regisss/math_qa huggingface dataset:
Problem: how many seconds will a 620 metre long train take to cross a man running with a speed of 8 km / hr in the direction of the moving train if the speed of the train is 80 km / hr ?
Options: a ) 25 , b ) 30 , c ) 31 , d ) 45 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 80 - 8 ) km / hr = 72 km / hr = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken to pass the man = ( 620 / 20 ) sec = 31 sec . answer : c"
Answer: c
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1040 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1040 20 x / 100 = 1040 x = 1040 * 100 / 20 = 5200 answer is b"
Answer: b
Problem: a person is traveling at 40 km / hr and reached his destiny in 6 hr then find the distance ?
Options: a ) 260 km , b ) 240 km , c ) 280 km , d ) 340 km , e ) 350 km
Rationale: "t = 6 hrs d = t * s = 40 * 6 = 240 km answer is b"
Answer: b
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.07 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.86 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.07 2 nd day fine - 0.07 * 2 = 0.14 ( as doubling gives lower value ) 3 rd day fine - 0.14 * 2 = 0.28 ( as doubling gives lower value ) 4 rd day fine - 0.28 * 2 = 0.56 ( as doubling gives lower value ) 5 th day fine - 0.56 + 0.3 = 0.86 ( as doubling gives higher value we add 0.3 this time ) answer : c ."
Answer: c
Problem: 7 , 26 , 63 , 124 , ( . . . . )
Options: a ) 342 , b ) 125 , c ) 289 , d ) 564 , e ) 36
Rationale: "explanation : numbers are 2 ^ 3 - 1 = 7 3 ^ 3 - 1 = 26 4 ^ 3 - 1 = 63 5 ^ 3 - 1 = 124 6 ^ 3 - 1 = 342 answer : a"
Answer: a
Problem: by selling 100 pens , a trader gains the cost of 40 pens . find his gain percentage ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 30 %
Rationale: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 40 pens = rs . 40 profit % = 40 / 100 * 100 = 40 % answer : a"
Answer: a
Problem: a sum of rs . 1870 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 330 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1870 = > 17 x / 12 = 1870 = > 1870 x 12 / 17 = rs . 1320 hence , b ’ s share = rs . ( 1320 / 4 ) = rs . 330 . answer d"
Answer: d
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 30 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 69 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 5.2 , so radius is 2.6 new area = 6.76 π increase in area is 2.76 π % increase in area = 2.76 / 4 * 100 so , % increase is 69 % answer will be ( c )"
Answer: c
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 15000 and b rs . 25000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4200 , e ) 7291
Rationale: "15 : 25 = > 3 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 3 / 8 = 3240 + 960 = 4200 answer : d"
Answer: d
Problem: how many numbers from 19 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12
Rationale: "19 / 11 = 1 and 79 / 11 = 7 = = > 7 - 1 = 6 numbers answer : b"
Answer: b
Problem: two pipes can fill a tank in 10 minutes and 15 minutes . an outlet pipe can empty the tank in 30 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 7.0 , b ) 7.5 , c ) 8.0 , d ) 8.5 , e ) 9.0
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 10 + v / 15 - v / 30 = 2 v / 15 per minute the tank will be filled in 15 / 2 = 7.5 minutes . the answer is b ."
Answer: b
Problem: the length of a rectangle is four times its width . if the area is 100 m 2 what is the length of the rectangle ?
Options: a ) 50 m , b ) 40 m , c ) 80 m , d ) 20 m , e ) 70 m
Rationale: "let l be the length and w be the width of the rectangle . hence l = 4 w we now use the area to write 100 = l ? w substitute l by 4 w in the equation above 100 = 4 w ? w = 4 w 2 solve for w and find l 4 w 2 = 100 w 2 = 25 , w = 5 and l = 4 w = 20 m correct answer d"
Answer: d
Problem: exactly 20 % of the reporters for a certain wire service cover local politics in country x . if 20 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 75 % , e ) 84 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 20 % of reporters who cover politics do not cover local politics so 80 % do cover local politics . reporters covering local politics = 80 % of reporters covering politics = 20 % ofall reporters reporters covering politics / all reporters = 20 / 80 = 1 / 4 reporters not covering politics / all reporters = 3 / 4 = 75 % = d"
Answer: d
Problem: we had $ 840 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 1000 , b ) $ 1050 , c ) $ 1100 , d ) $ 1150 , e ) $ 1200
Rationale: let x be the amount of money we started with . 0.7 x = 840 x = 1200 the answer is e .
