regisss/math_qa huggingface dataset:
Problem: how many times digit 6 is used while writing numbers from 100 to 1100 ?
Options: a ) 648 , b ) 320 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 320 . hence b ."
Answer: b
Problem: what is the total cost of 2 sandwiches at $ 3.49 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.46 , e ) $ 11.85
Rationale: "answer = d 2 * 3.49 + 4 * 0.87 = 2 ( 3.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 7 + 4 - 0.02 - 0.52 = 11 - 0.54 = 10.46"
Answer: d
Problem: gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 7 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 2 : 3
Rationale: "g = 10 w c = 5 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 10 w + 5 wx = x + 1 * 7 w 10 + 5 x = 7 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is e"
Answer: e
Problem: find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 6 : 7 , e ) none of these
Rationale: "solution required ratio = 60 : 70 = 6 : 7 answer d"
Answer: d
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 6 ) and ( 9 , 6 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 3 , b ) 2 , c ) 1 / 4 , d ) 3 / 5 , e ) 5 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 3 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 3 ) is 3 / 5 . the answer is d ."
Answer: d
Problem: calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 5 , 6 , 10 and 12 seconds . ?
Options: a ) 61 , b ) 60 , c ) 79 , d ) 70 , e ) 78
Rationale: "lcm of 5 , 6 , 10 and 12 is 60 lcm = 60 answer : b"
Answer: b
Problem: a water tank is one - fifth full . pipe a can fill a tank in 15 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the combined rate of filling / emptying the tank = 1 / 15 - 1 / 6 = - 1 / 10 since the rate is negative , the tank will be emptied . a full tank would take 10 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 10 = 2 minutes the answer is a ."
Answer: a
Problem: a jar contains 4 black and 3 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Rationale: "p ( 1 st black , 2 nd white ) = 4 / 7 * 3 / 6 = 4 / 14 ; p ( 1 st white , 2 nd black ) = 3 / 7 * 4 / 6 = 4 / 14 . p = 4 / 14 + 4 / 14 = 4 / 7 . answer : c ."
Answer: c
Problem: a can do a work in 3 days . b can do the same work in 6 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 3 b rate = 1 / 6 ( a + b ) rate = ( 1 / 3 ) + ( 1 / 6 ) = 1 / 2 a & b finish the work in 2 days correct option is d"
Answer: d
Problem: in an it company , there are a total of 100 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 65
Rationale: "you could pick 50 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 55 . c"
Answer: c
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 390 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 84 , b ) 96 , c ) 104 , d ) 112 , e ) 120
Rationale: "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 390 = 104 the answer is c ."
Answer: c
Problem: a train 280 m long , running with a speed of 36 km / hr will pass a tree in
Options: a ) 12 sec , b ) 15 sec , c ) 16 sec , d ) 28 sec , e ) none
Rationale: "sol . speed = ( 36 x 5 / 18 ) m / sec . = 10 m / sec . time taken = ( 280 x 1 / 10 ) sec = 28 sec answer d"
Answer: d
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 4 , then v =
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 4 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 9 the answer is b ."
Answer: b
Problem: a person buys an article at rs . 340 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 600 , b ) 882 , c ) 374 , d ) 356 , e ) 521
Rationale: "cost price = rs . 340 profit = 10 % of 340 = rs . 34 selling price = cost price + profit = 340 + 34 = 374 answer : c"
Answer: c
Problem: on dividing 12401 by a certain number , we get 76 as quotient and 13 as remainder . what is the divisor ?
Options: a ) 163 , b ) 785 , c ) 852 , d ) 456 , e ) 852
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 12401 - 13 ) / 76 = 163 answer ( a )"
Answer: a
Problem: the average of the marks of 10 students in a class is 40 . if the marks of each student are doubled , find the new average ?
Options: a ) 78 , b ) 56 , c ) 80 , d ) 27 , e ) 40
Rationale: "sum of the marks for the 10 students = 10 * 40 = 400 . the marks of each student are doubled , the sum also will be doubled . the new sum = 400 * 2 = 800 . so , the new average = 800 / 10 = 80 . answer : c"
Answer: c
Problem: how much interest will $ 10,000 earn in 9 months at an annual rate of 6 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 650
Rationale: "soln : - 9 months = 3 / 4 of year ; 6 % = 6 / 100 = 3 / 50 ; $ 10,000 ( principal ) * 3 / 50 ( interest rate ) * 3 / 4 ( time ) = $ 450 . answer : c"
Answer: c
Problem: what is the sum of the greatest common factor and the lowest common multiple of 72 and 36 ?
