Cheukting/mathqa huggingface dataset:
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 17 nor 21 ?
Options: a ) 4,514 , b ) 4,480 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 17 5000 / 17 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 17 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 17 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4480 answer b ."
Answer: b
Question (physics): 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 2 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 40 , d ) 60 , e ) 90
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 2 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 2 * ( 2 / 3 ) ) days = > 90 days answer : e"
Answer: e
Question (general): if x and y are positive integers and 42 x = 56 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 63 , d ) 196 , e ) 252
Rationale: "42 x = 56 y = > x / y = 4 / 3 = > 3 x = 4 y 3 ( 14 ) = 4 ( 14 ) = > x * y = 196 e"
Answer: e
Question (physics): a train 150 m long is running with a speed of 98 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going
Options: a ) 5 sec , b ) 6 sec , c ) 7 sec , d ) 8 sec , e ) 9 sec
Rationale: "explanation : speed of the train relative to man = ( 98 - 8 ) kmph = ( 90 × 5 / 18 ) m / sec = 25 m / sec time taken by the train to cross the man i = time taken by it to cover 150 m at 25 m / sec = 150 × 1 / 25 sec = 6 sec answer : option b"
Answer: b
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 36 and 56 ?
Options: a ) 512 , b ) 508 , c ) 451 , d ) 516 , e ) 451
Rationale: "prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 56 = 2 x 2 x 2 x 7 gcf = 4 lcm = 504 sum = 508 ans : b"
Answer: b
Question (general): vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 7225 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2500 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 7225 = x = 7225 / 2.89 = 2500 therefore , amount invested by raghu is rs . 2500 . answer : c"
Answer: c
Question (physics): the difference between two parallel sides of a trapezium is 4 cm . perpendicular distance between them is 10 cm . if the area of the trapezium is 250 cm 2 find the lengths of the parallel side
Options: a ) 27 , 23
b ) 25 , 25
c ) 24 , 26
d ) 23 , 29
e ) 24 , 45
Rationale: explanation : let the two parallel sides of the trapezium be a cm and b cm . then , a - b = 4 - - - - - - ( 1 ) and , ( 1 / 2 ) x ( a + b ) x 10 = 475 = > ( a + b ) = ( ( 250 x 2 ) / 10 ) = > a + b = 50 - - - - - - - ( 2 ) solving 1 and 2 , we get : a = 27 , b = 23 so , the two parallel sides are 27 cm and 23 cm . answer : option a
Answer: a
Question (general): in a box of 8 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 / 12 , b ) 5 / 14 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: "first , there are 6 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 8 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 6 c 3 / 8 c 3 = 20 / 56 = 5 / 14 answer is b"
Answer: b
Question (geometry): what is the area of square field whose side of length 17 m ?
Options: a ) 225 , b ) 777 , c ) 266 , d ) 289 , e ) 261
Rationale: "17 * 17 = 289 sq m answer : d"
Answer: d
Question (general): a sum is divided between a and b in the ratio of 1 : 2 . a purchased a car from his part , which depreciates 14 2 / 7 % per annum and b deposited his amount in a bank , which pays him 20 % interest per annum compounded annually . by what percentage will the total sum of money increase after two years due to this investment pattern ( approximately ) .
Options: a ) 22.48 % , b ) 20.48 % , c ) 24.48 % , d ) 25.48 % , e ) 26.48 %
Rationale: let the total money = 300 a ' s part = 100 b ' s part = 200 after 2 years a ' s part = 73.46 ( as it depreciates by 14.29 % per annum ) after 2 years b ' s part = 288 ( using the compound interest formula , a = p ( 1 + r / n ) ^ nt ) , where p = 200 , r = 0.2 , n = 1 , t = 2 ) so , after 2 years total amount = 361.46 therefore % increase in money = ( 361.46 - 300 ) * 100 / 300 = 20.48 % answer : b
Answer: b
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph ?
