regisss/math_qa huggingface dataset:
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 40 year . what is the age of the youngest child ?
Options: a ) 2 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 40 â ‡ ” 5 x = 10 â ‡ ” x = 2 . â ˆ ´ age of the youngest child = x = 2 years . answer a"
Answer: a
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 6 students is 14 years and that of the other 9 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 6 + 16 * 8 ) ] = 13 years . answer : c"
Answer: c
Problem: find the annual income derived by investing $ 6800 in 10 % stock at 136 .
Options: a ) 550 , b ) 500 , c ) 250 , d ) 300 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 10 . by investing $ 6800 , income obtained = $ [ ( 10 / 136 ) * 6800 ] = $ 500 . answer b ."
Answer: b
Problem: find the sum of first 32 natural numbers
Options: a ) 470 , b ) 468 , c ) 465 , d ) 463 , e ) 528
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 32 ( 32 + 1 ) / 2 = 32 ( 33 ) / 2 = 528 answer : option e"
Answer: e
Problem: how many 4 digit numbers are there , if it is known that the first digit is odd , the second is even , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 380
Rationale: "4 options for the first digit : 1 , 3 , 5 , 7 , 9 ; 5 options for the second digit : 0 , 2 , 4 , 6 , 8 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 5 * 5 * 4 * 4 = 400 numbers with two 2 - s , 2 x 2 x 5 * 1 * 1 * 4 = 20 . thus there are 400 - 20 = 380 such numbers . answer : e ."
Answer: e
Problem: there are 60 people and 3 clubs m , s , and z in a company . 16 people joined m , 18 people joined s and 11 people joined z . if the members of m did not join any other club , at most , how many people of the company did not join any club ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: answer e . key is ' atmost ' here . so 16 people joined m . 18 people joined s and 11 people joined z . to get maximum people who did not join any club , 11 people who joined z are among 18 people who joined s . so 18 + 16 = 34 60 - 34 = 26
Answer: e
Problem: 3 * 14 + 3 * 15 + 3 * 18 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 152
Rationale: "3 * 14 + 3 * 15 + 3 * 18 + 11 = 42 + 45 + 54 + 11 = 152 the answer is e ."
Answer: e
Problem: how many digits 2 ^ 10 has ?
Options: a ) 3 , b ) 35 , c ) 50 , d ) 99 , e ) 101
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 therefore 3 digits would be my best guess a"
Answer: a
Problem: 550 − ( 104 ÷ 20.8 ) = ?
Options: a ) 545 , b ) 525 , c ) 535 , d ) 625 , e ) 105
Rationale: "explanation : = 550 − ( 104 / 208 x 10 ) = 550 − 5 = 545 option a"
Answer: a
Problem: what is the greatest prime factor of 4 ^ 6 - 1 ?
Options: a ) 13 , b ) 17 , c ) 19 , d ) 23 , e ) 29
Rationale: "4 ^ 6 - 1 = ( 4 ^ 3 - 1 ) ( 4 ^ 3 + 1 ) = 63 * 65 = 7 * 9 * 5 * 13 the answer is a ."
Answer: a
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 4 ( 1 - x ) p 12 xp = 4 p - 4 xp 16 xp = 4 p x = 1 / 4 the answer is b ."
Answer: b
Problem: find the simple interest on rs . 620 for 10 months at 10 paisa per month ?
Options: a ) 277 , b ) 620 , c ) 640 , d ) 678 , e ) 121
Rationale: "i = ( 620 * 10 * 10 ) / 100 = 620 answer : b"
Answer: b
Problem: one pump drains one - half of a pond in 4 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 4 hours so 8 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 8 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 8 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 8 + 1 / a ) = 1 / 2 solving u get a = 8 / 7 = 1.1 hence answer is b"
Answer: b
Problem: if 0.60 : x : : 6 : 4 , then x is equal to
Options: a ) 0.1 , b ) 0.4 , c ) 0.82 , d ) 0.8 , e ) none
Rationale: "sol . ( x × 6 ) = ( 0.60 × 4 ) ⇒ x = 2.4 / 6 = 0.40 . answer b"
Answer: b
Problem: in a small snack shop , the average ( arithmetic mean ) revenue was $ 400 per day over a 10 - day period . during this period , if the average daily revenue was $ 360 for the first 6 days , what was the average daily revenue for the last 4 days ?