Options: a ) 120 , b ) 150 , c ) 145 , d ) 108 , e ) 112
Rationale: "prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 72 = 2 x 2 x 2 x 3 x 3 gcf = 36 lcm = 72 sum = 108 ans : d"
Answer: d
Problem: at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 19.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 13.7 , b ) 14.0 , c ) 14.3 , d ) 14.6 , e ) 14.9
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 19.6 x ^ 2 = 1.96 x = 1.4 at 4 : 00 pm , the amount of bacteria was 10 ( 1.4 ) = 14 grams . the answer is b ."
Answer: b
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 350 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 20289 , d ) 17500 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 350 = > x = 17500 answer : d"
Answer: d
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( e ) ."
Answer: e
Problem: if 3 spiders make 3 webs in 3 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 3 webs 3 : 1 1 x 3 x x = 3 x 1 x 3 = > x = 3 answer is e"
Answer: e
Problem: three machines , each working at the same constant rate , together can complete a certain job in 18 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 9 days ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 8
Rationale: "rate of one machine = 1 job / ( 18 * 3 ) days let x = number of machines needed to complete the job in 9 days 1 / ( 3 * 18 ) * 9 * x = 1 job x = 6 6 - 3 = 3 answer : a"
Answer: a
Problem: light glows for every 30 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 142 times , c ) 382 times , d ) 392 times , e ) 165 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 30 ) = 165 times . answer : e"
Answer: e
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 2 : 5 . the first number is :
Options: a ) a ) 33 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 2 : 5 x = 11 = > 3 x = 33 answer : a"
Answer: a
Problem: a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 33 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 35 ) + 2 = 2 ( x + 2 ) x + 37 = 2 x + 4 x = 33 . answer : e"
Answer: e
Problem: p and q invested in a business . the profit earned was divided in the ratio 4 : 6 . if p invested rs 60000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 90000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 60000 : q = 4 : 6 ⇒ 60000 × 6 = 4 q ⇒ q = ( 60000 × 6 ) / 4 = 90000 answer is c ."
Answer: c
Problem: on charlie ' s cell phone plan , he signed up for 8 gb of data per 4 week period . if he went over the 8 gb per month , it would cost him an extra $ 10.00 per gb . in the first week , he used 2 gb ; in the 2 nd week , he used 3 gb ; in the 3 rd week , he used 5 gb ; and in the 4 th week , he used a whopping 10 gb . how much extra did charlie need to pay on his cell phone bill ?
Options: a ) $ 120 , b ) $ 40 , c ) $ 80 , d ) $ 100 , e ) $ 140
Rationale: to determine how much extra he would need to pay , you have to add all 4 weeks of gb usage ( 2 + 3 + 5 + 10 = 20 ) . to determine the extra amount of gb usage , you have to subtract the the original amount of gb ( 8 ) allowed on his plan . 20 - 8 = 12 to determine the extra cost on his cell phone plan , you have to multiply $ 10.00 per extra usage ( 12 ) for a total of $ 120.00 . the correct answer is a
Answer: a
Problem: a pipe can fill a cistern in 44 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 4 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 44 minutes 1 / 11 part filled in = 44 * 1 / 11 = 4 minutes answer is a"
Answer: a
Problem: 0.0003 x 0.3 = ?
Options: a ) 0.0009 , b ) 9.0 e - 05 , c ) 0.09 , d ) 0.009 , e ) 9.0
Rationale: "3 x 3 = 9 . sum of decimal places = 5 0.0003 x 0.3 = 0.00009 answer : option b"
Answer: b
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams e ?
