regisss/math_qa huggingface dataset:
Problem: a part - time employee whose hourly wage was increased by 15 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9 , b ) 13.04 , c ) 10 , d ) 11 , e ) 12
Rationale: "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.15 x now we need to find number of hours worked so that x * y = 1.15 x * z i . e z = 1 / 1.15 y % decrease = ( y - 1 / 1.15 y ) / y * 100 = 13.04 % thus my answer is b ."
Answer: b
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , how much r will receive ?
Options: a ) 300 , b ) 600 , c ) 900 , d ) 800 , e ) 500
Rationale: "let p ' s capital be p , q ' s capital be q , and r ' s capital be r then 4 p = 6 q = 10 r 2 p = 3 q = 5 r ⋯ ( a ) from ( a ) , q = 2 p / 3 ⋯ ( 1 ) r = 2 p / 5 ⋯ ( 2 ) p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 × 6 / 31 = 150 × 6 = 900 answer is c ."
Answer: c
Problem: a 260 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 240 mts , b ) 270 mts , c ) 260 mts , d ) 250 mts , e ) none of these
Rationale: explanation : relative speed = 120 + 80 = 200 km / hr . = 200 x 5 / 18 = 500 / 9 m / sec . let the length of the other train be l mts . then , ( l + 260 ) / 9 = 500 / 9 = > l = 240 mts . answer is a
Answer: a
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers r are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes r in this range . answer : a ."
Answer: a
Problem: 25 people went to a hotel for combine dinner party 15 of them spent rs . 5 each on their dinner and rest spent 4 more than the average expenditure of all the 25 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 158.25 , e ) none of these
Rationale: "solution : let average expenditure of 25 people be x . then , 25 x = 15 * 5 + 10 * ( x + 4 ) ; or , 25 x = 15 * 5 + 10 x + 20 ; or , x = 6.33 ; so , total money spent = 6.33 * 25 = rs . 158.25 . answer : option d"
Answer: d
Problem: find the number of divisors of 1080 excluding the divisors which are perfect squares .
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: 1080 = 2 ^ 3 * 3 ^ 3 * 5 ^ 1 total no . of divisors = ( 3 + 1 ) * ( 3 + 1 ) * ( 1 + 1 ) = 32 only 4 divisors 1 , 2 ^ 2 = 4 , 3 ^ 2 = 9 & 2 ^ 2 * 3 ^ 2 = 36 are perfect squares so , number of divisors excluding perfect squares divisors = 32 - 4 = 28 answer : a
Answer: a
Problem: line q has the equation 5 y – 3 x = 60 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "5 y - 3 x = 60 and so y = 3 x / 5 + 12 when x = 0 , then y = 12 . when y = 0 , then x = - 20 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 20 , 0 ) , 0 = - 5 ( - 20 ) / 3 + c the y - intercept is c = - 100 / 3 < - 33 . thus the perpendicular line s can have y - intercepts from - 33 up to 11 . the number of possible lines is 33 + 11 + 1 = 45 the answer is c ."
Answer: c
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.70 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 357 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.7 = $ 357 answer b"
Answer: b
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number y of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "y = 7 is the correct answer . good solution buneul . b"
Answer: b
Problem: walking at 5 / 6 of its usual speed , a train is 10 minutes too late . what is usual time to cover the journey ?