Answer: e
Problem: if the sum and difference of two numbers are 10 and 8 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 80
Rationale: "let the numbers be x and y . then , x + y = 10 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 8 = 80 . answer : e"
Answer: e
Problem: how many times will the digit 5 be written when listing the integers from 1 to 1000 ?
Options: a ) 300 , b ) 380 , c ) 180 , d ) 415 , e ) 264
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 5 ) 3000 / 10 = 300 times . answer : a ."
Answer: a
Problem: the average of first six prime numbers which are between 30 and 70 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 67
Rationale: "explanation : first six prime numbers which are between 30 and 70 = 31 , 37 , 41 , 43 , 47 , 53 average = ( 31 + 37 + 41 + 43 + 47 + 53 ) / 6 = 42 answer : b"
Answer: b
Problem: what is the units digit of ( 3 ^ 11 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 13 = 3 ^ 4 * 3 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 13 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Problem: the distance from steve ' s house to work is 30 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 30 km = > speed = 15 kmph answer : d"
Answer: d
Problem: the sector of a circle has radius of 21 cm and central angle 270 o . find its perimeter ?
Options: a ) 145 cm , b ) 135 cm , c ) 121 cm , d ) 141 cm , e ) 151 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 270 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 99 + 42 = 141 cm answer : d"
Answer: d
Problem: how many times in a day the hands of a clock are straight ?
Options: a ) 21 , b ) 27 , c ) 24 , d ) 22 , e ) 25
Rationale: "in 12 hours , the hands coincide or are in oppesite direction 22 times . in 24 hours , they are at right angles 22 times . answer is d ."
Answer: d
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 9 / 16 , e ) 15 / 16
Rationale: "p ( missing all 3 ) = ( 1 / 2 ) ^ 3 = 1 / 8 p ( success on at least one attempt ) = 1 - 1 / 8 = 7 / 8 the answer is c ."
Answer: c
Problem: twelve machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 12 = 18 so we need 18 - 12 = 6 more machines . answer : d
Answer: d
Problem: if 49 ( 7 ^ x ) = 1 then x =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "7 ^ x = 1 / 49 7 ^ x = 1 / 7 ^ 2 7 ^ x = 7 ^ - 2 x = - 2 a"
Answer: a
Problem: a cab driver 5 days income was $ 200 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 420 , b ) $ 410 , c ) $ 400 , d ) $ 390 , e ) $ 380
Rationale: "avg = sum of observations / number of observations avg income = ( 200 + 150 + 750 + 400 + 500 ) / 5 = 400 answer is c"
Answer: c
Problem: x is able to do a piece of work in 14 days and y can do the same work in 20 days . if they can work together for 5 days , what is the fraction of work completed ?
Options: a ) 15 / 28 , b ) 17 / 28 , c ) 13 / 28 , d ) 19 / 28 , e ) 11 / 28
Rationale: explanation : amount of work x can do in 1 day = 1 / 14 amount of work y can do in 1 day = 1 / 20 amount of work x and y can do in 1 day = 1 / 14 + 1 / 20 = 17 / 140 amount of work x and y can together do in 5 days = 5 × ( 17 / 140 ) = 17 / 28 answer : option b
Answer: b
Problem: a football field is 9600 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards ?
Options: a ) 450
b ) 600
c ) 700
d ) 2400
e ) 3200
Rationale: answer c ) 9600 yards need 1200 lbs 1 yard will need 1200 / 9600 = 1 / 8 lbs 3600 yards will need 1 / 8 * 5600 yards = 700 lbs
Answer: c
Problem: if a man buys 1 liter of milk for 12 rs . and mixes it with 20 % water and sells it for 15 rs then what is the % age of gain . . .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: quantity after adding 20 % water = 1.2 liter sp of 1.2 lit . @ 15 rs . / liter = 15 * 1.2 = 18 rs cp = 12 rs / lit . % profit = 100 * ( 18 - 12 ) / 12 = 50 answer : c
Answer: c
Problem: a tightrope approximately 320 m long is suspended between two poles . during a performance , a break occurs in the line . assume that the line has an equal chance of breaking anywhere along its length . what is the probability that the break happened in the first 50 meters of the rope ?
