $ 90000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission for each sale made . if each of her sales is for $ 1500 , what is the least number of sales she must make per year if she is not to lose money because of the job change ?
Options: a ) 57 , b ) 177 , c ) 178 , d ) 377 , e ) 200
Rationale: lets say she sales x items so her commission will be : x * 1500 * 15 / 100 = 225 x salary difference is : 90000 - 45000 = 45000 so commission must at least be equal to salary difference i . e . x = 45000 / 225 = 200 ( approx ) . hence answer is e
Answer: e
Problem: if ( 1 – 1.25 ) n = 2 , then n =
Options: a ) − 400 , b ) − 140 , c ) − 8 , d ) 4 , e ) 400
Rationale: "( 1 – 1.25 ) n = 2 simplify to get : - 0.25 n = 2 rewrite as ( - 1 / 4 ) n = 2 multiply both sides by - 4 to get : n = - 8 answer : c"
Answer: c
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 6 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 196
Rationale: "by the question , the equation would be 150 p - 86 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 196 . answer e for me ."
Answer: e
Problem: an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 8 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 10
Rationale: 8 / 16 * 2 / 3 = 1 / 3 the answer is b .
Answer: b
Problem: if a ã — b = 2 a - 3 b + ab , then 3 ã — 4 + 4 ã — 3 is equal to :
Options: a ) 17 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "explanation : 3 ã — 4 + 4 ã — 3 = ( 2 ã — 3 - 3 ã — 4 + 3 ã — 4 ) + ( 2 ã — 4 - 3 ã — 3 + 4 ã — 3 ) = ( 6 + 8 - 9 + 12 ) = 17 . answer : a"
Answer: a
Problem: the simple interest on a sum of money will be rs . 1000 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 ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 2000
Rationale: "p - - - 10 - - - - 1000 p - - - 5 - - - - - 500 3 p - - - 5 - - - - - 1500 - - - - - - = > 2000 answer : e"
Answer: e
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 8 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 54 , d ) 22 : 56 , e ) 52 : 51
Rationale: let c . p . of the article be rs . x . then , required ratio = 104 % of x / 108 % of x = 104 / 108 = 52 / 54 = 52 : 54 answer : c
Answer: c
Problem: if shares of two persons in profits are rs . 700 and rs . 300 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 7 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 700 / 300 = 7 : 3 answer : c"
Answer: c
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 160 square feet and its length is 6 feet longer than its width . if the uniform width between the rug and room is 6 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 456 , c ) 40 , d ) 46 , e ) 104
Rationale: "rug ' s area = 160 which is ( x ) x ( 6 + x ) = 160 so x = 10 rug maintains a uniform distance of 6 feet so room has dimension 10 + 12 and 16 + 12 i . e . 22 and 28 area of room 22 x 28 = 616 area covered is 160 so uncovered area is 616 - 160 = 456 ( answer b )"
Answer: b
Problem: an advertising agency finds that , of its 180 clients , 115 use television , 110 use radio and 130 use magazines . also , 85 use television and magazines , 75 use television and radio , 95 use radio and magazines . how many use all the 3 ?
Options: a ) 56 , b ) 70 , c ) 90 , d ) 98 , e ) 80
Rationale: total = 180 television = 115 radio = 110 magazine = 130 all the three = 180 - 115 - 110 - 130 + 85 + 75 + 95 = 80 answer e
Answer: e
Problem: 8 friends met for lunch at an expensive restaurant , and everyone decided to contribute equally to the total bill of $ 290 . if one of the friends had a coupon for 29 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) $ 90 , b ) $ 70 , c ) $ 45 , d ) $ 37 , e ) $ 25
Rationale: 290 * 0,29 = 84 290 - 84 = 206 206 / 8 = 25 answer e
Answer: e
Problem: for a right angle triangle the hypotenuse is 5 and base is 3 . what is the area of the triangle ?
Options: a ) 6
b ) 7
c ) 8
d ) 9
e ) 10
Rationale: as we know that for a right angle triangle the are is 1 / 2 * base * height we know the base = 3 we need to calculate the height hypotenuse = h = 5 base = b = 3 height = c = ? as per pythagoras h ^ 2 = b ^ 2 + c ^ 2 5 ^ 2 = 3 ^ 2 + c ^ 2 25 = 9 + c ^ 2 c ^ 2 = 25 - 9 c ^ 2 = 16 c = 4 height = 4 area = 1 / 2 * base * height = 1 / 2 * 3 * 4 = 6 square units ans : a
Answer: a
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 210 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 560
Rationale: "easy 560 is the answer . 3 / 4 ( x / 2 ) = 210 x = 210 * 8 / 3 = 560 . answer e"
Answer: e
Problem: a train 1000 m long can cross an electric pole in 200 sec and then find the speed of the train ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "length = speed * time speed = l / t s = 1000 / 200 s = 5 m / sec speed = 5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 18 kmph answer : d"
Answer: d
Problem: joshua and jose work at an auto repair center with 6 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 28 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 8 probability of chosing jose second = 1 / 7 total = 1 / 56 probability of chosing jose first = 1 / 8 probability of chosing josh second = 1 / 7 total = 1 / 56 final = 1 / 56 + 1 / 56 = 1 / 28 c"
Answer: c
Problem: what is the units digit of 63 ^ 3 * 17 ^ 3 * 49 ^ 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 63 ^ 3 is the units digit of 3 * 3 * 3 = 27 which is 7 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 49 ^ 3 is the units digit of 9 * 9 * 9 = 729 which is 9 . the units digit of 7 * 3 * 9 = 189 is 9 . the answer is e ."
Answer: e
Problem: what is the probability of randomly selecting an arrangement of the letters of the word ` ` mediterranean ' ' in which the first letter is e and the last letter is r ?
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Rationale: there are 13 letters in mediterranean , out of which e appears thrice , n appears twice , a appears twice , and r appears twice . the number of arrangements of mediterranean is therefore 13 ! / 3 ! 2 ! 2 ! 2 ! the number of arrangements in which the first letter is e and the last letter is r is 11 ! / 2 ! 2 ! 2 ! ( we are left with 11 letters out of which e appears twice , n appears twice and a appears twice ) . p = ( 11 ! / 2 ! 2 ! 2 ! ) / ( 13 ! / 3 ! 2 ! 2 ! 2 ! ) = 11 / ! 2 ! 2 ! 2 ! ∗ 3 ! 2 ! 2 ! 2 ! / 13 ! = 3 ! / 12 ∗ 13 = 1 / 26 answer : c .
Answer: c