Options: a ) e = 16 , b ) e = 32 , c ) e = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Problem: a train running at the speed of 54 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 150 meter , b ) 105 meter , c ) 140 meter , d ) 135 meter , e ) none of these
Rationale: "explanation : speed = 54 * ( 5 / 18 ) m / sec = 15 m / sec length of train ( distance ) = speed * time = 15 * 7 = 105 meter option b"
Answer: b
Problem: what will be the fraction of 25 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 25 * 1 / 100 = 1 / 4 option a"
Answer: a
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 4
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 12 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 4 = 1.25 so biggest is 5 / 4 and smallest is 2 / 3 their difference is 5 / 4 - 2 / 3 = 7 / 12 option 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 4 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 5 : 8
b ) 3 : 2
c ) 6 : 1
d ) 8 : 7
e ) 5 : 6
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 4 y and y . 2 ( 3 x + 2 x ) = 2 ( 4 y + y ) 5 x = 5 y x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 4 y * y = 6 x ^ 2 : 4 y ^ 2 = 6 x ^ 2 : 4 x ^ 2 = 6 : 4 = 3 : 2 the answer is b .
Answer: b
Problem: if the sides of a triangle are 26 cm , 24 cm and 20 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 288 , d ) 266 , e ) 240
Rationale: "the triangle with sides 26 cm , 24 cm and 20 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 20 = 240 cm 2 answer : e"
Answer: e
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 38 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 ) 4830 , b ) 5632 , c ) 6420 , d ) 7500 , e ) 8960
Rationale: "l = ( 48 - 16 ) m = 32 m , b = ( 38 - 16 ) m = 22 m , h = 8 m . volume of the box = ( 32 x 22 x 8 ) m 3 = 5632 m 3 . answer : option b"
Answer: b
Problem: it takes 40 identical printing presses 9 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "40 printing presses can do 1 / 9 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 9 = 1 / 12 of the job each hour . the answer is d ."
Answer: d
Problem: the average age of 15 students of a class is 16 years . out of these , the average age of 6 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 10 years , b ) 11 years , c ) 12 years , d ) 13 years , e ) 14 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 6 + 16 * 9 ) ] = ( 240 - 228 ) = 12 years . answer : c"
Answer: c
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 6 inches wide on each side , the total area would have been ( m + 200 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 12 ) ( y + 12 ) = m and so ( 2 ) xy + 12 x + 12 y + 144 = m + 200 let ' s subtract equation ( 1 ) from equation ( 2 ) . 10 x + 10 y + 140 = 200 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b
Problem: how many numbers between 100 and 600 are divisible by 2 , 3 , and 7 together ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 600 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 600 : 600 / 42 = 14.28 hence , 42 * 14 = 588 is the last number divisible by 42 within 600 hence , total numbers divisible by 2 , 3 , 7 together are ( 14 – 2 ) = 12 answer : b"
Answer: b
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 5 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 22 hr , d ) 24 hr , e ) 26 hr
Rationale: work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 5 ) = 1 / 22 leak will empty the tank in 22 hrs . answer : c
Answer: c
Problem: the salary of a labourer increase consistently by 40 % per year . if his present salary is rs . 3000 then what will his salary be after 3 years ?
Options: a ) 8232 , b ) 3282 , c ) 4282 , d ) 8242 , e ) 2382
Rationale: explanation : salary = 3000 x 1.4 x 1.4 x 1.4 = 8232 answer : option a
Answer: a
Problem: in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 30 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 35 % , b ) 48 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 3 x not job of choice w / o diploma = . 7 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 30 % of 60 % = 18 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 10 % = 30 % ) . 30 % + 18 % = 48 % . therefore 48 % of the people in country z have a diploma . ans b
Answer: b
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 50 per square m ?
Options: a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 47500
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 50 * 950 = rs . 47500 e"
Answer: e
Problem: there is a 55 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 55 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: only the prime numbers greater than 10 and less than 55 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , and 53 . the total is 12 . the answer is e .
Answer: e
Problem: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 58,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 29,000 , e ) none of these
Rationale: 30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 58,000 i . e . rs . 29,000 answer : d
Answer: d
Problem: there is enough provisions for 600 men in an army camp for 35 days . if there were 300 men less , how long will the provision last ?