Options: a ) 70 minutes , b ) 2 hours , c ) 2 / 3 hours , d ) 5 / 6 hours , e ) 85 minutes
Rationale: "et speed be s and time to cover the journey be t s * t = d ( distance of journey ) - - - 1 now as per the question stem we have ( 5 / 6 ) s * ( t + 10 ) = d - - - - 2 equating value of d from ( 1 ) in ( 2 ) we get t = 50 mins or 5 / 6 hrs . answer : d"
Answer: d
Problem: a fruit seller sells mangoes at the rate of rs . 6 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 7.41 , b ) rs 9.81 , c ) rs 10.41 , d ) rs 11.81 , e ) none of these
Rationale: "explanation : 85 : 6 = 105 : x x = ( 6 × 105 / 85 ) = rs 7.41 option a"
Answer: a
Problem: the salaries of a and b together amount to $ 5000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 3500 , e ) $ 3750
Rationale: "let a ' s salary is x b ' s salary = 5000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 5000 - x ) x = $ 3750 answer is e"
Answer: e
Problem: when tossed , a certain coin has an equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 12 , e ) 1 / 16
Rationale: on the first toss , the coin will land on one side or the other . on the second toss , the probability of landing on the same side is 1 / 2 . on the third toss , the probability of landing on the same side is 1 / 2 . on the fourth toss , the probability of landing on the same side is 1 / 2 . p ( same side all four times ) = 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 . the answer is c .
Answer: c
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 9 minutes 42 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 9 % , e ) 12 %
Rationale: "bob ' s time = 640 secs . his sis ' time = 582 secs . percent increase needed = ( 640 - 582 / 640 ) * 100 = 58 / 640 * 100 = 9 % . ans ( d ) ."
Answer: d
Problem: convert 300 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 804670 , d ) 482802 , e ) 864520
Rationale: "1 mile = 1609.34 meters 300 mile = 300 * 1609.34 = 482802 meters answer is d"
Answer: d
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 9 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 9 ) = multiply and divide by 2 ^ 4 = 2 ^ 6 / ( 2 ^ 3 * 2 ^ 6 * 5 ^ 9 ) = 2 ^ 6 / 10 ^ 9 = > non zero digits are 64 = > ans b"
Answer: b
Problem: the average weight of 5 person ' s increases by 4 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ?
Options: a ) 70 , b ) 86.5 , c ) 80 , d ) 88.5 , e ) 75
Rationale: "total increase in weight = 5 × 4 = 20 if x is the weight of the new person , total increase in weight = x − 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : a"
Answer: a
Problem: what is the smallest integer that is multiple of 7 , 12 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 420
Rationale: "correct answer : e it is the lcm of 7 , 12 and 20 which is 420"
Answer: e
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 17 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 8 + 16 x 6 ) ] = ( 225 - 208 ) = 17 years . answer c"
Answer: c
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 174,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 45 %
Rationale: "increase = 174000 - 120000 = 54000 % increase = 54000 * 100 / 120000 = 45 % answer : option e"
Answer: e
Problem: in the faculty of reverse - engineering , 200 second year students study numeric methods , 400 second year students study automatic control of airborne vehicles and 100 second year students study them both . how many students are there in the faculty if the second year students are approximately 60 % of the total ?
Options: a ) 834 , b ) 750 , c ) 633 , d ) 654 , e ) 812
Rationale: "total number of students studying both are 400 + 200 - 100 = 500 ( subtracting the 100 since they were included in the both the other numbers already ) . so 60 % of total is 500 , so 100 % is approx . 834 . answer is a"
Answer: a
Problem: jerry went to a shop and bought things worth rs . 35 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 29.7
Rationale: "total cost of the items he purchased = rs . 35 given that out of this rs . 35 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 35 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 35 − 0.3 − x ) = 30 ⇒ ( 35 − 0.3 − x ) = 5 ⇒ x = 35 − 0.3 − 5 = 29.7 e )"
Answer: e
Problem: how long does a train 110 m long running at the speed of 36 km / hr takes to cross a bridge 132 m length ?