Options: a ) $ 420 , b ) $ 440 , c ) $ 450 , d ) $ 460 , e ) $ 480
Rationale: the average revenue was $ 400 per day over a 10 - day period - - > total revenue over 10 - day period is 10 * $ 400 = $ 4000 ; the average daily revenue was $ 360 for the first 6 days - - > total revenue for the first 6 days is 6 * $ 360 = 2160 ; total revenue for the last 4 days is $ 4000 - 2160 = $ 1840 ; average daily revenue for the last 4 days is $ 1840 / 4 = $ 460 . answer : d .
Answer: d
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 50 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 101 ° f , b ) 108 ° f , c ) 116 ° f , d ) 122 ° f , e ) 127 ° f
Rationale: let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 50 ) / 5 + 32 = 122 ° f the answer is d .
Answer: d
Problem: louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compunded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?
Options: a ) 333 , b ) 383 , c ) 402 , d ) 433 , e ) 483
Rationale: let the monthly payment be xx . after the 1 st month there will be 1000 ∗ 1.1 − x dollars left to repay ; after the 2 nd month there will be ( 1000 ∗ 1.1 − x ) ∗ 1.1 − x = 1210 − 2.1 x dollars left to repay ; after the 3 rd month there should be 0 dollars left to repay : ( 1210 − 2.1 x ) ∗ 1.1 − x = 0 - - > 1331 = 3.31 x - - > x ≈ 402 x ≈ 402 answer : c .
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 26 . if n / j = 150.40 , what is value of j ?
Options: a ) 75 , b ) 65 , c ) 60 , d ) 130 , e ) 30
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 150.40 here 150 the quotient . given that remainder = 26 so , 150.40 = 150 + 26 / j so , j = 65 answer : b"
Answer: b
Problem: kim has 9 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 18 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 11 / 5 , c ) 1 / 9 , d ) 1 / 17 , e ) 1 / 5
Rationale: "can be tackled in this way as well : probability of selecting any 1 out of 10 shoes = 18 / 18 = 1 probability of selecting the next shoe ( out of 18 available ) having the same color = 1 / 18 ( as after selecting the 1 st one , there is only 1 another shoe left with the same color ) . thus the total probability = 1 * 1 / 17 = 1 / 17 . d is the correct answer ."
Answer: d
Problem: rahim bought 4 pillows with the average cost of $ 5 . if rahim also buys the fifth pillow with the price of $ 10 , what is the average ( arithmetic mean ) price of those 5 pillows ?
Options: a ) $ 6 , b ) $ 5 , c ) $ 5.5 , d ) $ 6.5 , e ) $ 7
Rationale: 4 pillowss - > total cost = 4 * avg cost = 4 * 5 = 20 fifth pillow cost = 10 total cost for 5 pillows = 20 + 10 = 30 am = 30 / 5 = 6 hence a
Answer: a
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total e of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) 6 : 4 : 3 : 13 - - - - > this means , the total number e must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Problem: - 84 x 19 + 100 = ?
Options: a ) 2436 , b ) 2801 , c ) - 1496 , d ) - 2071 , e ) none of them
Rationale: "given exp . = - 84 x ( 20 - 1 ) + 100 = - ( 84 x 20 ) + 84 + 100 = - 1680 + 184 = - 1496 answer is c"
Answer: c
Problem: the length of a rectangle is halved , while its breadth is tripled . whatis the % change in area ?