Options: a ) 40 days , b ) 50 days , c ) 60 days , d ) 70 days , e ) 80 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 35 = 300 * d 2 d 2 = 600 * 35 / 300 = 70 days . answer : d"
Answer: d
Problem: if 8 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 784 , b ) 763 , c ) 120 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 8 c 2 for vertical 8 c 2 total parallelogram is 10 c 2 * 8 c 2 = 28 * 28 = 784 answer : a"
Answer: a
Problem: there are 100 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 13 , b ) 41 , c ) 47 , d ) 48 , e ) 53
Rationale: "number of switches = 100 number of switches turned on by a : 3 , 6 , . . . 99 = 33 number of switches turned on by b : 5 , 10 , . . . . 100 = 20 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 33 - 6 ) + ( 20 - 6 ) = 41 answer : b"
Answer: b
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 14 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 14 add both : 3 a + 3 b = 24 so a + b = 8 total number of people = 8 c
Answer: c
Problem: 30 % people of a village in sri lanka died by bombardment , 25 % of the remainder left the village on account of fear . if now the population is reduced to 6695 , how much was it in the beginning ?
Options: a ) 7000 , b ) 6700 , c ) 6695 , d ) 7645 , e ) 6575
Rationale: "x * ( 70 / 100 ) * ( 75 / 100 ) = 3515 x = 6695 answer : c"
Answer: c
Problem: i gain 70 paise on rs . 70 . my gain percent is
Options: a ) 0.1 % , b ) 1 % , c ) 7 % , d ) 10 % , e ) none
Rationale: "solution gain % = ( 0.70 / 70 × 100 ) % = 1 % . answer b"
Answer: b
Problem: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 , then the rise in the water level in the tank will be :
Options: a ) 22 , b ) 25 , c ) 32 , d ) 99 , e ) 88
Rationale: explanation : total volume of water displaced = ( 4 x 50 ) = 200 rise in water level = = 0.25 m = 25 cm answer : b ) 25 cm
Answer: b
Problem: the price of a t . v . set worth rs . 10000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 9000 , b ) 26699 , c ) 96000 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 10000 - 1000 ) = rs . 9000 answer : a"
Answer: a
Problem: find the principle on a certain sum of money at 5 % per annum for 3 years if the amount being rs . 1120 ?
Options: a ) 974 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 3 ) / 100 ] p = 974 answer : a"
Answer: a
Problem: a water tank is two - fifth full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how long will it take to empty or fill the tank completely ?
Options: a ) 6 min , b ) 4 min , c ) 2 min , d ) 5 min , e ) 8 min
Rationale: "clearly , pipe b is faster than pipe a and so , the tank will be emptied . part to be emptied = 2 / 5 part emptied by ( a + b ) in 1 minute = ( 1 / 6 - 1 / 10 ) = 1 / 15 1 / 15 : 2 / 5 : : 1 : x x = ( 2 / 5 * 1 * 15 ) = 6 min . so , the tank will be emptied in 6 min . answer : a"
Answer: a
Problem: how many two digit prime numbers are there in which both digits are prime numbers ? ( for example , 23 is one of these numbers but 31 is not , since 1 is not a prime number . )
Options: a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 15
Rationale: the second digit can only be 3 or 7 , so the choice quickly narrows down to 23 , 27 , 33 , 37 , 53 , 57 , 73 , and 77 . of these , 27 , 33 , and 57 are divisible by 3 , and 77 by 7 , leaving 23 , 37 , 53 , and 73 . it is easy to see that none of these is divisible by 2 , 3 , 5 , or 7 , and there is no need to look at greater prime divisors since root 77 < 11 . correct answer b
Answer: b
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2460 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 8200 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2460 100 % - - - - - - - - - ? = > 8200 answer : d"
Answer: d
Problem: { 8 , 46 , 53 , 127 } what number should be inserted in the set of 7 values to get a median of 9 ?
Options: a ) 20 , b ) 14 , c ) 16 , d ) 5 , e ) 8
Rationale: median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 9 . mentionable that given set is already sorted and number of items of new set will be 7 + 1 = 8 . to get median 9 , the sum of 4 th 5 th term should be 18 and it ' s 5 + 14 . so to keep the median 9 , the new item should be > = 14 . the answer is b
Answer: b
Problem: the ratio 2 : 3 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 67 % , d ) 125 % , e ) none
Rationale: "solution 2 : 3 = 2 / 3 = ( 2 / 3 x 100 ) % . = 66.6 % . answer c"
Answer: c
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 60 , c ) 2 / 63 , d ) 2 / 35 , e ) 2 / 38
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 7 ) ã — ( 2 / 5 ) = 2 / 35 answer : d ) 2 / 35"
Answer: d
Problem: 3 consecutive odd integers are in increasing order such that the sum of the last two integers is 17 more than the first integer . find the 3 integers ?
