regisss/math_qa huggingface dataset:
Problem: find the mean proportional between 7921 & 9409 ?
Options: a ) 8163 , b ) 8633 , c ) 8663 , d ) 8636 , e ) none of these
Rationale: "explanation : formula = √ a × b a = 7921 and b = 9409 √ 7921 × 9409 = 89 × 97 = 8633 answer : option b"
Answer: b
Problem: 25 % of 1250
Options: a ) 330 , b ) 315 , c ) 312.5 , d ) 370 , e ) 350
Rationale: 1 % of 1250 is = 12.50 25 % of 1250 is = 12.50 * 25 = 312.5 answer : c
Answer: c
Problem: there are 3 vessels of equal capacity . vessel a contains milk and water in the ratio 7 : 3 ; vessel b contains milk and water in the ratio 2 : 1 and vessel c contains milk and water in the ratio 3 : 2 . if the mixture in all the 3 vessels is mixed up . what will be the ratio of milk and water ?
Options: a ) 59 : 31 , b ) 3 : 2 , c ) 118 : 126 , d ) 193 : 122 , e ) 201 : 132
Rationale: 7 : 3 = > 7 x + 3 x = 10 x 2 : 1 = > 2 y + 1 y = 3 y 3 : 2 = > 3 z + 2 z = 5 z 10 x = 3 y = 5 z take lcm of 10 , 3,5 = 30 or simply ; x = 3 y = 10 z = 6 so , ratio of milk : water = ( 7 x + 2 y + 3 z ) / ( 3 x + y + 2 z ) = 59 / 31 ans : a
Answer: a
Problem: from a total of 5 boys and 5 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 24 , c ) 60 , d ) 100 , e ) 240
Rationale: "answer = d = 100 no of 4 person committees that can be formed = 5 c 2 * 5 c 2 = 100 answer d"
Answer: d
Problem: a train moves with a speed of 108 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 25 , d ) 30 , e ) none
Rationale: "sol . 108 kmph = [ 108 x 5 / 18 ] m / sec = 30 m / sec . answer d"
Answer: d
Problem: ( 132 ) ^ 7 × ( 132 ) ^ ? = ( 132 ) ^ 11.5 .
Options: a ) 4.5 , b ) 3 , c ) 4 , d ) 3.5 , e ) 8.5
Rationale: "( 132 ) ^ 7 × ( 132 ) ^ x = ( 132 ) ^ 11.5 = > 7 + x = 11.5 = > x = 11.5 - 7 = 4.5 answer is a"
Answer: a
Problem: a batsman in his 10 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 53 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 10 th innings = 85 - 3 × 10 = 50 average score after 10 th innings = > 50 + 3 = 53 answer : b"
Answer: b
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were right - handed - - > 6 * 2 / 3 = 4 were right - handed and 2 left - handed . the number of right - handed players who were not at practice that day is 9 - 4 = 5 . the number of left - handed players who were not at practice that days is 9 - 2 = 7 . the ratio = 5 / 7 . answer : c"
Answer: c
Problem: martin bought 5 packet milk at an average price ( arithmetic mean ) of 20 ¢ . if martin returned two packet to the retailer , and the average price of the remaining millk packet was 12 ¢ , then what is the average price , in cents , of the two returned milk packets ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: total price of 5 packet milk = 5 * 20 = 100 total price of 3 packet milk = 3 * 12 = 36 total price of 2 packet returned milk = 100 - 36 = 64 average price of 2 packet milk = 64 / 2 = 32 correct option answer : c
Answer: c
Problem: 20 beavers , working together in a constant pace , can build a dam in 18 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 22 . , b ) 24 . , c ) 30 . , d ) 36 , e ) 38 .
Rationale: total work = 20 * 18 = 360 beaver hours 12 beaver * x = 360 beaver hours x = 360 / 12 = 30 answer : c
Answer: c
Problem: a , b , c , d and e are ve consecutive odd numbers the sum of a and c is 146 . what is the value of e ?