Options: a ) 30 % , b ) 40 % , c ) 50 percent , d ) 60 % , e ) 70 %
Rationale: "let original length = x and original breadth new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 15 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 26.66 , e ) $ 65.23
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 15 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 15 solve for x x = $ 26.66 correct answer d"
Answer: d
Problem: the average of first six prime numbers which are between 20 and 60 is
Options: a ) 34 , b ) 42 , c ) 45.7 , d ) 57 , e ) 67
Rationale: "explanation : first six prime numbers which are between 20 and 60 = 23 , 29 , 31 , 37 , 41 , 43 average = ( 23 + 29 + 31 + 37 + 41 + 43 ) / 6 = 34 answer : a"
Answer: a
Problem: the length of the bridge , which a train 155 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 220 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 155 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 220 m answer : a"
Answer: a
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 20 % of 300 seeds germinated , so 0.20 x 300 = 60 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 130 / 500 ) x 100 % , or 26 % . answer : b ."
Answer: b
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 3 / 5 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 150 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 3 / 5 ) of total igneous rocks . ( 3 / 5 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 5 / 3 ) = 50 total sedimentary rocks = 2 * total igneous rocks = 2 * 50 = 100 total number of rocks = 50 + 100 = 150 answer ( d )"
Answer: d
Problem: there are 20 poles with a constant distance between each pole . a car takes 22 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 38 , b ) 41 , c ) 28 , d ) 88 , e ) 22
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 22 seconds 1 pole ( 22 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 22 / 11 ) seconds = 38 seconds answer : a"
Answer: a
Problem: meena wrote all the numbers from 1 to 39,999 inclusive . how many digits did she write in total ?
Options: a ) 156,789 , b ) 188,889 , c ) 192,389 , d ) 241,689 , e ) 275,889
Rationale: 1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 39999 = > 5 * 30,000 = 150,000 the answer is 188,889 the answer is b .
Answer: b
Problem: solution a is 20 % salt and solution b is 70 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 2 : 3 , d ) 4 : 6 , e ) 3 : 7
Rationale: "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 70 - 50 ) / ( 50 - 20 ) = 2 / 3 so the volume of the two solutions will be equal . answer has to be 2 : 3 c"
Answer: c
Problem: what is the smallest integer that satisfies the inequality ( x - 3 ) / ( x ^ 2 - 8 x - 20 ) > 0 > 0 ?
Options: a ) - 2 , b ) 10 , c ) 3 , d ) - 1 , e ) 0
Rationale: "explanatory answer let us factorize the denominator and rewrite the expression as x − 3 / ( x − 10 ) ( x + 2 ) > 0 equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good . the values that are relevant to us are x = 3 , x = 10 and x = - 2 . let us arrange these values in ascending order : - 2 , 3 and 10 . the quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals . interval 1 : x < - 2 . pick a value in that range and check whether the inequality holds good . let us take x = - 10 . when x = - 10 , x − 3 / ( x − 10 ) ( x + 2 ) < 0 ; the inequality does not hold good in this interval . interval 2 : - 2 < x < 3 . let us take x = 0 . when x = 0 , x − 3 / ( x − 10 ) ( x + 2 ) = 0 − 3 / ( 0 − 10 ) ( 0 + 2 ) > 0 ; the inequality holds good in this interval . the least integer value that x can take if x > - 2 is x = - 1 . so , the correct answer is - 1 . choice d . remember : we have to find out the least integer value . and we have arrived at - 1 . do , not waste time computing the entire range of values of x that satisfy the inequality . note : in any inequality question , when the question asks us to determine the intervals in which the inequality holds good , we have to eliminate values of x that will result in the denominator becoming zero . choice d"
Answer: d
Problem: in a 100 m race , a covers the distance in 36 seconds and b in 45 second . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) none of these
Rationale: "solution distance covered by b in 9 sec . = ( 100 / 45 x 9 ) m = 20 m . ∴ a beats b by 20 metres . answer a"
Answer: a
Problem: a owner of a mart earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just double of that made on the previous day . on the 10 th day of business , he earns an income of :
Options: a ) 18 , b ) 21 , c ) 22 , d ) 20 , e ) 30
Rationale: 2 nd day he earns = 2 ( 2 – 1 ) 3 rd day he earns = 2 ( 3 – 1 ) on 10 th day he earns 2 ( 10 - 1 ) = 18 rupees answer : a
Answer: a
Problem: if p = 125 × 243 × 16 / 405 , how many digits are in p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: p = 125 * 243 * 16 / 405 p = 5 ^ 3 * 3 * 9 ^ 2 * 4 ^ 2 / ( 5 * 9 ^ 2 ) p = 5 ^ 2 * 3 * 4 ^ 2 p = 20 ^ 2 * 3 = 1200 answer d
Answer: d
Problem: jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 34 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25
Rationale: "check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 24 , child = 12 , years ago = 34 - 24 = 10 - - > child ' s age now = 12 + 10 = 22 . answer : e ."