Options: a ) 11 , 1315 , b ) 7 , 2 , 10 , c ) 7 , 9 , 10 , d ) 7 , 9 , 11 , e ) 7 , 9 , 29
Rationale: explanation : let the three consecutive odd integers be x , x + 2 and x + 4 respectively . x + 4 + x + 2 = x + 17 = > x = 11 hence three consecutive odd integers are 11 , 13 and 15 answer : a
Answer: a
Problem: p is able to do a piece of work in 5 days and q can do the same work in 10 days . if they can work together for 3 days , what is the fraction of work completed ?
Options: a ) 13 / 10 , b ) 4 / 5 , c ) 11 / 10 , d ) 7 / 10 , e ) 9 / 10
Rationale: "explanation : amount of work p can do in 1 day = 1 / 5 amount of work q can do in 1 day = 1 / 10 amount of work p and q can do in 1 day = 1 / 5 + 1 / 10 = 3 / 10 amount of work p and q can together do in 3 days = 3 × ( 3 / 10 ) = 9 / 10 answer : option e"
Answer: e
Problem: the sum of three consecutive multiples of 3 is 81 . what is the largest number ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 35
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 81 9 x = 72 x = 8 largest number = 3 x + 6 = 30 . answer : c"
Answer: c
Problem: what is the area of square field whose side of length 15 m ?
Options: a ) 225 sq m
b ) 186 sq m
c ) 586 sq m
d ) 287 sq m
e ) 296 sq m
Rationale: 15 * 15 = 225 sq m answer : a
Answer: a
Problem: how many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 10 percent sugar solution ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 28 , e ) 30
Rationale: "let x be the amount that needs to be evaporated . 0.04 ( 50 ) = 0.1 ( 50 - x ) 0.1 x = 5 - 2 x = 3 / 0.1 = 30 liters the answer is e ."
Answer: e
Problem: at what rate percent per annum will a sum of money double in 16 years ?
Options: a ) 10.6 % , b ) 3.65 % , c ) 6.25 % , d ) 8.32 % , e ) 11 %
Rationale: "let principle = p s . i . = p t = 16 yrs rate = 100 * p / p * 16 = 25 / 4 % = 6.25 % answer is c"
Answer: c
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 240,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,875 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 240,000 / ( 8 * 10 * 12 ) = 250 one box costs 7.50 , so 250 box will cost = 250 * 7.5 = 1875 b is the answer"
Answer: b
Problem: 10 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 45
Rationale: "there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 7 other chairmen for total of 70 handshake . total = 45 + 70 = 115 ans : c"
Answer: c
Problem: in what ratio must water be mixed with milk to gain 16 ( 2 / 3 ) % on selling the mixture at cost price ?
Options: a ) 1 : 6 , b ) 6 : 1 , c ) 2 : 3 , d ) 4 : 3 , e ) 3 : 2
Rationale: "explanation : let c . p . of 1 litre milk be re . 1 . s . p . of 1 litre of mixture = re . 1 , gain = 50 / 3 % c . p . of 1 litre of mixture = ( 100 x 3 / 350 x 1 ) = 6 / 7 by the rule of alligation , we have : ratio of water and milk = 1 / 7 : 6 / 7 = 1 : 6 . answer is a"
Answer: a
Problem: two pipes a and b can fill a tank in 2 and 6 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 2.5 min , b ) 1.8 min , c ) 1.5 min , d ) 3.5 min , e ) 2 min
Rationale: "part filled by the first pipe in 1 minute = 1 / 2 part filled by the second pipe in 1 minute = 1 / 6 net part filled by pipe a and pipe b in 1 minute = ( 1 / 2 ) + ( 1 / 6 ) = 2 / 3 i . e , pipe a and b together can fill the tank in 3 / 2 minutes = 1.5 minutes answer is c"
Answer: c
Problem: a train requires 8 seconds to pass a pole while it requires 18 seconds to cross a stationary train which is 400 mtrs long . find the speed of the train .