Options: a ) 82.1 sec , b ) 12.1 sec , c ) 24.2 sec , d ) 13.1 sec , e ) 12.15 sec
Rationale: "speed = 36 * 5 / 18 = 10 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 10 = 24.2 sec . answer : c"
Answer: c
Problem: kathleen can paint a room in 3 hours , and anthony can paint an identical room in 5 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 4 / 3 , c ) 15 / 8 , d ) 9 / 4 , e ) 15 / 4
Rationale: "kat - - - 3 hrs - - - 1 room ; so rate is work / time = 1 / 3 anthony - - - 5 hrs - - - 1 room ; rate = 1 / 5 rate of kat and anthony together = 1 / 3 + 1 / 5 = 8 / 15 but we are told that they both paint 2 rooms which are identical . so ; work is 2 rooms , rate is 8 / 15 , total time required for both of them together to complete the work = 2 / ( 8 / 15 ) = 30 / 8 = 15 / 4 hence answer = e"
Answer: e
Problem: 1200 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12.85 , b ) 12.62 , c ) 12.5 , d ) 12.24 , e ) 12.1
Rationale: "1200 * 15 = 1400 * x x = 12.85 . answer : a"
Answer: a
Problem: the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 35 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 65 , c ) 100 , d ) 109 , e ) 129
Rationale: "a + b + c + d = 200 a + b = 70 c + d = 130 greatest possible = 129 ( just less than 1 ) answer = e"
Answer: e
Problem: what will be the compound interest on a sum of rs . 21,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 8503.49 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 21000 * ( 1 + 12 / 100 ) 3 ] = 21000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 29503.49 c . i . = ( 29503.49 - 21000 ) = rs . 8503.49 answer : a"
Answer: a
Problem: a man swims downstream 72 km and upstream 45 km taking 10 hours each time ; what is the speed of the current ?
Options: a ) 1.55 , b ) 1.85 , c ) 1.65 , d ) 1.35 , e ) 1.15
Rationale: "72 - - - 10 ds = 7.2 ? - - - - 1 45 - - - - 10 us = 4.5 ? - - - - 1 s = ? s = ( 7.2 - 4.5 ) / 2 = 1.35 answer : d"
Answer: d
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 65 sq . cm . find the length of the rectangle .
Options: a ) 12 cm , b ) 14 cm , c ) 16 cm , d ) 18 cm , e ) 20 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 65 = > 5 x - 25 = 65 = > x = 16 . length of the rectangle = 16 cm . answer : option c"
Answer: c
Problem: find the amount on rs . 6000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 5568 , b ) 6369 , c ) 5460 , d ) 5635 , e ) 6552
Rationale: "6000 * 104 / 100 * 105 / 100 = > 6552 answer : e"
Answer: e
Problem: an aeroplane covers a certain distance at a speed of 320 kmph in 4 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 820 , d ) 768 , e ) 720
Rationale: "distance = ( 240 x 5 ) = 1280 km . speed = distance / time speed = 1280 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1280 x 3 / 5 ) km / hr = 768 km / hr answer d ) 768 km / hr"
Answer: d
Problem: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 70 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 16 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: let x be the amount of money paid for the first purchase . the second time , the customer paid 0.7 ( 1.2 x ) = 0.84 x . the difference is 16 % . the answer is a .
Answer: a
Problem: a group of men decided to do a work in 10 days , but 5 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 25 , e ) 18
Rationale: original number of men = 5 * 12 / ( 12 - 10 ) = 30 answer is c
Answer: c
Problem: george can do a piece of work in 8 hours . paul can do the same work in 10 hours , hari can do the same work in 12 hours . george , paul and hari start the same work at 9 am , while george stops at 11 am , the remaining two complete the work . what time will the work complete ?
Options: a ) 12 : 00 pm , b ) 1 : 00 pm , c ) 2 : 00 pm , d ) 3 : 00 pm , e ) 4 : 00 pm
Rationale: ( ( 1 / 8 ) + ( 1 / 10 ) + ( 1 / 12 ) ) 2 + ( ( 1 / 10 ) + ( 1 / 12 ) ) ( x - 2 ) = 1 x = 4 hrs work started at 9 am . . takes 4 hrs to complete 9 am + 4 hrs = 1 : 00 pm answer : b
Answer: b
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: the solution should be the same for all numbers that fulfill the condition above . as x and y are odd prime numbers , they must be > 2 . also , they must be distinct as x < y . i choose x = 3 and y = 5 : how many factors does 2 x 3 x 5 = 30 have : 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 = 8 distinct positive integer factors . hence , the correct answer is d .
