regisss/math_qa huggingface dataset:
Problem: if 65 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 15 % = 35 % . the answer is c ."
Answer: c
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 73000 , 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 73000 / 129000 = 73 / 129 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 6 more than the average of 10 , 70 , and what number ?
Options: a ) 15 , b ) 25 , c ) 35 , d ) 22 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 6 = 34 sum of second list = 34 * 3 = 102 therefore the number = 102 - 80 = 22 answer : d"
Answer: d
Problem: if 150 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 38 , b ) 47 , c ) 32 , d ) 36 , e ) 37
Rationale: the question actually asks the highest power of 10 which divides 150 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 150 factorial will have 37 as - 150 / 5 = 30 30 / 5 = 6 6 / 5 = 1 so answer will be ( e ) 37
Answer: e
Problem: the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 131 cm . what was the actual average height of the students in the class ?
Options: a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm
Rationale: "the total height was 20 cm too much . the average height should be reduced by 20 cm / 20 = 1 cm the answer is a ."
Answer: a
Problem: a certain number of workers can do a work in 85 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 75 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 85 - 10 ) / 10 = 75 answer is a"
Answer: a
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 4 / 5 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 150 , c ) 60 , d ) 90 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 4 / 5 ) of total igneous rocks . ( 4 / 5 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 5 / 4 ) = 50 total sedimentary rocks = 2 * total igneous rocks = 2 * 50 = 100 total number of rocks = 50 + 100 = 150 answer ( b )"
Answer: b
Problem: car z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 384 , c ) 400 , d ) 408.3 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 48 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 38.4 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 38.4 miles / gallon * 10 gallons = 384 miles . answer b ."
Answer: b
Problem: mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24000 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 2000 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24000 ⁄ 12 = 2000 answer a"
Answer: a
Problem: in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ?
Options: a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32
Rationale: let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )
Answer: c
Problem: two trains start simultaneously from opposite ends of a 175 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 175 - km trip in 4 hours . train y , travelling at a constant rate , completes the 175 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 66 , b ) 69 , c ) 72 , d ) 75 , e ) 78
Rationale: if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 175 km to the meeting point , then train x travels ( 3 / 7 ) * 175 = 75 km . the answer is d .
Answer: d
Problem: the sum of two numbers is 16 . the difference is 4 . what are the two numbers ? let x be the first number . ley y be the second number x + y = 16 x - y = 4
Options: a ) 10 and 6 , b ) 10 and 5 , c ) 10 and 4 , d ) 10 and 3 , e ) 10 and 2
Rationale: solution let x be the first number . ley y be the second number x + y = 16 x - y = 4 solve the system of equations by elimination adding the left sides and the right sides gives : x + x + y + - y = 16 + 4 2 x = 20 x = 10 since x + y = 16 , 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 the numbers are 10 and 6 answer a
Answer: a
Problem: if 6 x = 8 y = 10 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 58 , c ) 84 , d ) 94 , e ) 168
Rationale: "6 x = 8 y = 10 z 3 x = 4 y = 5 z 3 ( 4 * 5 ) = 4 ( 3 * 5 ) = 5 ( 3 * 4 ) addition = 20 + 15 + 12 = 47 answer would be multiple of 47 which is 94 answer : d"
Answer: d
Problem: what is the rate percent when the simple interest on rs . 2000 amount to rs . 320 in 4 years ?
Options: a ) 4.5 % , b ) 4.25 % , c ) 4 % , d ) 4.3 % , e ) 4.1 %
Rationale: "interest for 1 year = 320 / 4 = 80 interest on rs 2000 p / a = 80 interest rate = 80 / 2000 * 100 = 4 % answer : c"
Answer: c
Problem: a ratio between two numbers is 4 : 5 and their l . c . m . is 200 . the first number is
Options: a ) 60 , b ) 40 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 4 x and 5 x . then , their l . c . m . is 20 x . ∴ 20 x = 200 ⇔ x = 10 . hence , the first number is 40 . answer b"
Answer: b
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?