Options: a ) 144 kmph , b ) 124 kmph , c ) 134 kmph , d ) 150 kmph , e ) 160 kmph
Rationale: in 8 s the train crosses the pole and in 18 sec the train crosses one more stationary train in 10 sec the train travels a distance of 400 mtrs speed = 400 / 10 = 40 m / s = 40 ( 3600 / 1000 ) = 40 * 18 / 5 = 144 kmph answer : a
Answer: a
Problem: there are 6 people in the elevator . their average weight is 154 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 133 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 154 ) = 1057 - 924 = 133 . answer a"
Answer: a
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.25 – 6.25 * ?
Options: a ) 1.5 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.25 * = 6 ( the greatest positive even integer less than or equal to 6.25 is 6 ) . hence , 6.25 – 6.25 * = 6.25 - 6 = 0.25 answer : d ."
Answer: d
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 3 kilometers per hour . it returns by the same route at an average speed of 7 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 4.2 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: pick a number which is lcm of 7 and 3 = 21 . upstream time = 21 / 3 = 7 hrs downstream time = 21 / 7 = 3 hrs total time = 10 hrs total distance = 42 average speed = 42 / 10 = 4.2 km / hr
Answer: a
Problem: 6 friends visited a book stall and brought 6 books , and everyone decided to contribute equally to the total bill of $ 400 . if one of the friends had a coupon for 5 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) 62.12 , b ) 63 , c ) 63.33 , d ) 64 , e ) 65
Rationale: at the non - discounted price , each friend would pay $ 66.66 , as $ 400 divided by 6 friends is $ 66.66 per friend . but if the bill is 5 % off , then each friend would pay 5 % less . 5 % of $ 66.66 is $ 3.33 , so each friend saves $ 3.33 and pays the remaining $ 63.33 correct option : option c
Answer: c
Problem: the ages of two persons differ by 32 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 46,14 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 32 ) years . 5 ( x - 5 ) = ( x + 32 - 5 ) or 4 x = 52 or x = 14 . their present ages are 46 years and 14 years option b"
Answer: b
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 5 ) = 0 and f ( - 3 ) = 0 , then b + c =
Options: a ) 18 , b ) - 17 , c ) - 15 , d ) - 21 , e ) - 24
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 5 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 5 ) = 0 = 25 + 5 b + c - - - taking 25 to the other side - > 5 b + c = - 25 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 8 b = - 16 - - - > b = - 2 and while substituting b = - 2 we get c = - 15 . b + c = - 17 - - - answer b"
Answer: b
Problem: the average weight of 8 person ' s increases by 5 kg when a new person comes in place of one of them weighing 35 kg . what might be the weight of the new person ?
Options: a ) 80 kg , b ) 85 kg , c ) 75 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 35 + 40 ) kg = 75 kg . answer : c"
Answer: c
Problem: the average marks of a class of 22 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?
Options: a ) 51.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 52.1
Rationale: "sum of the marks for the class of 22 students = 22 * 40 = 880 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 50 students = 880 + 1680 = 2560 average marks of all the students = 2560 / 50 = 51.2 answer : a"
Answer: a
Problem: y = x ^ 2 + bx + 512 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
Options: a ) - 512 , b ) - 257 , c ) - 256 , d ) - 513 , e ) 128
Rationale: as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form of ax ^ 2 + bx + c = 0 , the product of the roots = c / a = 512 / 1 = 256 and the sum of the roots = - b / a = - b 512 can be expressed as product of two numbers in the following ways : 1 * 512 2 * 256 4 * 128 8 * 64 16 * 32 the sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513 . the least value possible for b is therefore - 513 . d
Answer: d
Problem: the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone .
Options: a ) 250 , b ) 170 , c ) 148 , d ) 157 , e ) 150
Rationale: "π * 5 * 10 = 157 answer : d"
Answer: d
Problem: find the area of a parallelogram with base 30 cm and height 12 cm ?
Options: a ) 290 cm 2 , b ) 360 cm 2 , c ) 270 cm 2 , d ) 280 cm 2 , e ) 260 cm 2
Rationale: "area of a parallelogram = base * height = 30 * 12 = 360 cm 2 answer : b"
Answer: b
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 18 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 = > 45 - [ 28 - { 37 - 15 + * } ] = 57 45 - [ 28 - 37 + 15 - * ] = 57 = > 45 [ 43 - 37 - * ] = 57 45 - [ 6 - * ] = 57 = > 45 - 6 + * = 57 39 + * = 57 = > * = 57 - 39 = 18 answer : c"
Answer: c
Problem: in a kilometer race , a beats b by 51 meters or 11 seconds . what time does a take to complete the race ?