Answer: d
Problem: if 3 cats can kill 3 rats in 3 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
Rationale: "it will take 3 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 3 minutes , so 100 cats can kill 100 rats in 3 minutes answer c"
Answer: c
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and three wrenches is one - third that of 6 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 2 x + 3 y ) = 1 / 3 * ( 7 x + 5 y ) 3 ( 2 x + 3 y ) = ( 7 x + 5 y ) 6 x + 9 y = 7 x + 5 y 4 y = x y = x / 4 ans - a"
Answer: a
Problem: a certain quantity of 80 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 9 / 11
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 80 ml and 25 ml is 55 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 45 % . therefore , 45 out of 55 is 9 / 11 and e is the answer ."
Answer: e
Problem: the number of diagonals of a polygon of n sides is given by the formula c = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: c = n ( n - 3 ) c = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b
Answer: b
Problem: 5358 x 53 = ?
Options: a ) 272258 , b ) 272358 , c ) 283974 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 3 ) = 5358 x 50 + 5358 x 3 = 267900 + 16074 = 283974 . c )"
Answer: c
Problem: 80 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 120 , d ) 30 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 80 + 50 % ( 80 ) = 80 + 40 = 120 . answer c"
Answer: c
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 81 , c ) 77 , d ) 66 , e ) 73
Rationale: "( a + b ) - ( b + c ) = 12 a - c = 12 answer : a"
Answer: a
Problem: in a bag , there are 2400 ball , and their colors are red , green blue . . the ratio of the balls are 15 : 13 : 17 . then how many red color balls are available in the bag ?
Options: a ) 900 , b ) 1600 , c ) 750 , d ) 890 , e ) 1010
Rationale: red : green : blue = 15 + 13 + 17 = 45 ; ratio of the red balls = 15 / 40 simplify = 3 / 8 * 2400 = 900 . answer = a
Answer: a
Problem: the average age of 39 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 ) 50 , b ) 55 , c ) 60 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 40 × 11 – 39 × 10 ) years = 50 years . answer a"
Answer: a
Problem: an alloy is to contain copper and zinc in the ratio 9 : 4 . the zinc required to be melted with 24 kg of copper is ?
Options: a ) 12 kg , b ) 8.3 kg , c ) 10.7 kg , d ) 15.5 kg , e ) 7 kg
Rationale: "let the required quantity of copper be x kg 9 : 4 : : 24 : x 9 x = 4 * 24 x = 10 2 / 3 kg = 32 / 3 = 10.7 kg answer is c"
Answer: c
Problem: two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 10 , b ) 11.3 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed of the first train = 120 / 9 = 13.3 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 13.3 + 8 = 21.3 m / sec . required time = ( 120 + 120 ) / 21.3 = 11.3 sec . answer : option b"
Answer: b
Problem: trains a and b start simultaneously from stations 350 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 40 miles per hour and 30 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 112 , b ) 133 , c ) 150 , d ) 167 , e ) 200
Rationale: since we know the distance ( 350 ) and the combined rate ( 70 ) , we plug it into the formula : distance = rate * time 350 = 70 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 350 / 70 from dividing 70 on both sides to isolate time in the equation above . time will be 5 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 40 * 5 distance = 200 according to answer choice e .
Answer: e
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7
Rationale: the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 6 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 6 x = 12 x august tips as a fraction of total tips = 6 x / 12 x = 1 / 2 . so d
Answer: d
Problem: for how many values of n , is | | | n - 5 | - 10 | - 5 | = 2 ? ( those ls are mods )
Options: a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8
Rationale: i think its 8 | | | n - 5 | - 10 | - 5 | = 2 let | n - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; x has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d
Answer: d
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 42 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 17 % , e ) 20 %
Rationale: "let me try a simpler one . lets assume that candidate got 42 % votes and total votes is 100 . candidate won = 42 remaining = 58 to get 50 % , candidate requires 8 votes from 100 which is 8 % and 8 votes from 58 . 8 / 58 = . 137 = 13.7 % which is approx 14 % . hence the answer is c ."