Options: a ) rs . 9800 , b ) rs . 3800 , c ) rs . 9800 , d ) rs . 6800 , e ) rs . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 65280000 / 9600 ) = > p = rs . 6800 answer : d"
Answer: d
Problem: a sum of money at simple interest amounts to rs . 835 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 698 , c ) 778 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 835 ) = rs . 19 . s . i . for 3 years = rs . ( 19 x 3 ) = rs . 57 . principal = rs . ( 835 - 57 ) = rs . 778 . answer : c"
Answer: c
Problem: when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 81.1 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"
Answer: e
Problem: if a person walks at 10 km / hr instead of 8 km / hr , he would have walked 14 km more . the actual distance traveled by him is ?
Options: a ) 50 , b ) 40 , c ) 56 , d ) 16 , e ) 20
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 14 ) / 10 2 x - 112 = > x = 56 km . answer : c"
Answer: c
Problem: if twice of a number divided by 3 d gives 20 as the remainder , and 5 times of the same number gives 32 as the remainder . what will be the value of d ?
Options: a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 18
Rationale: remainder in second case is , 32 . so , 3 d > = 33 . so , minimum value of d should 11 . if number = 28 . double of number = 56 and take d = 12 so 56 / 36 remainder = 20 . now 5 times of number = 140 . so 140 / 36 remainder = 32 . that is , 3 d = 36 satisfy the conditions . so d = 12 . answer : b
Answer: b
Problem: 17 : 71 : : 18 : ?
Options: a ) 80 , b ) 25 , c ) 36 , d ) 81 , e ) 56
Rationale: "ans 81 reverse of 18 answer : d"
Answer: d
Problem: 3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
Options: a ) 40 % , b ) 45 % , c ) 57 % , d ) 58 % , e ) 60 %
Rationale: tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c
Answer: c
Problem: in the faculty of reverse - engineering , 500 second year students study numeric methods , 300 second year students study automatic control of airborne vehicles and 300 second year students study them both . how many students are there in the faculty if the second year students are approximately 50 % of the total ?
Options: a ) 1100 , b ) 1200 , c ) 1150 , d ) 1000 , e ) 1050
Rationale: "total number of students studying both are 500 + 300 - 300 = 500 ( subtracting the 300 since they were included in the both the other numbers already ) . so 50 % of total is 500 , so 100 % is 1000 answer is d"
Answer: d
Problem: two pipes a and b can separately fill a tank in 8 and 10 minutes respectively . a third pipe c can drain off 15 liters of water per minute . if all the pipes are opened , the tank can be filled in 10 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 160 liters , c ) 740 liters , d ) 560 liters , e ) 120 liters
Rationale: "1 / 8 + 1 / 10 - 1 / x = 1 / 10 x = 8 8 * 15 = 120 answer : e"
Answer: e
Problem: what annual installment will discharge a debt of $ 1092 due in 3 years at 12 % simple interest ?
Options: a ) $ 210 , b ) $ 115 , c ) $ 295 , d ) $ 325 , e ) $ 415
Rationale: "let each installment be x [ x + ( x * 12 * 1 / 100 ) ] + [ x + ( x * 12 * 2 / 100 ) ] + x = 1092 28 x / 25 + 31 x / 25 + x = 1092 x = 325 answer is d"
Answer: d
Problem: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 40 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 40 , b ) 33 , c ) 50 , d ) 51 , e ) 52
Rationale: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 40 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 20 cents . fraction of spirit is 1 / 2 . 20 = k * ( 1 / 2 ) k = 40 cost per liter = 40 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 40 * ( 1 / 3 ) * 3 = 40 cents a . 40 cents"
Answer: a
Problem: if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "e 40 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 54 days . so , 27 women can do it in ( 20 * 54 ) / 27 = 40 days ."