Options: a ) 75 , b ) 81 , c ) 71 , d ) 79 , e ) none of these
Rationale: a + c = 146 ⇒ a + a + 4 = 146 ⇒ a = 146 - 4 / 2 = 71 ∴ e = a + 8 = 71 + 8 = 79 answer d
Answer: d
Problem: in the coordinate plane , points ( x , 5 ) and ( 9 , y ) are on line k . if line k passes through the origin and has slope 5 / 9 , then x - y =
Options: a ) 4 , b ) 6 , c ) 5 , d ) 8 , e ) 7
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 5 / 9 * x . thus : ( x , 5 ) = ( 9 , 5 ) and ( 9 , y ) = ( 9,5 ) - - > x - y = 9 - 5 = 4 . answer : a"
Answer: a
Problem: the radius of a cylindrical vessel is 7 cm and height is 3 cm . find the whole surface of the cylinder ?
Options: a ) 520 sq cm
b ) 840 sq cm
c ) 440 sq cm
d ) 120 sq cm
e ) 5 sq cm
Rationale: explanation : r = 7 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 10 ) = 440 sq cm answer : c
Answer: c
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3
Options: a ) 26 , b ) 22 , c ) 25 , d ) 30 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 3 = 2 ^ 22 x 7 ^ 5 x 11 ^ 3 total number of prime factors = ( 22 + 5 + 3 ) = 30 . answer is d ."
Answer: d
Problem: a jar contains 20 red , 20 blue , 6 yellow and 4 pink balls . if two balls are to be selected at random and without replacement , approximately what is the probability both of them to be the same colour ?
Options: a ) 1 / 25 , b ) 1 / 15 , c ) 1 / 3 , d ) 1 / 2 , e ) 1
Rationale: ok so jar contains 20 red 20 blue 6 yellow and 4 pink . . adding the number of balls we get 50 total . . now its a counting + probability exercise . . 2 stages exist : pick first ball then second ball . . denominator for first ball = 50 since there are 50 balls denominator for second ball = 49 since only 49 would remain for each type ball i constructed probability of getting 2 of same . . i used a counting method . . first ball 20 chances blue and 2 nd ball 19 chances blue and so on and so forth blue = ( 20 * 19 ) / ( 50 * 49 ) rounded to 400 / 2500 red = ( 20 * 19 ) / ( 50 * 49 ) rounded to 400 / 2500 yellow = ( 6 * 5 ) / ( 50 * 49 ) rounded to 30 / 2500 pink = ( 4 * 3 ) / ( 49 * 50 ) rounded to 12 / 2500 then i summed these individual probabilities to get 842 / 2500 this is ~ 1 / 3 as 800 * 3 = 2400 ans : c
Answer: c
Problem: diana is painting statues . she has 7 / 8 of a gallon of paint remaining . each statue requires 1 / 8 gallon of paint . how many statues can she paint ?
Options: a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 7 / 8 ÷ 1 / 8 = 7 / 8 * 8 / 1 = 7 / 1 = 7 answer is a ."
Answer: a
Problem: jonathan can type a 10 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 10 / 40 + 10 / 30 + 10 / 24 = 10 / x if you solve this equation , you get the same answer b ( 10 )"
Answer: b
Problem: a train 220 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 12 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 220 * 3 / 55 = 12 sec . answer : option a"
Answer: a
Problem: in the hillside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 20 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 35 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: "given there are 50 students , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to or 20 % . . if we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it . now boys are 80 % and girls are 20 % . ( out of 100 students = 80 boys + 20 girls ) . imo option a is correct ."
Answer: a
Problem: a cyclist rides a bicycle 8 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?
Options: a ) 8.58 , b ) 8.76 , c ) 9.04 , d ) 9.12 , e ) 9.25
Rationale: "distance = 19 km time = 8 / 11 + 11 / 8 = ( 64 + 121 ) / 88 = 185 / 88 hours average speed = ( 19 * 88 ) / 185 = 9.04 km / h the answer is c ."