Answer: c
Problem: a certain bus driver is paid a regular rate of $ 15 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 56 , b ) 51 , c ) 59 , d ) 54 , e ) 52
Rationale: "for 40 hrs = 40 * 15 = 600 excess = 976 - 600 = 376 for extra hours = . 75 ( 15 ) = 11.25 + 15 = 26.25 number of extra hrs = 376 / 26.25 = 14.3 = 14 approx . total hrs = 40 + 14 = 54 answer d"
Answer: d
Problem: in a class , 6 students can speak tamil , 15 can speak gujarati and 6 can speak h . if two students can speak two languages and one student can speak all the 3 languages , then how many students are there in the class ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: t = 6 g = 15 h = 6 students can speak two languages ( suppose tamil & gujarati ) = 2 student can speak all the three languages = 1 student can speak only tamil language = 6 - 2 - 1 = 3 student can speak only gujarati language = 15 - 2 - 1 = 12 student can speak only h language = 6 - 1 = 5 so , total number of student = 2 + 1 + 3 + 12 + 5 = 23 answer : d
Answer: d
Problem: what should be the least number to be added to the 3198 number to make it divisible by 8 ?
Options: a ) 12 , b ) 17 , c ) 2 , d ) 77 , e ) 26
Rationale: "answer : 2 option : c"
Answer: c
Problem: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3168 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 3168 x = 4400 answer : c"
Answer: c
Problem: 60 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 210 , d ) 1770 , e ) 230
Rationale: "1 st person will shake hand with 59 people 2 nd person will shake hand with 58 people 3 rd person will shake hand with 57 people . . . . . . total no . of handshakes = 59 + 58 + 57 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1770 or , if there are n persons then no . of shakehands = nc 2 = 60 c 2 = 1770 answer : d"
Answer: d
Problem: what is the difference between the c . i . on rs . 4000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 1.63 , d ) s . 2.83 , e ) s . 2.42
Rationale: "c . i . when interest is compounded yearly = [ 4000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 4000 * 26 / 25 * 51 / 50 = rs . 4243.2 c . i . when interest is compounded half - yearly = [ 4000 * ( 1 + 2 / 100 ) 2 ] = ( 4000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 4244.83 difference = ( 4244.83 - 4243.2 ) = rs . 1.63 . answer : c"
Answer: c
Problem: 657.987 - ? + 56.84 = 324.943
Options: a ) a ) 899.015 , b ) b ) 752.804 , c ) c ) 389.884 , d ) d ) 629.906 , e ) of these
Rationale: "explanation : 389.884 answer : option c"
Answer: c
Problem: approximately what percentage of the world ’ s forested area is represented by finland given that finland has 53.42 million hectares of forested land of the world ’ s 8.076 billion hectares of forested land .
Options: a ) 0.0066 % , b ) 0.066 % , c ) 0.66 % , d ) 6.6 % , e ) 66 %
Rationale: since 1 billion is 1000 million soc changing all quantities to million finland forest area = 53.42 million hect . worlds ' s forest area = 8.076 billion hect . % = 53.42 * 100 / 8.076 * 1000 = 0.66 % answer c
Answer: c
Problem: two stations a and b are 65 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 65 45 x = 90 x = 2 . so , they meet at 9 a . m . answer : option a
Answer: a
Problem: divide rs . 800 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 200 , c ) s . 600 , d ) s . 500 , e ) s . 900
Rationale: "a + b + c = 800 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 800 = > 200 answer : b"
Answer: b
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 60,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 90,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 60000 / y = 2 / 3 â € ¹ = â € º y = ( 60000 ã — 3 / 2 ) . â € ¹ = â € º y = 90000 . answer d"
Answer: d
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 10 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,00 , d ) $ 4,500 , e ) $ 15,000
Rationale: sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 1000 ) = 0.1 x x = 15,000 ans : e
Answer: e
Problem: what is the smallest positive integer k such that the product of 61347 x k is a perfect square ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 61347 = 13 ^ 2 * 11 ^ 2 * 3 , so if k = 3 then 61347 k = ( 13 * 11 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Problem: the total age of a and b is 13 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 13
Rationale: "( a + b ) - ( b - c ) = 13 a - c = 13 answer is e"
Answer: e
Problem: a pupil ' s marks were wrongly entered as 67 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 44 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 67 - 45 ) = > x / 2 = 22 = > x = 44 . answer : c"
Answer: c
Problem: how long does a train 100 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 100 + 170 = 270 m s = 60 * 5 / 18 = 50 / 3 t = 270 * 3 / 50 = 16.2 sec answer : d"
Answer: d
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 9,100 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2600 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 9100 = > 7 x = 9100 = > x = 1300 total number of motorcycles = 2 x = 2 * 1300 = 2600 answer b
Answer: b
Problem: in a particular state , 60 % of the counties received some rain on monday , and 55 % of the counties received some rain on tuesday . no rain fell either day in 25 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 12.5 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 67.5 %
Rationale: "60 + 55 + 25 = 140 % the number is 40 % above 100 % because 40 % of the counties were counted twice . the answer is b ."