Answer: e
Problem: from the sale of sleeping bags , a retailer made a gross profit of 17 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 23.93 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.17 = selling price - - > cost price * 1.17 = $ 28 - - > cost price = $ 23.93 . answer : c ."
Answer: c
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 6.5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 22 , e ) 5.6
Rationale: let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 26 x = 4 ( 3 x + 5 ) 14 x = 20 x = 1.4 quantity of alcohol = ( 4 x 1.4 ) litres = 5.6 litres . answer : e
Answer: e
Problem: if the diagonals of a rhombus are 24 cm and 10 cm , what will be its perimeter
Options: a ) 42 cm
b ) 64 cm
c ) 56 cm
d ) 52 cm
e ) none of these
Rationale: explanation : let the diagonals be pr and sq such that pr = 24 cm and sq = 10 cm po = or = 24 / 2 = 12 cm so = oq = 10 / 2 = 5 cm pq = qr = rs = sp = √ ( 122 + 52 ) = √ ( 144 + 25 ) = √ 169 = √ 13 cm perimeter = 4 × 13 = 52 cm answer : option d
Answer: d
Problem: the cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810 . the breadth of the room is :
Options: a ) 7 m , b ) 7.5 m , c ) 8 m , d ) 8.5 m , e ) none of these
Rationale: length of the carpet = totalcost / rate / m = ( 8100 ⁄ 45 ) m = 180 m . area of the room = area of the carpet = ( 180 × 75 ⁄ 100 ) m 2 = 135 m 2 ∴ breadth of the room = arealength = 135 / 18 m = 7.5 m answer b
Answer: b
Problem: a farmer with 1350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 300 = 450 more acres were planted with tobacco . the answer is e .
Answer: e
Problem: a metallic sheet is of rectangular shape with dimensions 50 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 5440 , b ) 5120 , c ) 6420 , d ) 7500 , e ) 8960
Rationale: "l = ( 50 - 16 ) m = 34 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 34 x 20 x 8 ) m 3 = 5440 m 3 . answer : option a"
Answer: a
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 3.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 1998 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 3.0 = 1998 answer : c"
Answer: c
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 9 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 9 pounds of clothes doubles the ratio of books to clothes , then 9 pounds represents half the weight of the clothes . 2 k = 9 pounds and then k = 4.5 pounds . the electronics weigh 2 ( 4.5 ) = 9 pounds . the answer is c ."
Answer: c
Problem: for a race a distance of 224 meters can be covered by p in 7 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 800 m , b ) 838 m , c ) 834 m , d ) 831 m , e ) 836 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 7 = 32 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 25 seconds therefore , distance covered by p in that time = 32 m / s x 25 seconds = 800 metres answer : a"
Answer: a
Problem: in a particular state , 70 % of the counties received some rain on monday , and 55 % of the counties received some rain on tuesday . no rain fell either day in 35 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: 70 + 55 + 35 = 160 % the number is 60 % above 100 % because 60 % of the counties were counted twice . the answer is d .
Answer: d
Problem: the present worth of a certain bill due sometime hence is rs . 400 and the true discount is rs . 20 . what is the banker ' s discount ?