Options: a ) 54 sec , b ) 35 sec , c ) 25 sec , d ) 45 sec , e ) 24 sec
Rationale: "d = 100 + 250 = 350 s = 36 * 5 / 18 = 10 mps t = 350 / 10 = 35 sec answer : b"
Answer: b
Question (physics): two trains of length 100 m and 160 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 18 sec , b ) 70 sec , c ) 13 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 160 = 260 m . the time required = d / s = 260 / 20 = 13 sec . answer : c"
Answer: c
Question (physics): pipe a fills a tank in 30 minutes . pipe b can fill the same tank 5 times as fast as pipe a . if both the pipes were kept open when the tank is empty , how much time will it take for the tank to overflow ?
Options: a ) 4 mins , b ) 6 mins , c ) 5 mins , d ) 3 mins , e ) 7 mins
Rationale: "let the total capacity of tank be 90 liters . capacity of tank filled in 1 minute by a = 3 liters . capacity of tank filled in 1 minute by b = 15 liters . therefore , capacity of the tank filled by both a and b in 1 minute = 18 liters . hence , time taken by both the pipes to overflow the tank = 90 / 18 = 5 minutes . answer : c"
Answer: c
Question (general): the average age of a class of 15 students is 10 years . if the age of the teacher be included , then the average increased by 1 year . find the age of the teacher ?
Options: a ) 22 , b ) 23 , c ) 26 , d ) 29 , e ) 31
Rationale: "total age of 15 persons = 15 * 10 = 150 years average age of 16 persons = 11 years total age of 16 persons = 16 * 11 = 176 years age of the teacher = 176 - 150 = 26 years answer is c"
Answer: c
Question (general): the sum of digits of a two digit number is 12 , the difference between the digits is 4 . find the number
Options: a ) 84 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 12 , x - y = 4 adding these 2 x = 16 = > x = 8 , y = 4 . thus the number is 84 answer a"
Answer: a
Question (gain): find number which is 80 % less than 80 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 26 , e ) 16
Rationale: "explanation : 80 % less is 20 % of the given number therefore , 20 % of 80 is 16 . answer : e"
Answer: e
Question (general): there are some birds in cage , 1 / 3 rd fly away . then 2 / 5 th of the remaining left the cage , then 2 / 3 rd of the remaining left the cage . at last 8 were remaining . how many birds were in total ?
Options: a ) 60 , b ) 27 , c ) 28 , d ) 26 , e ) 91
Rationale: sol : if x birds were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 8 x × 2 / 3 × 3 / 5 × 1 / 3 = 8 x = 60 answer : a
Answer: a
Question (physics): x is 3 times as fast as y and working together , they can complete a work in 20 days . in how many days can y alone complete the work ?
Options: a ) 11 days , b ) 80 days , c ) 13 days , d ) 15 days , e ) 19 days
Rationale: x = 3 y x + y = 3 y + y = 4 y these 4 y people together can do the work in 20 days , which means y can alone do the work in 4 * 20 = 80 days . answer : b
Answer: b
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 9 m wide at the top and 7 m wide at the bottom and the area of cross - section is 560 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 70 , d ) 80 , e ) 71
Rationale: "1 / 2 * d ( 9 + 7 ) = 560 d = 70 answer : c"
Answer: c
Question (general): on dividing 199 by a number , the quotient is 11 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 199 - 1 ) / 11 = 198 / 11 = 18 d )"
Answer: d
Question (other): of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak hindi and 20 % of the diplomats spoke neither french nor hindi . if 10 % of the diplomats spoke both french and hindi , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer"
Answer: d
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 59 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.20 $ , b ) 380.20 $ , c ) 421.20 $ , d ) 451.20 $ , e ) 481.20 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 59 ) = 481.20 hence answer will be ( e )"
Answer: e
Question (general): what is the nearest no . to 2304 which is divisible by 21 ?