Answer: b
Problem: triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 5 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 9 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: dan travels 4 miles round trip . running part : ( 2 / 10 = 1 / 5 * 60 = 12 minutes ) swimming part : ( 2 / 5 = 2 / 5 * 60 = 24 minutes ) 4 miles in ( 12 + 24 ) minutes 4 / 36 = 1 / 9 mile per minute answer : 1 / 9 mile per minute
Answer: a
Problem: what is the smallest number which when increased by 3 is divisible by 12 , 15 , 35 , and 40 ?
Options: a ) 837 , b ) 947 , c ) 1027 , d ) 1155 , e ) 1231
Rationale: "factor each of the numbers 8 , 15 , 35 , and 40 into primes : 12 = 2 * 2 * 3 ; 15 = 3 * 5 ; 35 = 5 * 7 ; 40 = 2 * 2 * 2 * 5 the smallest number divisible by all of them is thus 2 * 2 * 2 * 3 * 5 * 7 = 840 837 + 3 = 840 a"
Answer: a
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number r of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "r = 7 is the correct answer . good solution buneul . b"
Answer: b
Problem: if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 2 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 10 / 3 , d ) 2 , e ) 4
Rationale: "n = 2 d / 5 j = n / 2 = d / 5 the average of november and january is ( n + j ) / 2 = 3 d / 5 / 2 = 3 d / 10 d is 10 / 3 times the average of november and january . the answer is c ."
Answer: c
Problem: 7 people average age is 30 . youngest person age is 5 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 35 = 161 so average age would be 175 / 7 = 25 answer : c
Answer: c
Problem: the average age of applicants for a new job is 35 , with a standard deviation of 30 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 31 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 35 - 30 = 5 maximum age = average + 1 standard deviation = 35 + 30 = 35 maximum number of different ages of the applicants = 35 - 5 + 1 = 31 answer c"
Answer: c
Problem: linda spent 3 / 5 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 600 , d ) $ 1000 , e ) $ 800
Rationale: "if linda spent 3 / 5 of her savings on furnitute , the rest 5 / 5 - 3 / 5 = 2 / 5 on a tv but the tv cost her $ 400 . so 2 / 5 of her savings is $ 400 . so her original savings are 5 / 2 times $ 400 = $ 2000 / 2 = $ 1000 correct answer d"
Answer: d
Problem: a man buys an item at rs . 1300 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 760 , c ) rs . 860 , d ) rs . 1040 , e ) none of these
Rationale: explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 1300 = 80 / 100 * 1300 = 1040 option d
Answer: d
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer w between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) w = 18 , e ) 20
Rationale: "since we are concerned with integers w between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Problem: a sum of money lent out at s . i . amounts to rs . 850 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 782 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 850 ) = rs . 170 . s . i . for 2 years = 170 / 5 * 2 = rs . 68 . principal = ( 850 - 68 ) = rs . 782 . answer : d"
Answer: d
Problem: on dividing 15698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 852 , d ) 176 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 15698 - 14 ) / 89 = 176 answer ( d )"
Answer: d
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 570 in base salary plus 8 percent of the portion of his sales above $ 1,000 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 ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 570 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 24500 answer : b"
Answer: b
Problem: income and expenditure of a person are in the ratio 4 : 3 . if the income of the person is rs . 20000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 5000
Rationale: "let the income and the expenditure of the person be rs . 4 x and rs . 3 x respectively . income , 4 x = 20000 = > x = 5000 savings = income - expenditure = 4 x - 3 x = x so , savings = rs . 5000 answer : e"
Answer: e
Problem: given that 268 x 74 = 19832 , find the value of 2.68 x . 74 .