Answer: e
Problem: set q consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set q , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: a = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 0,16 , - 5,9 } y > 21 so l = median of q = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 13 times as heavy as water ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 13 w 19 + 9 x = 13 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is b"
Answer: b
Problem: x and y are both integers . if x / y = 59.60 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 315 , c ) 672 , d ) 900 , e ) 1024
Rationale: "remainder = 0.60 - - > 60 / 100 - - > can be written as ( 60 / 4 ) / ( 100 / 4 ) = 15 / 25 so remainders can be 15 , 30 , 45 , 60 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 15 + 30 + 45 + 60 + 75 + 90 = 315 answer : b"
Answer: b
Problem: a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is
Options: a ) 23477 , b ) 28000 , c ) 28877 , d ) 1987 , e ) 1771
Rationale: "explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000"
Answer: b
Problem: excluding stoppages , the average speed of a bus is 100 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 36 min
Rationale: in 1 hr , the bus covers 100 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 100 - 40 ) km i . e 60 km at 100 km / hr . stoppage time = 60 / 100 hrs = 36 min answer : e
Answer: e
Problem: tom traveled the entire 60 miles trip . if he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 35.62 mph , b ) 25.45 mph , c ) 34.52 mph , d ) 36.92 mph , e ) 36.29 mph
Rationale: avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 15 + 45 ) / ( ( 15 / 24 ) + ( 45 / 45 ) ) = 60 * 2 / 3 = 36.92 mph d
Answer: d
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 325,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,354 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 325000 [ 1 ] 0.04 x = 0.80 * 325000 = 260000 [ 2 ] 260000 + 0.09 y = 325000 - - > 0.09 y = 65000 [ 3 ] 260000 / 12 = 21666.67 [ 4 ] 65000 / 12 = 5416.667 [ 5 ] adding [ 4,5 ] we get : 27083.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.354 , ans a"
Answer: a
Problem: 80 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 60
Rationale: "answer = e please refer diagram below 70 - 10 = 60"
Answer: e
Problem: if w is the set of all the integers between 49 and 114 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 34 , b ) 44 , c ) 45 , d ) 55 , e ) 72
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 114 , the smallest is 51 ) : 114 - 51 = 63 step 2 . divide by 3 : 63 / 3 = 21 step 3 . add 1 : 21 + 1 = 22 . so there are 22 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 114 , the smallest is 50 ) : 114 - 50 = 64 step 2 . divide by 2 : 64 / 2 = 32 step 3 . add 1 : 32 + 1 = 33 . so there are 33 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 22 multiples of 3 and the 33 multiples of 2 : 22 + 33 = 55 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 22 + 33 = 55 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 55 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 114 - 54 = 60 step 2 . divide by 6 : 60 / 6 = 10 step 3 . add 1 : 10 + 1 = 11 . so there are 11 multiples of 6 within the range : we counted 11 numbers twice . subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3 : = 22 + 33 - 11 = 55 - 11 = 44 therefore , the final number of multiples of 2 , 3 or 6 is 44 . hence , this is the correct answer . ( b )"
Answer: b
Problem: four machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 4 = 6 so we need 6 - 4 = 2 more machines . answer : a"
Answer: a
Problem: a shopkeeper sold 8 articles at the cost price of 10 articles . then find the profit % or lost %
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 30 % , e ) 50 %
Rationale: "here 8 articles selling price = 10 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 8 = 25 % correct option is b"
Answer: b
Problem: what is the maximum number of pieces that a circular pizza can be cut into with 5 linear cuts ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 cut makes 2 pieces a second cut can make 4 pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces d"
Answer: d
Problem: the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 24 , e ) 1 / 25
Rationale: ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d
Answer: d
Problem: 45 pupil , out of them 12 in debate only and 22 in singing only . then how many in both ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c
Answer: c
Problem: of the 75 cars on a car lot , 45 have air - conditioning , 35 have power steering , and 12 have both air - conditioning and power steering . how many of the cars on the lot have neither air - conditioning nor power steering ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 18
Rationale: "total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a"
Answer: a
Problem: a corporation 5 times its annual bonus to 10 of its employees . what percent of the employees ’ new bonus is the increase ?
Options: a ) 12 % , b ) 18 % , c ) 80 % , d ) 20 % , e ) 15 %
Rationale: let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees ’ new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c .
Answer: c
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?
Options: a ) 4 years , b ) 8 years , c ) 10 years , d ) none of these , e ) can not be determined
Rationale: "explanation let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . age of the youngest child = x = 4 years . answer a"
Answer: a
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 25 % cut in the magazine budget , how much less must be spent ?