Options: a ) rs . 19 , b ) rs . 22 , c ) rs . 20 , d ) rs . 21 , e ) none of these
Rationale: "explanation : bg = ( td ) 2 / pw = 202 / 400 = rs . 1 bg = bd – td = > 1 = bd - 20 = > bd = 1 + 20 = rs . 21 answer : option d"
Answer: d
Problem: the true discount on a bill of rs . 2660 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 416 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2660 td = rs . 360 pw = f - td = 2660 - 360 = rs . 2300 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2300 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 2300 × 2660 = 0.16 × 2660 = rs . 416 answer : option c"
Answer: c
Problem: a train covered half of the distance between stations a and b at the speed of 48 km / hr , but then it had to stop for 15 min . to make up for the delay , it increased its speed by 53 m / sec and it arrived to station b on time . find the distance between the two stations and the speed of the train after the stop .
Options: a ) 206 , b ) 216 , c ) 226 , d ) 256 , e ) 246
Rationale: first let us determine the speed of the train after the stop . the speed was increased by 53 m / sec = 5 ⋅ 60 ⋅ 6031000 km / hr = 6 km / hr . therefore , the new speed is 48 + 6 = 54 km / hr . if it took x hours to cover the first half of the distance , then it took x − 1560 = x − 0.25 hr to cover the second part . so the equation is : 48 ⋅ x = 54 ⋅ ( x − 0.25 ) 48 ⋅ x = 54 ⋅ x − 54 ⋅ 0.25 48 ⋅ x − 54 ⋅ x = − 13.5 − 6 x = − 13.5 x = 2.25 h . the whole distance is 2 × 48 × 2.25 = 216 km . answer is b .
Answer: b
Problem: a certain city with a population of 84,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 7,000 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 84 k x = 7,000 answer : c"
Answer: c
Problem: if the number 892 , 132,27 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 132,27 x sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 7 = 19 ( ii ) ( i ) - ( ii ) = 15 + x - 19 = x - 4 hence x should be = 4 to make this a multiple of 11 ( 0 ) option d"
Answer: d
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.0 , 9.0 , 6.0 , and 8.8 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 77.76
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.8 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8 + 8.8 ) = 24.3 point of value of the dive = 24 * 3.2 = 77.76 answer e"
Answer: e
Problem: square p is inscribed in circle q . if the perimeter of p is 40 , what is the circumference of q ?
Options: a ) 11 √ 2 π
b ) 10 √ 2 π
c ) 9 √ 2 π
d ) 8 √ 2 π
e ) 7 √ 2 π
Rationale: square forms two right angled triangles . any time we have a right angle triangle inside a circle , the hypotenuse is the diameter . hypotenuse here = diagonal of the square = 10 sqrt ( 2 ) = diameter = > radius = 5 sqrt ( 2 ) circumference of the circle = 2 pi r = 10 pi sqrt ( 2 ) answer is b .
Answer: b
Problem: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 19 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 2,470
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 19 and c = 1 / 2 into the equation and simplify to get the answer 2470 . option e ."
Answer: e
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams . find the profit percent .
Options: a ) 20 , b ) 15 , c ) 25 , d ) 18 , e ) 19
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 800 100 + g / 100 + 0 = 1000 / 800 100 + g = 5 / 4 * 100 g = 25 answer : c"
Answer: c
Problem: the unit digit in the product ( 293 * 567 * 917 * 343 ) is :
Options: a ) 2 , b ) 1 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 3 * 7 * 7 * 4 ) = 1 answer : b"
Answer: b
Problem: what percent is 120 of 80 ?
Options: a ) 150 % , b ) 134 1 / 3 % , c ) 135 1 / 3 % , d ) 140 1 / 3 % , e ) 143 1 / 3 %
Rationale: "120 / 80 = 3 / 2 3 / 2 × 100 = 300 / 2 = 150 % a"
Answer: a
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 20 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 4 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 20 more blue balls than white balls . . . equation # 2 : y = 20 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 20 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 20 ) = 100 5 y - 20 = 100 5 y = 120 y = 24 there are 24 blue balls . this is 20 more than the number of white balls , so z = 4 . that ' s the answer . just as a check , x = 72 , and 72 + 24 + 4 = 100 . answer = 4 , ( a )"
Answer: a
Problem: the cost of 2 chairs and 3 tables is rs . 1600 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 400
Rationale: explanation : 2 c + 3 t = 1600 - - - ( 1 ) 3 c + 3 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 400 = > t - c = 400 answer : e
Answer: e
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 6 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 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 35 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 6 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 6 or 45 * 18 - 45 * x + 36 * x = 6 * 100 or 9 x = - 6 * 100 + 45 * 18 x = 210 / 6 = 35 % d"
Answer: d
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 20 % of the total school population of x students , what is x ?