Answer: c
Problem: the balance of a trader weighs 8 % less than it should . still the trader marks up his goods to get an overall profit of 20 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 10.4 % , d ) 16.66 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 92 gms because it weighs 8 % less . say , the cost price is $ 92 ( $ 1 / gm ) . since he gets a profit of 20 % , the selling price must be 92 + ( 20 / 100 ) * 92 = $ 110.4 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 110.4 , the mark up is simply 10.4 % . ans : c"
Answer: c
Problem: how many numbers from 13 to 76 are exactly divisible by 10 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' b ' 13 / 10 = 1 and 76 / 10 = 7 = = > 7 - 1 = 6 numbers"
Answer: b
Problem: among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco ' s sales staff . listco employs 60 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 46 , b ) 42 , c ) 56 , d ) 70 , e ) 58
Rationale: i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 60 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 60 = 140 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 30 = 70 . thus d is the correct answer choice
Answer: d
Problem: 90 % of the population of a village is 8100 . the total population of the village is ?
Options: a ) 9000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312
Rationale: "x * ( 90 / 100 ) = 8100 x = 90 * 100 x = 9000 answer : a"
Answer: a
Problem: a tank is filled by 3 pipes a , b , c in 4 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 28 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 4 7 / x = 1 / 4 x = 28 hours answer is e"
Answer: e
Problem: a rectangular garden is to be twice as long as it is wide . if 240 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 240 so , 2 ( l + b ) = 240 or , l + b = 120 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 80 l = 80 ; b = 40 l + b = 120 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( d )"
Answer: d
Problem: at what rate percent on simple interest will rs . 415 amount to rs . 514 in 4 years ?
Options: a ) 4.58 % , b ) 5.96 % , c ) 6.52 % , d ) 4.98 % , e ) none of these
Rationale: "explanation : difference in amount = 514 - 415 = 99 99 = ( 415 x 4 x r ) / 100 r = 5.96 % answer is b"
Answer: b
Problem: the number 90 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "7 ^ 2 + 5 ^ 2 + 4 ^ 2 = 49 + 25 + 16 = 90 7 + 5 + 4 = 16 hence answer is b"
Answer: b
Problem: the diagonals of a rhombus are 14 cm and 18 cm . find its area ?
Options: a ) 176 , b ) 190 , c ) 150 , d ) 126 , e ) 292
Rationale: "1 / 2 * 14 * 18 = 126 answer : d"
Answer: d
Problem: 75 is what percent of 125 ?
Options: a ) 60 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 75 / 125 × 100 = 50 % answer : a
Answer: a
Problem: how much more would rs . 50000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 1205 , c ) 992 , d ) 837 , e ) 923
Rationale: "50000 ( 11 / 10 ) 4 - 50000 ( 6 / 5 ) 2 = 1205 answer : b"
Answer: b
Problem: a certain psychologist charges $ 40 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 375 , what is the total charge to a patient who receives only 2 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 174 , e ) $ 192
Rationale: let the charge for first hour = x + 40 then charge for each additional hour = x x + 40 + 4 x = 375 = > 5 x = 335 = > x = 67 total charge for patient for 3 hours of therapy = x + 40 + x = 2 x + 40 = 174 $ answer d
Answer: d
Problem: if the product 4864 * 9 p 2 is divisible by 12 , the value of p ?
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: explanation : clearly 4864 is divisible by 4 so 9 p 2 must be divisible by 3 . so ( 9 + p + 2 ) must be divisible by 3 . so p = 1 . answer : a ) 1
Answer: a
Problem: the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked the second cow in the second year ?