Options: a ) 705 , b ) 655 , c ) 656 , d ) 657 , e ) 658
Rationale: total cost 940 940 * 25 / 100 = 235 so the cut in amount is 235 the less amount to be spend is 940 - 235 = 705 answer : a
Answer: a
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 4 children and 5 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "20 / 5 = 4 answer : c"
Answer: c
Problem: if the selling price of 50 articles is equal to the cost price of 20 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 56 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 20 . loss % = 30 / 50 * 100 = 60 % answer d"
Answer: d
Problem: the mean of 50 observations was 40 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 40.46 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 40 × 50 + 48 – 23 ) = 2023 . therefore correct mean = 2023 / 50 = 40.46 . answer a"
Answer: a
Problem: a certain tests consists 8 sections with 25 questions , numbered from 1 to 25 , in each section . if a student answered all of the even - numbered questions correctly and 3 / 4 of the odd - numbered questions correctly , what was the total number of questions he answered correctly ? a . 150 b . 172 c . 174 d . 175 e . 176
Options: a ) 174 , b ) 150 , c ) 180 , d ) 175 , e ) 190
Rationale: each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 â ˆ — 104 = 96 + 78 = 17496 + 3 / 4 â ˆ — 104 = 96 + 78 = 174 answer : a
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 30 seconds . what is the length of the train ?
Options: a ) 500 m , b ) 620 m , c ) 872 m , d ) 150 m , e ) 765 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 30 ) m = 500 m . answer : a"
Answer: a
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 $ 0.60 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 ) $ 306 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.6 = $ 306 answer a"
Answer: a
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 10 xy / 3 = ?
Options: a ) a ) 10 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 10 * 3 * 1 ) / 3 = 30 / 3 = 10 a"
Answer: a
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 80 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 10 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 80 5 x = 50 x = 10 . age of the youngest child = x = 10 years . e )"
Answer: e
Problem: 2 is what percent of 40 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %
Rationale: "2 = x * 40 / 100 x = 5 % ans ; c"
Answer: c
Problem: a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividing the same number 19 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 15
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg
Options: a ) 175.59 , b ) 175.5 , c ) 175.57 , d ) 175.52 , e ) 175.11
Rationale: "explanation : since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c ) rs . 175.50"
Answer: c
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , the number of questions he attempts correctly , is :
Options: a ) 35 , b ) 46 , c ) 42 , d ) 30 , e ) 40
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 80 â € “ x ) . 4 x â € “ 1 ( 80 â € “ x ) = 120 or 5 x = 200 or x = 40 . answer : e"
Answer: e
Problem: find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 4 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 1 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 4 = 2 / 1 = 1 : 1 answer is c"
Answer: c
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?
Options: a ) 220010 , b ) 145778 , c ) 220110 , d ) 235467 , e ) 220001
Rationale: "( 555 + 445 ) * 2 * 110 + 10 = 220000 + 10 = 220010 a"
Answer: a
Problem: in a sports club with 55 members , 23 play badminton and 29 play tennis and 7 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 8
Rationale: "23 + 29 = 52 but where as total number is 55 - 7 = 48 therefore answer is 52 - 48 = 4 hence answer is c"
Answer: c
Problem: a garrison of 500 men has provisions for 20 days . at the end of 14 days , a reinforcement arrives , and it is now found that the provisions will last only for 3 days more . what is the reinforcement ?
Options: a ) 500 , b ) 1000 , c ) 1500 , d ) 3000 , e ) 2000
Rationale: "500 - - - - 20 500 - - - - 6 x - - - - - 3 x * 3 = 500 * 6 x = 1000 500 - - - - - - - 500 answer : a"
Answer: a
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 55 sec , b ) 40 sec , c ) 45 sec , d ) 30 sec , e ) 35 sec
Rationale: "t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer a"
Answer: a
Problem: in covering a distance of 54 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 9 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 54 / x - 54 / 2 x = 3 6 x = 54 x = 9 km / hr . answer : option e"
Answer: e
Problem: the length of minute hand of a clock is 5.6 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 16.41 , e ) 19.27
Rationale: area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.6 ^ 2 ) * ( 60 / 360 ) = 16.41 cm ^ 2 answer : d
Answer: d
Problem: john has $ 1600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e
Answer: e
Problem: a train 1000 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 m , b ) 256 m , c ) 1000 m , d ) 278 m , e ) 287 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1000 + x ) / 60 = 65 / 3 x = 300 m . answer : c"
Answer: c
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 181 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 10 : 1
Rationale: we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 181 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 181 m ) / ( w + m ) = 180 170 w + 181 m = 180 w + 180 m 1 m = 10 w m / w = 10 / 1 the ratio of men to women is 10 to 1 . e
Answer: e
Problem: if the length of the longest chord of a certain circle is 18 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 9 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - b"
Answer: b
Problem: a cistern 10 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 10 x 1.25 ) + 10 x 4 ] = 75 the answer is d .