Options: a ) 125 , b ) 150 , c ) 212 , d ) 250 , e ) 500
Rationale: 90 = x / 100 * 20 / 100 * x = > x ^ 2 = 9 * 10000 / 2 = > x = 212 c
Answer: c
Problem: a sells a bicycle to b and makes a profit of 20 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 150
Rationale: "explanation : answer : e"
Answer: e
Problem: 16 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 16 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 16 * 21 * 8 = 14 * x * 6 x = 32 answer : a"
Answer: a
Problem: a and b complete a work in 4 days . a alone can do it in 6 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.7 days , c ) 3.6 days , d ) 2.4 days , e ) 5.75 days
Rationale: "1 / 4 + 1 / 6 = 5 / 12 12 / 5 = 2.4 days answer : d"
Answer: d
Problem: a 5 digit number divisible by 3 is to be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 without repetitions . that total no of ways it can be done is ?
Options: a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 220
Rationale: first step : we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0,1 , 2,3 , 4,5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = ( 1 , 2,3 , 4,5 ) and 15 - 3 = ( 0 , 1,2 , 4,5 ) . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2,3 , 4,5 and 0 , 1,2 , 4,5 . how many 5 digit numbers can be formed using this two sets : 1 , 2,3 , 4,5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1,2 , 4,5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 96 120 + 96 = 216 answer : c .
Answer: c
Problem: solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 8 kilograms of solutions y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new liquid solution is liquid x ?
Options: a ) 30 % , b ) 33 1 / 3 % , c ) 37 1 / 2 % , d ) 40 % , e ) 50 %
Rationale: "at the beginning , you have 8 kg of solution y , i . e . 70 % * 8 kg = 5,6 kg of water 30 % * 8 kg = 2,4 kg of x 2 kg of water evaporate : 5,6 kg - 2 kg = 3,6 kg of water 2,4 kg of x 2 kg of liquid are added : 3,6 kg + 2 * 0,70 = 5 kg of water 2,4 kg + 2 * 0,30 = 3 kg of x so you have 3 kg of x in 8 kg ( 3 + 5 ) solution . therefore x concentration is 3 / 8 = 37,5 % answer : c"
Answer: c
Problem: the sum of ages of 5 children born 1 year different each is 50 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 ) and ( x + 4 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 5 x = 40 x = 8 x + 4 = 8 + 1 = 9 answer : b"
Answer: b
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 15 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 146.6 , b ) $ 120 , c ) $ 180 , d ) $ 220 , e ) $ 260
Rationale: lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.15 e = = > 11 a = 220 + 11.5 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 220 + 11.5 e = = > 1.5 e = 220 or e = 440 / 3 = 146.6 a
Answer: a
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 52.5 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 3 , e ) 2
Rationale: "going down = 20 m going up = 10 - - > total = 30 going down = 10 - - > total = 40 going up = 5 - - > total = 45 going down = 5 - - > total = 50 going up = 2.5 - - > total = 52.5 ( caught ) no of bouncing = 3 answer : d"
Answer: d
Problem: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?
Options: a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 76
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 21 ^ 2 / 2 - 17 ^ 2 / 2 = 152 / 2 = 76 ans e ."