Options: a ) 4730 lt , b ) 4356 lt , c ) 7665 lt , d ) 2314 lt , e ) 6545 lt
Rationale: "let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 − x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % or 10 % so 8100 + 15 / 100 ⋅ x + 10 / 100 ⋅ ( 8100 − x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 − x ) = 9100 120 x = 190 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively . correct answer a"
Answer: a
Problem: how many multiples of 4 are there between 20 and 112 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 5 up to 4 * 28 . 28 - 5 + 1 = 24 . the answer is d ."
Answer: d
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 90 % of the total ?
Options: a ) 515 . , b ) 572 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is b : 572 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 90 % of total is 515 , so 100 % is approx . 572 ."
Answer: b
Problem: a fellow borrowed a certain sum of money at 5 % per annum at simple interest and in 5 years the interest amounted to rs . 750 less than the sum lent . what was the sum lent ?
Options: a ) 1000 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 1110
Rationale: p - 750 = ( p * 5 * 5 ) / 100 p = 1000 answer : a
Answer: a
Problem: the product x of two prime numbers is between 15 and 90 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 85
Rationale: "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 85 = 5 * 17 > > answer answer = e"
Answer: e
Problem: if an object travels at ten feet per second , how many feet does it travel in one hour ?
Options: a ) 34880 , b ) 37780 , c ) 36000 , d ) 18000 , e ) 28810
Rationale: "explanation : if an object travels at 5 feet per second it covers 5 x 60 feet in one minute , and 5 x 60 x 60 feet in one hour . answer = 36000 answer : c ) 36000"
Answer: c
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.32 – 6.32 * ?
Options: a ) 1.5 , b ) 0.5 , c ) 0.32 , d ) 0.25 , e ) 6.32
Rationale: since z * is defined as the greatest positive even integer less than or equal to z , then 6.32 * = 6 ( the greatest positive even integer less than or equal to 6.32 is 6 ) . hence , 6.32 – 6.32 * = 6.32 - 6 = 0.32 answer : c .
Answer: c
Problem: the area of a triangle will be when a = 2 m , b = 4 m , c = 6 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 7 , c ) 5 , d ) 6 , e ) 4
Rationale: "s = ( 2 + 4 + 6 ) / 2 = 6 answer : d"
Answer: d
Problem: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 20 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: let the total solution is 150 l with 80 l water 70 l syrup . to make 20 % syrup solution , the result solution must have 120 l syrup and 30 l syrup . therefore we are taking 40 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 40 l syrup in 85.7 l solution we started by multiplying 10 now to get to the result we need to divide by 40 = > amount of solution to be replaced with water = ( 85.7 / 40 ) = 2.14 . correct option : c
Answer: c
Problem: the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 27 , c ) 21 , d ) 18 , e ) 11
Rationale: ( a + b ) - ( b + c ) = 18 a - c = 18 . c is younger than a by 18 years . answer : d
Answer: d
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 4 of the mice are white . if there are 16 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 32 , b ) 36 , c ) 34 , d ) 39 , e ) 42
Rationale: "let total number of mice = m number of white mice = 2 / 4 m number of brown mice = 2 / 4 m = 16 = > m = 32 answer a"
Answer: a
Problem: if x is divided by 7 , the remainder is 5 . what is the remainder if 4 x is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: x = 7 q + 5 4 x = 7 * 4 q + 20 4 x = 7 * 4 q + 7 * 2 + 6 4 x = 7 ( 4 q + 2 ) + 6 4 x = 7 k + 6 ( k = 4 q + 2 ) answer d
Answer: d
Problem: the speed of a boat in still water is 21 km / hr and the rate of current is 8 km / hr . the distance travelled downstream in 13 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 6.3 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 21 + 8 ) kmph = 18 kmph . distance travelled = ( 29 x 13 / 60 ) km = 6.3 km option c"
Answer: c
Problem: jolene entered an 16 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 920.24 answer : d ."