Options: a ) 2289 , b ) 2310 , c ) 2333 , d ) 2456 , e ) 2309
Rationale: remainder when 2304 is divided by 21 = 15 so , no . should added to make 15 to 21 = 6 no . = 2304 + 6 = 2310 answer b
Answer: b
Question (gain): the population of a town is 10000 . it increases annually at the rate of 25 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 14500 , d ) 15625 , e ) 14700
Rationale: formula : 10000 × 125 / 100 × 125 / 100 = 15625 answer : d
Answer: d
Question (general): when asked what the time is , a person answered that the amount of time left is 4 / 8 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 4 pm , d ) 8 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 4 / 8 x ⇒ x = 20 time is 4 pm answer : c"
Answer: c
Question (general): if x and y are integers , what is the least positive number of 24 x + 20 y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: 24 x + 20 y = 4 ( 6 x + 5 y ) which will be a minimum positive number when 6 x + 5 y = 1 . 6 ( 1 ) + 5 ( - 1 ) = 1 then 4 ( 6 x + 5 y ) can have a minimum positive value of 4 . the answer is c .
Answer: c
Question (general): of 25 applicants for a job , 14 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 25 - 3 = 22 aub = a + b - aib aib = 18 + 14 - 22 = 10 answer b"
Answer: b
Question (physics): the sector of a circle has radius of 28 cm and central angle 90 o . find its perimeter ?
Options: a ) 100 cm , b ) 85 cm , c ) 75 cm , d ) 95 cm , e ) 110 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 90 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 28 ) = 44 + 56 = 100 cm answer : a"
Answer: a
Question (physics): jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . [ ( 2 - 1 ) / 1 ] * 100 % = 100 % answer : c"
Answer: c
Question (general): 3 * 11 + 3 * 12 + 3 * 15 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 151
Rationale: "we have : 3 * 11 = 33 3 * 12 = 36 3 * 15 = 45 all of this is : ( 33 + 36 + 45 ) + 11 = 114 + 11 = 125 correct answer a"
Answer: a
Question (physics): one pump drains one - half of a pond in 8 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: first pump drains 1 / 2 of the tank in 8 hours so 16 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 16 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 16 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 16 + 1 / a ) = 1 / 2 solving u get a = 16 / 15 = 1.1 hence answer is b
Answer: b
Question (general): there are 2 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 4 _ 3 _ 2 _ 1 r _ r _ b _ b so . . 4 ! / number of repeated letters ( 2 ! ) ( 2 ! ) = 6 ans : d"
Answer: d
Question (physics): the speed of a car is 50 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 85 kmph , c ) 55 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 55 + 60 ) / 2 = 55 kmph answer : c"
Answer: c
Question (physics): the top and bottom of a tower were seen to be at angles of depression 30 ° and 60 ° from the top of a hill of height 100 m . find the height of the tower
Options: a ) 64.67 m , b ) 66.67 m , c ) 68.67 m , d ) 56.67 m , e ) 46.67 m
Rationale: by making a diagram ac represents the hill and de represents the pole given that ac = 100 m anglexad = angleadb = 30 ° ( ∵ ax | | bd ) anglexae = angleaec = 60 ° ( ∵ ax | | ce ) let de = h then , bc = de = h , ab = ( 100 - h ) ( ∵ ac = 100 and bc = h ) , bd = ce tan 60 ° = acce = > 3 √ = 100 ce = > ce = 1003 √ - - - ( 1 ) tan 30 ° = abbd = > 13 √ = 100 − hbd = > 13 √ = 100 − h ( 1003 √ ) ( ∵ bd = ce and substituted the value of ce from equation 1 ) = > ( 100 − h ) = 13 √ × 1003 √ = 1003 = 33.33 = > h = 100 − 33.33 = 66.67 m i . e . , the height of the pole = 66.67 m answer : b
Answer: b
Question (general): the age of the daughter is same as the digit in the mother ' s age , but in reverse order . in thirteen years mother will be twice as old as daughter will be then . what is the difference in their current age ?