Answer: e
Problem: in a urban village of india named ` ` owlna ' ' , 80 % people have refrigerator , 82 % people have television , 70 % people got computers and 75 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 3 % , b ) 8 % , c ) 7 % , d ) 10 % , e ) 15 %
Rationale: "c 7 % 100 - [ ( 100 - 80 ) + ( 100 - 82 ) + ( 100 - 70 ) + ( 100 - 75 ) ] = 100 - ( 20 + 18 + 30 + 25 ) = 100 - 93"
Answer: c
Problem: in a certain alphabet , 8 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 8 + 24 = 32 ; next , we find the total # of letters without line : 40 - 32 = 8 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 8 - 0 = 8 . b"
Answer: b
Problem: ( 18 ) 7 x ( 5832 ) - 2 ÷ ( 324 ) - 1 = ( 18 ) 7
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "explanation : ( 18 ) 7 x ( 183 ) - 2 ÷ ( 182 ) - 1 ( 18 ) 7 x ( 18 ) - 6 ÷ ( 18 ) - 2 ( 18 ) 7 - 6 + 2 = ( 18 ) 3 answer : option c"
Answer: c
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number w of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see w = 5 or 1 will give you same equation . . ans d"
Answer: d
Problem: rajan is sixth from the left end and vinay is tenth from the right end in a row of boys . if there are 8 boys between rajan and vinay , how many boys are there in the row ?
Options: a ) 24 , b ) 66 , c ) 88 , d ) 27 , e ) 91
Rationale: explanation : number of boys in the row = ( 6 + 10 + 8 ) = 24 answer : a ) 24
Answer: a
Problem: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 2.98 , b ) 2.88 , c ) 2.82 , d ) 2.86 , e ) 2.81
Rationale: "m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"
Answer: b
Problem: find k if 64 / k = 8 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 64 / k = 8 and 64 / 8 = 8 , then k = 8 correct answer c"
Answer: c
Problem: the unit digit in the product ( 445 * 534 * 999 * 234 ) is :
Options: a ) 2 , b ) 0 , c ) 6 , d ) 5 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 4 * 9 * 4 ) = 0 answer : b"
Answer: b
Problem: the difference of two numbers is 1097 . on dividing the larger number by the smaller , we get 10 as quotient and the 17 as remainder . what is the smaller number ?
Options: a ) 230 , b ) 120 , c ) 95 , d ) 310 , e ) 320
Rationale: "solution : let the smaller number be x . then larger number = ( x + 1097 ) x + 1097 = 10 x + 17 9 x = 1080 x = 120 answer b"
Answer: b
Problem: a boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream , it takes 5 hours . what is the speed of the boat in still water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 1
Rationale: explanation : rate downstream = ( 20 / 2 ) kmph = 10 kmph ; rate upstream = ( 20 / 5 ) kmph = 4 kmph speed in still water = 1 / 2 ( 10 + 4 ) kmph = 7 kmph answer : b
Answer: b
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required .
Options: a ) 30 , b ) 60 , c ) 120 , d ) 240 , e ) 480
Rationale: "the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b"
Answer: b
Problem: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 6 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 8 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 6 days whole work will be done by a in 6 * 4 / 3 = 8 days answer is d"
Answer: d
Problem: what distance will be covered by a bus moving at 72 kmph in 30 seconds ?
Options: a ) 877 m , b ) 600 m , c ) 167 m , d ) 176 m , e ) 546 m
Rationale: "explanation : 72 kmph = 72 * 5 / 18 = 20 mps d = speed * time = 20 * 30 = 600 m . answer : b"
Answer: b
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 40 * 2 + 80 * 2 ) / ( 2 + 2 ) = 240 / 4 = 60 answer : c"
Answer: c
Problem: a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 130 feet , b ) 22 feet , c ) 20 feet , d ) 15 feet , e ) 10 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 10 * breadth = 600 = > breadth = 60 feet area to be fenced = 2 b + l = 2 * 60 + 10 = 130 feet answer : option a"
Answer: a
Problem: find the greatest number which leaves the same remainder when it divides 20 , 40 and 90 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 10 , e ) none of these
Rationale: "90 - 40 = 50 40 - 20 = 20 90 - 20 = 70 the h . c . f of 20 , 50 and 70 is 10 . answer : d"
Answer: d
Problem: what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 p . c . p . a ?