Answer: d
Problem: divide $ 600 among a , b in the ratio 1 : 3 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 3 = 4 a = 600 * 1 / 4 = $ 150 answer is c"
Answer: c
Problem: 3 candidates in an election and received 3000 , 5000 and 20000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45.12 % , b ) 50 % , c ) 57 % , d ) 71.42 % , e ) 65 %
Rationale: "total number of votes polled = ( 3000 + 5000 + 20000 ) = 28000 so , required percentage = 11628 / 20400 * 100 = 71.42 % d"
Answer: d
Problem: what number times ( 1 ⁄ 5 ) ^ 2 will give the value of 5 ^ 3 ?
Options: a ) 5 , b ) 25 , c ) 125 , d ) 625 , e ) 3125
Rationale: "x * ( 1 / 5 ) ^ 2 = 5 ^ 3 x = 5 ^ 2 * 5 ^ 3 = 5 ^ 5 = 3125 the answer is e ."
Answer: e
Problem: a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 4 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min
Rationale: there are 7 hours in between 9 a . m . to 4 p . m . 7 * 5 = 35 minutes . answer : b
Answer: b
Problem: the average weight of 4 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 82 kg , c ) 86 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 4 x 3 ) kg = 12 kg . weight of new person = ( 70 + 12 ) kg = 82 kg . answer : option b"
Answer: b
Problem: the no . of girls in a class are 7 times the no . of boys , which value cannever be the of total students ?
Options: a ) 20 , b ) 35 , c ) 30 , d ) 40 , e ) 42
Rationale: let the boys are x , then girls are 7 x , total = x + 7 x = 8 x so it should be multiple of 8 , 30 is not a multiple of 8 . c
Answer: c
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 650 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 85 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 650 sq . ft . so , b = 32.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 65 ) ft = 85 ft . answer c"
Answer: c
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 50 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 50 = 50 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 50 / 100 ) * 100 = ( 0.5 ) * 100 = 50 % . c"
Answer: c
Problem: 10 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 3200 , c ) 800 , d ) 267 , e ) 121
Rationale: "( 10 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 10 x = 320 x = 3200 answer : b"
Answer: b
Problem: a clock store sold a certain clock to a collector for 25 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 55 percent of what the collector had paid . the shop then sold the clock again at a profit of 70 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 125 , for how much did the shop sell the clock the second time ?
Options: a ) $ 500 , b ) $ 467.5 , c ) $ 935 , d ) $ 525.5 , e ) $ 465.5
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 25 % profit . this means the clocks ' selling price was c ( 1.25 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 55 % the price at which the collector bought it . thus , you get = 1.25 * 0.55 * c = 0.6875 c furthermore , the store sells the clock for the second time for 70 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.7 = 1.7 * 0.6875 c finally given that c - 0.6875 c = 125 - - - - > c = 400 $ thus , the cost of the clock the second time around = 1.7 * 0.6875 c = 1.7 * 0.6875 * 400 = 467.5 $ . hence b is the correct answer ."
Answer: b
Problem: the ratio of spinsters to cats is 2 to 9 . if there are 63 more cats than spinsters , how many spinsters are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 63 x = 9 and the number of spinsters is 2 ( 9 ) = 18 . the answer is e ."
Answer: e
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 8.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 9 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.085 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 85 f - - > s = 10 f - - > f / s = 1 / 10 - - > f / ( s + f ) = 1 / ( 1 + 10 ) = 1 / 11 = 0.09 . answer : b ."
Answer: b
Problem: the time it took car p to travel 600 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 600 / x ) - ( 600 / ( x + 10 ) ) = 2 solving for x = 50 miles \ hr answer : b"
Answer: b
Problem: the h . c . f . of two numbers is 60 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 300 , c ) 500 , d ) 700 , e ) 900
Rationale: "the numbers are ( 60 x 11 ) and ( 60 x 15 ) . larger number = ( 60 x 15 ) = 900 . answer : e"
Answer: e
Problem: the number of even factors of 21600 is
Options: a ) 32 , b ) 42 , c ) 60 , d ) 25 , e ) 52
Rationale: make a prime factorization of the number : 21,600 = 25 ∗ 33 ∗ 52 according to the above the number of factors is ( 5 + 1 ) ( 3 + 1 ) ( 2 + 1 ) = 72 now , get rid of powers of 2 as they give even factors - - > you ' ll have 33 ∗ 52 which has ( 3 + 1 ) ( 2 + 1 ) = 12 factors . all the remaining factors will be odd , therefore 21,600 has 72 - 12 = 60 even factors . answer : c .