Options: a ) 22 , b ) 190 , c ) 277 , d ) 204 , e ) 208
Rationale: "time taken by b run 1000 meters = ( 1000 * 11 ) / 51 = 215 sec . time taken by a = 215 - 11 = 204 sec . answer : d"
Answer: d
Problem: how many three - digit numbers that do not contain the digits 2 or 5 are there ?
Options: a ) 488 , b ) 996 , c ) 228 , d ) 456 , e ) 1986
Rationale: "we can have 7 digits ( 1 , 3,4 , 6,7 , 8,9 ) for the first place ( hundred ' s place ) . and similarly 8 digits for tenth ' s and unit digit . ( 0,1 , 3,4 , 6,7 , 8,9 ) so in total 7 * 8 * 8 = 488 hence b"
Answer: b
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 6 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 6 × 2 / 100 = 600 his overall gain in 2 years = rs . 600 - rs . 400 = rs . 200 his overall gain in 1 year = 200 / 2 = rs . 100 answer : option a"
Answer: a
Problem: shop offered 25 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 746 , d ) 700 , e ) 750
Rationale: sp * ( 75 / 100 ) = 560 sp = 7.46 * 100 = > cp = 746 answer : c
Answer: c
Problem: what is the least number of square tiles required to pave the floor of a room 10 m 17 cm long and 9 m 9 cm broad ?
Options: a ) 724 , b ) 804 , c ) 11413 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1017 cm & 909 cm = 9 cm . area of each tile = ( 9 x 9 ) cm 2 ∴ required number of tiles = [ 1017 x 909 / 9 x 9 ] = 11413 . answer c"
Answer: c
Problem: if a person walks at 15 km / hr instead of 9 km / hr , he would have walked 20 km more . the time traveled by him is ?
Options: a ) 8 hours , b ) 9 / 5 hours , c ) 10 / 3 hours , d ) 6 hours , e ) 11 / 3 hours
Rationale: "let the actual distance traveled be x km . then , x / 9 = ( x + 20 ) / 15 5 x - 3 x = 60 = > x = 30 km . travel time is = 30 / 9 hours = 10 / 3 hours answer : c"
Answer: c
Problem: the sum of 3 consecutive odd natural numbers , each divisible by 3 is 72 . what is the largest among them ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 45
Rationale: let the 3 consecutive odd numbers each divisible by 3 be x , x + 3 , x + 6 given , x + x + 3 + x + 6 = 72 3 x = 63 x = 21 the numbers are 21 , 24 , 27 therefore the largest number is 27 answer c .
Answer: c
Problem: if sum of two no . is 12 and subtraction to that is 4 . so how much min . should added to smaller no . to make it even ?
Options: a ) 1 , b ) 2 , c ) 0.5 , d ) 1.5 , e ) 0
Rationale: let smaller no . be x . bigger no . = 12 - x . 12 - x - x = 4 . 12 - 2 x = 4 2 x = 8 , x = 4 . so 4 is itself even no . so , zero should be added . answer e
Answer: e
Problem: consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 5400 interest only for the period . the principal amount borrowed by her was
Options: a ) rs . 2000 , b ) rs . 10000 , c ) rs . 15000 , d ) rs . 20000 , e ) none of these
Rationale: "explanation : principal = rs . ( 100 × 5400 / 12 × 3 ) = > rs . 15,000 . answer : c"
Answer: c
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase q in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase q = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Problem: one computer can upload 120 megabytes worth of data in 6 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 42 seconds . how long would it take for the second computer , working on its own , to upload 120 megabytes of data ?
Options: a ) 6 , b ) 7 , c ) 9.13 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 120 megabytes worth of data in 6 seconds then in 6 * 7 = 42 seconds it can upload 7 * 120 = 840 megabytes worth of data , hence the second compute in 42 seconds uploads 1300 - 840 = 460 megabytes worth of data . the second computer can upload 120 megabytes of data in 9.13 seconds . answer : c ."
Answer: c
Problem: set k contains every multiple of 6 from 18 to 306 inclusive . if w is the median of set k , and x is the average ( arithmetic mean ) of set k , what is the value of w - x ?