Options: a ) 1.9832 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9832 answer a
Answer: a
Problem: the average age of 60 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 71 , b ) 65 , c ) 61 , d ) 45 , e ) 36
Rationale: "total age of 50 students = 60 * 10 = 600 total age of 51 persons = 61 * 11 = 671 age of teacher = 671 - 600 = 71 years answer is a"
Answer: a
Problem: the ratio of investments of two partners p and q is 7 : 5.00001 and the ratio of their profits is 7.00001 : 10 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 28 , b ) 10 , c ) 288 , d ) 277 , e ) 211
Rationale: 7 * 5 : 5 * x = 7 : 10 x = 10 answer : b
Answer: b
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance traveled downstream in 15 minutes is :
Options: a ) 9.25 , b ) 5.25 , c ) 7.25 , d ) 6.25 , e ) 5.1
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 15 / 60 ) ) km = 6.25 km . answer : d"
Answer: d
Problem: by selling 80 pens , a trader gains the cost of 20 pens . find his gain percentage ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: "let the cp of each pen be rs . 1 . cp of 80 pens = rs . 80 profit = cost of 20 pens = rs . 20 profit % = 20 / 80 * 100 = 25 % answer : a"
Answer: a
Problem: a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its average monthly production for that year ?
Options: a ) 1750 , b ) 2789 , c ) 2500 , d ) 1550 , e ) 2000
Rationale: total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 12 = 1550 . answer : d
Answer: d
Problem: a batsman in his 11 th inning makes a score of 69 and their by increasing his average by 1 . what is his average after the 11 th inning ?
Options: a ) 58 , b ) 59 , c ) 68 , d ) 69 , e ) 78
Rationale: "10 x + 69 = 11 ( x + 1 ) x = 58 + 1 = 59 answer : b"
Answer: b
Problem: john makes $ 40 a week from his job . he earns a raise andnow makes $ 55 a week . what is the % increase ?
Options: a ) 15 % , b ) 16.66 % , c ) 17.8 % , d ) 19 % , e ) 37.5 %
Rationale: "increase = ( 15 / 40 ) * 100 = 37.5 % . e"
Answer: e
Problem: if x and y are positive integers and y ≠ 1 , then xy ( y − 1 ) is
Options: a ) always even , b ) always odd , c ) odd only when x is odd , d ) even only when y is even , e ) odd only when xy is odd
Rationale: "expression is xy ( y - 1 ) . we can ignore x and only work with y . if y = even - > entire expression is even since anything multiplied by even is even if y = odd , y - 1 - > even - > entire expression is even since anything multiplied by even is even hence , entire expression will always be even . answer ( a ) ."
Answer: a
Problem: you collect baseball cards . suppose you start out with 13 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 15 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 13 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 13 + 1 which is 7 , so you ' re left with 13 - 7 = 6 . peter takes 1 baseball card from you : 6 - 1 = 5 baseball cards . paul triples the number of baseball cards you have : 5 ã — 3 = 15 baseball cards . so you have 15 at the end . correct answer : a"
Answer: a
Problem: the list price of an article is rs . 70 . a customer pays rs . 61.74 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 2 % , e ) 4 %
Rationale: "explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 61.74 x = 2 % option d"
Answer: d
Problem: what is the smallest integer b for which 27 ^ b > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ b > 3 ^ 24 converting into the same bases : 27 ^ b > 27 ^ 8 therefore for the equation to hold true , b > 8 or b = 9 option c"
Answer: c
Problem: the median annual household income in a certain community of 21 households is $ 50000 . if the mean r income of a household increases by 10 % per year over the next 2 years , what will the median income in the community be in 2 years ?