Answer: c
Problem: at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 10 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 5 / 6 , c ) 7 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 10 = 5 / 6 ans b"
Answer: b
Problem: what least number should be subtracted from 2590 so that the remainder when divided by 9 , 11 , and 13 will leave in each case the same remainder 6 ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 10 , e ) 11
Rationale: "the lcm of 9 , 11 , and 13 is 1,287 . the next multiple is 2 * 1,287 = 2,574 . 2,574 + { remainder } = 2,574 + 6 = 2,580 , which is 10 less than 2,590 . answer : d ."
Answer: d
Problem: the second angle of a triangle is double the first ( 110 ) . the third angle is 40 less than the first ( 15 ) . find the first angle .
Options: a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75
Rationale: first x with nothing given about the firstwemake that x second 2 x the second is double the first , third x − 40 the third is 40 less than the first f + s + t = 180 all three angles add to 180 ( x ) + ( 2 x ) + ( x − 40 ) = 180 replace f , s , and t with the labeled values . x + 2 x + x − 40 = 180 here the parenthesis are not needed . 4 x − 40 = 180 combine like terms , x + 2 x + x + 40 + 40 add 40 to both sides 4 x = 220 the variable ismultiplied by 4 4 4 divide both sides by 4 x = 55 our solution for x first 55 replace xwith 55 in the original list of angles second 2 ( 55 ) = 110 our angles are 55 , 110 , and 15 third ( 55 ) − 40 = 15 correct answer c
Answer: c
Problem: find the compound interest on $ 36,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.6 , b ) 2552.2 , c ) 2524.1 , d ) 5674.5 , e ) 2512.9
Rationale: "principal = $ 36000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 36000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 41674.5 ci . = $ ( 41674.5 - 36000 ) = $ 5674.5 answer d ."
Answer: d
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 25 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 25 / 100 ) * 300 = 100 + 75 = 175 % comission = ( 175 / 800 ) * 100 = 21.8 ~ 22 % answer is a"
Answer: a
Problem: mike took a bus from home to market , that travels at 30 kmph . while walking back at 6 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 20 kmph . find the average speed .
Options: a ) 21.2 kmph , b ) 12.1 kmph , c ) 23.4 kmph , d ) 20.4 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 30 , by walking = x / 6 , by cycling = x / 20 hours : . average speed = total distance / total time = 6 x / x / 15 + x / 6 + x / 20 = 6 * 60 / 4 + 10 + 3 = 21.2 answer : a
Answer: a
Problem: circular gears l and r start to rotate at the same time at the same rate . gear l makes 10 complete revolutions per minute and gear r makes 30 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 12 , e ) e ) 18
Rationale: "gear l - - 10 rotations per 60 seconds - - 1 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 3 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 2 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 2 units . required net difference should be 6 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : e"
Answer: e
Problem: in the youth summer village there are 100 people , 50 of them are not working , 25 of them have families and 75 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 100 , b ) 75 , c ) 25 , d ) 50 , e ) 125
Rationale: "total = 100 not working = 50 having family = 25 like to sing in shower = 75 working = 100 - 50 = 50 not having family = 100 - 25 = 75 like to sing in shower = 75 largest possible number is the lowest possible among the above thus 50 d"
Answer: d
Problem: what is the smallest no . which must be added to 3245613 so as to obtain a sum which is divisible by 11 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 9 , e ) 3
Rationale: "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 3245613 , difference = ( 3 + 4 + 6 + 3 ) - ( 2 + 5 + 1 ) = 16 - 8 = 8 . the units digit is at odd place . so we add 3 to the number = > 3245613 + 3 = 3245616 now , ( 3 + 4 + 6 + 6 ) - ( 2 + 5 + 1 ) = 19 - 8 = 11 = > 11 is a multiple of 11 and hence 3245616 is also divisible by 11 e"
Answer: e
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm
Options: a ) 178 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 228 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : e"
Answer: e
Problem: a train 130 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 4 , b ) 7 , c ) 5 , d ) 9 , e ) 8
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 130 * 3 / 55 ] sec = 7 sec answer : b"
Answer: b
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent j of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , j = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d"
Answer: d
Problem: in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many z different victory circles are possible ?