Answer: d
Problem: a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 20 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 40,000 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 800 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 20 / ( 800 * 1000 ) = 1 / 40,000 d"
Answer: d
Problem: if 50 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 30 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 5 ( x - y ) = 3 ( x + y ) 2 x = 8 y x = 4 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 4 y ) x 100 ) = 25 % answer is e ."
Answer: e
Problem: how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 18 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: 18 km / hr = 18000 m / 3600 s = 5 m / s time = 600 / 5 = 120 seconds the answer is b .
Answer: b
Problem: calculate how many days it will take for 10 boys to paint a 80 m long wall if 6 boys can paint a 70 m long wall in 8 days ,
Options: a ) 9.48 days , b ) 3.48 days , c ) 7.48 days , d ) 5.48 days , e ) 6.48 days
Rationale: "the length of wall painted by one boy in one day = 70 / 6 * 1 / 8 = 1.46 m no . of days required to paint 50 m cloth by 8 boys = 80 / 10 * 1 / 1.46 = 5.48 days . d"
Answer: d
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 60 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220060
Rationale: "( 555 + 445 ) * 2 * 110 + 60 = 220000 + 60 = 220060 e"
Answer: e
Problem: a monkey start climbing up a tree 18 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 15 hrs it wil be 15 ft . bt since the height of the tree is 18 ft , so if the monkey hops up the tree in the next hr i . e 16 th hr then it reaches at the top of the tree . hence it takes 16 hrs for monkey to reach at the top answer : e"
Answer: e
Problem: jane and ashley take 8 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 14 days , b ) 15 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: "let us assume that the work is laying 40 bricks . jane = 5 bricks per day ashley = 1 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 20 remaining bricks = 40 - 28 = 12 so together , they would take 12 / 6 = 2 total no . of days = 8 + 4 + 2 = 14 answer is a"
Answer: a
Problem: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 32 ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 1 / 16 , d ) 1 / 14 , e ) 1 / 12
Rationale: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c"
Answer: c
Problem: today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d
Answer: d
Problem: a bullet train 150 m long is running with a speed of 30 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 15 sec
Rationale: e 15 sec speed of the bullet train relative to man = ( 30 + 6 ) kmph = 36 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 150 m at ( 30 / 3 ) m / sec = ( 150 * 3 / 30 ) sec = 15 sec
Answer: e
Problem: the sum of all the integers k such that – 21 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 39 , e ) - 51
Rationale: "- 20 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 20 - 19 sum of which is - 39 . hence option d . d"
Answer: d
Problem: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 30 . find the profit percentage ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 5 % , e ) none of these
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 150 ( 30 * 5 ) profit percentage = ( 150 - 100 ) / 100 * 100 = 50 % answer : b"
Answer: b
Problem: the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 130 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 8 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 14 ways . . c"
Answer: c
Problem: a worker ' s daily wage is increased by 50 % and the new wage is $ 30 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 15 , b ) $ 18 , c ) $ 20 , d ) $ 22 , e ) $ 25
Rationale: let x be the daily wage before the increase . 1.5 x = $ 30 x = $ 20 the answer is c .
Answer: c
Problem: what is 120 % of 13 / 24 of 600 ?
Options: a ) 320 , b ) 390 , c ) 440 , d ) 480 , e ) 510
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 25 = 390 the answer is b ."
Answer: b
Problem: if the weight of 12 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 6.7 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 12 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 12 kg ∴ weight of 6 m long rod = 13.4 x 6 / 12 = 6.7 kg option : a"
Answer: a
Problem: evaluate : 60 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 52 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 60 - 12 * 3 * 2 = 60 - 8 = 52 correct answer b"
Answer: b
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 108 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 16 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 108 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 108 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 8 ) ( b + 8 ) - 108 lb + 2 l + 2 b + 4 = lb + 8 l + 8 b + 64 - 108 simplify 6 l + 6 b = 48 - - - - - - > 2 ( l + b ) = 16 ( check eq ( 1 ) ) answer is c"
Answer: c
Problem: a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e
Answer: e
Problem: find the greatest common factor ( gfc ) of 24 , 40 and 60 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: we first write the prime factorization of each given number 24 = 2 × 2 × 2 × 3 = 23 * cubic * × 3 40 = 2 × 2 × 2 × 5 = 23 * cubic * × 5 60 = 2 × 2 × 3 × 5 = 22 * square * × 3 × 5 gfc = 22 * square * = 4 corect answer is d ) 4
Answer: d
Problem: when 242 is divided by a certain divisor the remainder obtained is 12 . when 698 is divided by the same divisor the remainder obtained is 16 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 10 . what is the value of the divisor ?