Options: a ) rs . 10111.00 , b ) rs . 10123.20 , c ) rs . 10123.00 , d ) rs . 10100.00 , e ) rs . 10110.00
Rationale: "= rs . ( 25000 x ( 1 + 12 / 100 ) ³ = rs . ( 25000 x 28 / 25 x 28 / 25 x 28 / 25 ) = rs . 35123.20 . c . i = rs ( 35123.20 - 25000 ) = rs . 10123.20 answer : b"
Answer: b
Problem: a bag contains 2 white marbles and 2 black marbles . if each of 2 girls and 2 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "first , total ways to select for all boys and girls , i . e 4 ! / ( 2 ! * 2 ! ) = 4 * 3 * 2 * 1 / 2 * 1 * 2 * 1 = 6 then there are one two way girls can have all same colors , either white or black . the number of ways in which 2 girls can select 2 white balls = 2 c 2 = 1 the number of ways in which 2 girls can select 2 black balls = 2 c 2 = 1 therefore , total favorable outcomes / total outcomes = 2 / 6 = 1 / 3 c"
Answer: c
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 100000 . if the profit at the end of a year is rs . 108000 , then the share of b is ?
Options: a ) 40000 , b ) 50000 , c ) 70000 , d ) 60000 , e ) 80000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 100000 * 6 ) = 7 : 20 total profit = rs . 108000 share of b = 20 / 27 ( 108000 ) = rs . 80000 answer : e"
Answer: e
Problem: matt and peter can do together a piece of work in 20 days . after they have worked together for 10 days matt stops and peter completes the remaining work in 10 days . in how many days peter complete the work separately .
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "together they complete the job in 20 days means they complete 10 / 20 of the job after 10 days . peter completes the remaining ( 10 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 10 / 20 ) = 20 b"
Answer: b
Problem: a grocer has a sale of rs . 7435 , rs . 7927 , rs . 7855 , rs . 8230 and rs . 7562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) rs . 1991 , b ) rs . 2991 , c ) rs . 3991 , d ) rs . 4991 , e ) rs . 5991
Rationale: "explanation : total sale for 5 months = rs . ( 7435 + 7927 + 7855 + 8230 + 7562 ) = rs . 39009 . required sale = rs . [ ( 7500 x 6 ) â € “ 39009 ] = rs . ( 45000 â € “ 39009 ) = rs . 5991 . answer e"
Answer: e
Problem: how many seconds will a 150 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 sec , b ) 30 sec , c ) 86 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 150 * 3 / 50 = 15 sec . answer : d"
Answer: d
Problem: in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the fifth row ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 16
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 5 th row is 1 + 3 ( 4 ) = 13 the answer is c ."
Answer: c
Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 7 : 5 , b ) 12 : 11 , c ) 17 : 15 , d ) 22 : 17 , e ) 27 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 2 y and y . 2 ( 3 x + 2 x ) = 2 ( 2 y + y ) 5 x = 3 y ( 5 / 3 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 2 y * y = 6 x ^ 2 : 2 y ^ 2 = 6 x ^ 2 : 2 * ( 25 / 9 ) * x ^ 2 = 54 : 50 = 27 : 25 the answer is e ."
Answer: e
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 6 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 6.8 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 24 x = 4 ( 3 x + 5 ) 12 x = 20 x = 1.7 quantity of alcohol = ( 4 x 1.7 ) litres = 6.8 litres . answer : b"
Answer: b
Problem: a cistern is filled by pipe a in 8 hours and the full cistern can be leaked out by an exhaust pipe b in 12 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 24 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: time taken to full the cistern = ( 1 / 8 - 1 / 12 ) hrs = 1 / 24 = 24 hrs answer : a
Answer: a
Problem: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 238 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 220 : 113 , b ) 201 : 200 , c ) 210 : 201 , d ) 100 : 99 , e ) 113 : 77
Rationale: "explanation : 3 : 4 a = 3 / 7 * 238 = 102 402 : 400 201 : 200 answer : b"
Answer: b