Options: a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648
Rationale: possible scenarios are : 1 . gold / silver / bronze / no medal ( no ties ) - 4 ! = 24 ; 2 . gold / gold / silver / no medal - 4 ! / 2 ! = 12 ; 3 . gold / silver / silver / no medal - 4 ! / 2 ! = 12 ; 4 . gold / gold / gold / no medal - 4 ! / 3 ! = 4 . total z : 24 + 12 + 12 + 4 = 52 answer : b .
Answer: b
Problem: an air - conditioning unit costs $ 470 . on december there was a discount for christmas of 16 % . 6 months later , the holiday season was over so the company raised the price of the air - conditioning by 12 % . how much will an air - conditioning unit cost in november ?
Options: a ) $ 442 , b ) $ 470 , c ) $ 472 , d ) $ 484 , e ) $ 491
Rationale: if its previous november ( before discount ) then price is $ 470 . but if its november of next year then 16 % discount on $ 470 = 470 ( 1 - 16 / 100 ) = $ 394.8 again a corrected raised price of 12 % over $ 394.8 = 394.8 ( 1 + 12 / 100 ) = 442.176 ~ $ 4442 ans a
Answer: a
Problem: in the hillside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: "given there are 50 students , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . answer : option a is correct ."
Answer: a
Problem: the average of first five multiples of 5 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e"
Answer: e
Problem: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability e , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , e = 9 provide the desired outcome , making the answer e ."
Answer: e
Problem: how many diagonals does a polygon with 17 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 102 , b ) 104 , c ) 110 , d ) 90 , e ) 84
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 17 - 1 then 16 * ( 16 - 3 ) / 2 = 104 correct option : b"
Answer: b
Problem: the sum of 3 consecutive multiples of 3 is 72 . what is the larget number ?
Options: a ) 26 , b ) 27 , c ) 46 , d ) 57 , e ) none
Rationale: sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 ⇔ 9 x = 63 ⇔ x = 7 . ∴ largest number = 3 x + 6 = 27 . answer b
Answer: b
Problem: find the value of sin 75 ° + sin 15 ° = ?
Options: a ) 0 , b ) 1 / 2 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "sin a + sin b = 2 sin [ ( a + b ) / 2 ] cos [ ( a - b ) / 2 ] = 2 sin [ ( 75 + 15 ) / 2 ] cos [ ( 75 - 15 ) / 2 ] = 2 sin 90 cos 60 = 2 * 1 * ( 1 / 2 ) = 1 answer : c"
Answer: c
Problem: a train traveling at 180 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 180 kmph * 12 seconds convert 180 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 180 kmph = 5 / 18 ∗ 180 = 50 m / sec therefore , length of the platform = 50 m / s * 12 sec = 600 meters . choice d"
Answer: d
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 7 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 84 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: ans : c solution : simple multiplication s students , c classes , 7 books / month = 84 books a year total number of books = 84 cs
Answer: c
Problem: a man , a woman and a boy can complete a job in 3,4 and 12 days respectively . how many boys must assist 1 man and 1 woman to complete the job in ¼ of a day ?