Options: a ) - 6 , b ) - 3 , c ) 0 , d ) 3 , e ) 6
Rationale: set k = { 18 , 24,30 , . . . . 306 } let the no . of terms be n . so we know the ap formulae to calculate the the tn term : tn = a + ( n - 1 ) * d where d = common difference of the terms . 306 = 18 + ( n - 1 ) * 6 n = 49 . so the set k consist of n terms . the median of the set having odd nos of elements is ( n + 1 ) / 2 . , which in this case is 25 . let ' s find the 25 th term using the same formulae again : t 25 = 18 + ( 25 - 1 ) * 6 t 25 = 162 so , the median of the set k is 162 i . e . w = 162 . now . lets find the average ( arithmetic mean ) of the set . for that we need to find the sum of all the elements first , lets call it s . since , set k is nothing but a arithmetic progression series having first element ( a ) as 18 , common difference ( d ) as 6 and no . of terms ( n ) as 49 . using the formulae to calculate sum of an ap series , which is s = n / 2 [ 2 a + ( n - 1 ) * d ] , we will calculate the sum . so , s = 49 / 2 [ 2 * 18 + ( 49 - 1 ) * 6 ] this gives us s = 7938 . now arithmetic mean of set k = 7938 / no . of terms = 7938 / 49 = 162 . so x = 162 . now , ( w - x ) = ( 162 - 162 ) = 0 . therefore correct answer = c
Answer: c
Problem: # p is defined as 2 p + 20 for any number p . what is p , if # ( # ( # p ) ) = 4 ?
Options: a ) – 108 , b ) – 44 , c ) 10 , d ) - 17 , e ) 18
Rationale: # p = 2 p + 20 - - - > # ( # p ) = 2 ( 2 p + 20 ) + 20 = 4 p + 60 and thus # ( 4 p + 60 ) = 2 ( 4 p + 60 ) + 20 = 8 p + 140 = 4 - - - > 8 p = - 136 - - - > p = - 17 , d is the correct answer .
Answer: d
Problem: if n = 3 ^ 0.15 and n ^ b = 9 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 5 / 3 , e ) 40 / 3
Rationale: "15 / 100 = 3 / 20 n = 3 ^ 3 / 20 n ^ b = 3 ^ 2 ( 3 ^ 3 / 20 ) ^ b = 3 ^ 2 b = 40 / 3 answer : e"
Answer: e
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 36 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 4 : 3 , c ) 4 : 6 , d ) 4 : 9 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 36 = 4 : 6 answer : c"
Answer: c
Problem: john makes $ 55 a week from his job . he earns a raise andnow makes $ 60 a week . what is the % increase ?
Options: a ) 16 % , b ) 9.66 % , c ) 9.09 % , d ) 9.98 % , e ) 17 %
Rationale: "increase = ( 5 / 55 ) * 100 = ( 1 / 11 ) * 100 = 9.09 % . c"
Answer: c
Problem: what is the sum of all the prime numbers greater than 10 but less than 40 ?
Options: a ) 190 , b ) 189 , c ) 180 , d ) 199 , e ) 1981
Rationale: "required sum = ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) = 180 note : 1 is not a prime number answer c"
Answer: c
Problem: the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs . 8748 , its purchase price was
Options: a ) rs . 12008 , b ) rs . 12000 , c ) rs . 12002 , d ) rs . 1229 , e ) rs . 12021
Rationale: explanation : = rs . 12000 answer : b
Answer: b
Problem: find 95 × × 97
Options: a ) 92 / 198 , b ) 92 / 12 , c ) 92 / 13 , d ) 92 / 10 , e ) 92 / 15
Rationale: "here both numbers are less than 100 . so they are deficient of - 5 and - 3 compared with 100 . so answer : e"
Answer: e
Problem: what is the units digit of 17 ^ 73 × 13 ^ 82 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 8 correct option : e"
Answer: e
Problem: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 70 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 70 = 90 cents on commodity y , which will take 9 years . the answer is a ."
Answer: a
Problem: how many bricks , each measuring 100 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 1600 , b ) 2400 , c ) 5500 , d ) 7400 , e ) 3400
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 100 x 11.25 x 6 ) = 1600 answer : a"
Answer: a