Options: a ) 15 , b ) 23 , c ) 27 , d ) 46 , e ) 32
Rationale: daughter ' s age = 10 x + y so mother ' s age = 10 y + x . . after 13 years , 10 x + y + 13 = 2 * ( 10 y + x + 13 ) . . . . so 13 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 4 . . . so ages are 41 and 14 and ans as found correctly by u is c . . 27
Answer: c
Question (physics): working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel four times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 4 and w = 4 s then we have 1 / ( 4 * s ) + 1 / s = 1 / 4 < = > 5 / ( 4 * s ) = 1 / 4 < = > s = 5 ans : c"
Answer: c
Question (geometry): a larger cube has 125 cubic inch as a volume and in the cube there are 125 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 125 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 600 , c ) 81 , d ) 108 , e ) 120
Rationale: "volume of larger cube = 125 = 5 ^ 3 side of larger cube = 5 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 5 ^ 2 = 150 surface area of 27 smaller cubes = 125 * 6 * 1 = 750 difference = 750 - 150 = 600 answer : b"
Answer: b
Question (physics): the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 12 , find the other ?
Options: a ) 100 , b ) 600 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 12 = 600 answer is b"
Answer: b
Question (other): if below equation are true 24 $ 6 = 64 35 $ 5 = 87 63 $ 7 = 99 by using same logic what is the value of the below question 88 $ 8 = ?
Options: a ) 1621 , b ) 1711 , c ) 1611 , d ) 1511 , e ) 1311
Rationale: correct answer : c the number on the right side is formed as ( sum of digits of the 1 st number ) no 1 / no 2 ex : 35 $ 5 = 87 ( 3 + 5 = 8 ) ( 35 / 5 = 7 ) 63 $ 7 = 99 ( 6 + 3 = 9 ) ( 63 / 7 = 9 )
Answer: c
Question (general): the average weight of 10 persons increases by 3.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) 97 kg , e ) none
Rationale: "solution total weight increased = ( 10 x 3.2 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer d"
Answer: d
Question (general): the average of runs of a cricket player of 10 innings was 37 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 81 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 37 so , total = average x no . of innings = 37 x 10 = 370 . now increase in avg = 4 runs . so , new avg = 37 + 4 = 41 runs total runs = new avg x new no . of innings = 41 x 11 = 451 runs made in the 11 th inning = 451 - 370 = 81 answer : b"
Answer: b
Question (gain): a , b , and c started a partnership business by investing $ 45,000 , $ 63,000 , and $ 72,000 respectively . at the end of the year , the profit was distributed among them . if c ' s share of profit is $ 24,000 , what is the total profit ?
Options: a ) $ 48,000 , b ) $ 52,000 , c ) $ 56,000 , d ) $ 60,000 , e ) $ 64,000
Rationale: a : b : c = 45000 : 63000 : 72000 which is a ratio of 5 : 7 : 8 . let the total profit be x . x * 8 / 20 = 24000 x = 24000 * 20 / 8 = 60,000 . the answer is d .
Answer: d
Question (general): what will be the vulgar fraction of 0.75
Options: a ) 3 / 5 , b ) 3 / 4 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.75 = 75 / 100 = 3 / 4 option b"
Answer: b
Question (general): a company decreased the price of its main product by 75 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 1.33 , b ) 2.33 , c ) 3.33 , d ) 4.33 , e ) 1.45
Rationale: "for the total revenue to remain the same when the price is 3 / 4 , the number of products sold must 3 / 4 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 75 % = 1.33 answer : a"
Answer: a
Question (general): a ' s speed is 15 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?
Options: a ) 35 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %
Rationale: first calculate the distance , b has covered with his speed in the time , in which a reached 80 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.75 ) = 0.65 % ( which means b would have covered 0.65 of the race length during the time in which a has covered 0.75 of the race length . therefore to win , b needs a headstart of ( 1 - 0.65 = ) 0.35 of the race length . so the answer is a
Answer: a
Question (general): company c sells a line of 20 products with an average retail price of $ 1200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000
Rationale: the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b .
Answer: b
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (general): 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