Options: a ) 11 , b ) 18 , c ) 13 , d ) 23 , e ) none of these
Rationale: "let that divisor be x since remainder is 12 or 16 it means divisor is greater than 16 . now 242 - 12 = 230 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 16 = 682 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 230 + 682 ) + 12 + 16 = x ( k + l ) + 28 when we divide this number by x then remainder will be equal to remainder of ( 28 divided by x ) = 10 hence x = 28 - 10 = 18 hence b"
Answer: b
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 20 % ?
Options: a ) 37.5 % , b ) 48 % , c ) 50.5 % , d ) 52 % , e ) 25 %
Rationale: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 80 gain % = 16 / 64 * 100 = 25 % . answer : option e"
Answer: e
Problem: by selling 22 pens for a rupee a woman loses 10 % . how many for a rupee should he sell in order to gain 50 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65
Rationale: "d 90 % - - - 22 150 % - - - ? 90 / 150 * 22 = 13"
Answer: d
Problem: 1394 x 1394
Options: a ) 1943236 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1394 x 1394 = ( 1394 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 6 ) 2 - ( 6 x 1400 x 6 ) = 1943236 . answer : option a"
Answer: a
Problem: a and b start a business jointly . a invests rs 16000 for 8 month and b remains in the business for 4 months . out of total profit , b claims 2 / 7 of the profit . how much money was contributed by b ?
Options: a ) 12800 , b ) 13000 , c ) 11500 , d ) 12500 , e ) 12000
Rationale: b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 × 8 : b × 4 therefore , 16000 × 8 : b × 4 = 5 : 2 16000 × 8 × 2 = b × 4 × 5 16000 × 2 × 2 = b × 5 3200 × 2 × 2 = b b = 12800 answer is a .
Answer: a
Problem: the second of two numbers is two less than 3 times the first . find the numbers if there sum is 82 .
Options: a ) 7 - 19 , b ) 8 - 20 , c ) 10 - 16 , d ) 15 - 9 , e ) 21 - 61
Rationale: we are looking for two numbers . # 1 - x # 2 - 3 x â € “ 2 the sum is 82 . # 1 + # 2 = 82 substituting x + 3 x â € “ 2 = 82 4 x â € “ 2 = 82 4 x = 84 x = 21 the first number is 21 , the second number is two less than three times 21 or 61 . correct answer e
Answer: e
Problem: john and steve are speed walkers in a race . john is 10 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 24 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 10 + 2 - - - > 0.5 t = 12 - - - > t = 24 seconds . c is the correct answer ."
Answer: c
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 171 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1425 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 171 . ∴ x 16 x 9 / 12 x 1 / 100 } = 171 or x = 1425 . ∴ p . w . = rs . 1425 . answer c"
Answer: c
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 540 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 720 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 15 , e ) 16
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 540 . . . eq 1 8 x + 32 y = 720 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1080 8 x = 720 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 720 . . . then we get 32 y = 640 then y = 20 differenece between x and y is 10 answer : c"
Answer: c
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45
b ) 50
c ) 55
d ) 60
e ) 63
Rationale: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a
Answer: a
Problem: sum of two numbers prime to each other is 12 and their l . c . m . is 35 . what are the numbers ?
Options: a ) 8 and 4 , b ) 7 and 5 , c ) 6 and 5 , d ) 8 and 5 , e ) 6 and 5
Rationale: "as two numbers are prime , only options satisfy ie option b and c and d , e but option a will not make the product of numbers i . e 35 answer : b"
Answer: b
Problem: two employees x and y are paid a total of rs . 440 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 440 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 440 â ‡ ’ y [ 12 / 10 + 1 ] = 440 â ‡ ’ 22 y / 10 = 440 â ‡ ’ 22 y = 4400 â ‡ ’ y = 4400 / 22 = 400 / 2 = rs . 200 b )"
Answer: b
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 4 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.25 * 8 = 0.2 ( x + 8 ) - - > x = 4 . answer : a ."
Answer: a