Options: a ) 1 day , b ) 4 days , c ) 19 days , d ) 41 days , e ) 52 days
Rationale: ( 1 man + 1 woman ) ' s 1 days work = 1 / 3 + 1 / 4 = 7 / 12 work done by 1 man and 1 women n 1 / 4 day = ( ( 7 / 12 ) * ( 1 / 4 ) ) = 7 / 48 remaining work = 1 - 7 / 48 = 41 / 48 work done by 1 boy in ¼ day = ( ( 1 / 12 ) * ( 1 / 4 ) ) = 1 / 48 therefore , number of boys required = ( ( 41 / 48 ) * 48 ) = 41 days answer d 41 days
Answer: d
Problem: if the radius of the sphere is 14 m . then its total surface area is
Options: a ) 2644
b ) 2446
c ) 2464
d ) 6442
e ) 6424
Rationale: sphere total surface area = 4 π r ( power 2 ) = 4 × 22 / 7 × 14 × 14 = 2464 answer is c .
Answer: c
Problem: a train covers a distance of 12 km in 12 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 , b ) 168 , c ) 100 , d ) 120 , e ) 122
Rationale: "speed = ( 12 / 12 * 60 ) km / hr = ( 60 * 5 / 18 ) m / sec = 16.6 m / sec . length of the train = 16.6 * 6 = 100 m . answer : c"
Answer: c
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 25 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 7.0 , b ) 5.0 , c ) 6.0 , d ) 4.0 , e ) 8.0
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 25 kg joins the group , total weight of boys = 20 x + 25 so 20 x + 25 = 21 ( x + 1 ) = > x = 4 . answer : d"
Answer: d
Problem: a dealer offers a cash discount of 10 % and still makes a profit of 35 % when he further allows 20 articles to be sold at the cost price of 15 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 80 % , b ) 100 % , c ) 120 % , d ) 60 % , e ) 90 %
Rationale: "given cash discount - 10 % profit - 35 % items sold - 20 price sold at = list price of 15 assume list price = $ 20 total invoice = $ 300 - 10 % cash discount = $ 270 let cost price of 20 items be x so total cost = 20 * x given the shopkeeper had a profit of 20 % 20 * x * 135 / 100 = 270 or x = $ 10 which means his products were listed at $ 20 which is a 100 % markup over $ 10 answer b"
Answer: b
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 20 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 18 %
Rationale: "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.22 - x ) + 2 * 20 x = 9 - - > x = 0.18 = 18 % answer : e ."
Answer: e
Problem: if ( 5 ^ 7 ) ( 9 ^ 4 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 7 ) ( 9 ^ 4 ) = 3 ( 15 ^ x ) = > 5 ^ 7 * 3 ^ 8 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 7 * 3 ^ 8 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 7 answer a"
Answer: a
Problem: henrikh lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work . if it takes him exactly 8 minutes more to walk to work than to ride his bicycle , then x equals
Options: a ) 4 , b ) 7 , c ) 12 , d ) 15 , e ) 20
Rationale: the best way would be . . . per km , he takes 40 secs extra if he walks so he will take 8 mins or 8 * 60 secs in 8 * 60 / 40 = 12 km answer : c
Answer: c
Problem: george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of christopher .
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 answer : a
Answer: a
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 74000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 74000 / 128000 = 74 / 128 = 37 / 65 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Problem: 10 ^ ( 65 ) ã · 10 ^ ( 64 ) = ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 1000 , e ) 10000
Rationale: "10 ^ ( 65 ) ã · 10 ^ ( 64 ) = 10 ^ ( 65 - 64 ) = 10 ^ 1 = 10 answer : b"
Answer: b
Problem: the average of the marks of 11 students in a class is 36 . if the marks of each student are doubled , find the new average ?
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 75
Rationale: sum of the marks for the 11 students = 11 * 36 = 396 . the marks of each student are doubled , the sum also will be doubled . the new sum = 396 * 2 = 792 . so , the new average = 792 / 11 = 72 . 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 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 9
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 : b"
Answer: b