Options: a ) $ 50000 , b ) $ 60000 , c ) $ 60500 , d ) $ 65000 , e ) can not be determined
Rationale: answer is e , because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean r is increase by 10 % . it could be the case that small number of higher end incomes increased a little or many low end incomes increased - it can not be identified .
Answer: e
Problem: the contents of a certain box consist of 80 apples and 30 oranges . how many oranges must be added to the box so that exactly 50 % of the pieces of fruit in the box will be apples ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 65
Rationale: "apple = ( apple + orange + x ) * 0.5 80 = ( 30 + 80 + x ) * 0.5 x = 50 answer : b"
Answer: b
Problem: the sum of the squares of three numbers is 125 , while the sum of their products taken two at a time is 50 . their sum is :
Options: a ) 15 , b ) 30 , c ) 40 , d ) 50 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 125 xy + yz + zx = 50 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 125 + ( 2 * 50 ) ( x + y + z ) ^ 2 = 225 so x + y + z = 15 answer : a"
Answer: a
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 3 , - 1 ) , ( 3 , 8 ) , ( 14 , 2 ) , ( 14 , - 5 ) ?
Options: a ) 76 , b ) 88 , c ) 100 , d ) 112 , e ) 124
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 9 + 7 ) × 11 = 88 . the answer is b ."
Answer: b
Problem: a man was engaged on a job for 30 days on the condition that he would get a wage of rs . 10 for the day he works , but he have to pay a fine of rs . 2 for each day of his absence . if he gets rs . 216 at the end , he was absent for work for . . . days .
Options: a ) 7 days , b ) 5 days , c ) 3 days , d ) 4 days , e ) 8 days
Rationale: the equation portraying the given problem is : 10 * x – 2 * ( 30 – x ) = 216 where x is the number of working days . solving this we get x = 23 number of days he was absent was 7 ( 30 - 23 ) days . answer : a
Answer: a
Problem: if 9 ^ y = 3 ^ 16 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "9 ^ y = 3 ^ 2 y = 3 ^ 16 2 y = 16 y = 8 the answer is e ."
Answer: e
Problem: the average age of 3 boys is 15 years and their ages are in proportion 3 : 5 : 7 . what is the age in years of the eldest boy ?
Options: a ) 6 , b ) 9 , c ) 16 , d ) 4 , e ) 21
Rationale: 3 x + 5 x + 7 x = 45 x = 3 7 x = 21 answer : e
Answer: e
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 19 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 10 , e ) 29 / 100
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 19 - 2 cmb = 100 b - cb - mb - 2 cmb = 29 hence the probability = 29 / 100 . e"
Answer: e
Problem: a towel , when bleached , lost 30 % of its length and 15 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 40.5 % , c ) 44 % , d ) 54 % , e ) 64 %
Rationale: "percentage change in area = ( − 30 − 15 + ( 30 × 15 ) / 100 ) % = − 40.5 % i . e . , area is decreased by 40.5 % answer : b"
Answer: b
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 24 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: c = 1 / 4 - 1 / 12 – 1 / 24 = 1 / 8 = > 8 days ' answer : c
Answer: c
Problem: at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 15 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 25 % , c ) 62.5 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 15 short - stemmed pink = 15 = > short - stemmed red = 10 15 / p = 10 / r = > r = 2 r / 3 so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + 2 r / 3 + 20 = 120 = > 5 r = 300 and r = 60 long stemmed r = 60 - 10 = 50 so long stemmed red / r = 50 / 80 = 62.5 % answer - c"
Answer: c