Options: a ) 27 / 32 , b ) 1 / 2 , c ) 5 / 32 , d ) 5 / 27 , e ) . 2 / 3
Rationale: simly 50 / 320 = 5 / 32 answer will be ( c )
Answer: c
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 18 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 18 more transactions than cal . jade = 66 + 18 = 84 jade handled = 84 transactions . answer : e"
Answer: e
Problem: while working alone at their constant rates , computer x can process 240 files in 4 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 2 , b ) 2.2 , c ) 2.4 , d ) 2.6 , e ) 2.8
Rationale: both computers together process files at a rate of 240 / 4 + 240 / 6 = 60 + 40 = 100 files per hour . the time required to process 240 files is 240 / 100 = 2.4 hours the answer is c .
Answer: c
Problem: $ 2,000 is deposited in a savings account that pays 4 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 2125.15 , b ) $ 2083.12 , c ) $ 2184.22 , d ) $ 2150.84 , e ) $ 2080.80
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 4 / 2 = 2 % now , ca = 2000 ( 1 + 2 / 100 ) ^ 2 = $ 2080.80 hence answer is e"
Answer: e
Problem: a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 140 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 45 , c ) 25 , d ) 36 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 140 × 9 / 35 = 4 × 9 = 36 answer is d"
Answer: d
Problem: what is the rate percent when the simple interest on rs . 1000 amount to rs . 400 in 4 years ?
Options: a ) 5 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 10 %
Rationale: "interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1000 x 100 = 10 % answer : e"
Answer: e
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 9.5 , b ) 9.4 , c ) 9.3 , d ) 9.2 , e ) 9.1
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 7 ) = 3 / 28 the cistern will be filled in 28 / 3 hrs i . e . , 9.3 hrs . answer : c"
Answer: c
Problem: by how much is 12 % of 24.2 more than 10 % of 14.2 ?
Options: a ) 0.1484 , b ) 14.84 , c ) 1.484 , d ) 2.762 , e ) none
Rationale: "answer required difference = ( 12 x 24.2 ) / 100 - ( 10 x 14.2 ) / 100 = 2.904 - 1.42 = 1.484 . correct option : c"
Answer: c
Problem: the jogging track in a sports complex is 627 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 4.56 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 627 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 627 m apart , they take ( 100 / 825 * 627 / 1000 ) hrs = ( 627 / 8250 * 60 ) min = 4.56 min . answer : a"
Answer: a
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 72 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 27 - 9 = 18 km / hr . = 18 * 5 / 18 = 5 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 5 = 72 sec . answer : b"
Answer: b
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 36 , what is the total amount ?
Options: a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 156
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 36 39 - - - ? = > 156 answer : e"
Answer: e
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1989 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2008 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1989 + 19 = 2008 . answer : a ."
Answer: a
Problem: carina has 115 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 3
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 115 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 105 / 15 . = 7 b"
Answer: b
Problem: by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 400 grams of solution p are mixed with 600 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 3.6 % , b ) 3.9 % , c ) 4.2 % , d ) 4.5 % , e ) 4.8 %
Rationale: "the number of grams of liquid x is 1.5 ( 400 ) / 100 + 6.5 ( 600 ) / 100 = 6 + 39 = 45 grams . 45 / 1000 = 4.5 % the answer is d ."
Answer: d
Problem: a trader bought a car at 40 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 8 % , b ) 62 % , c ) 2 % , d ) 9 % , e ) 22 %
Rationale: "original price = 100 cp = 60 s = 60 * ( 180 / 100 ) = 112 100 - 108 = 8 % answer : a"
Answer: a
Problem: what is the sum of 100 consecutive integers from - 49 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 50 , c ) - 30 , d ) 30 , e ) 60
Rationale: "from - 49 to - 1 - - > 49 nos . zero - - > 1 number from + 1 to + 49 - - > 49 nos . when we add up nos . from - 49 to + 49 sum will be zero . total 99 nos will be added . 100 th number will be 50 . sum of these 100 nos . = 50 . b is the answer ."
Answer: b
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 64 more for rs . 40.00001 , what is reduced price per dozen ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: 40 * ( 40 / 100 ) = 16 - - - 64 ? - - - 12 = > rs . 3 answer : d
Answer: d
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 24 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 188 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 24 : x = > x = { \ color { blue } \ frac { 24 \ times 1 } { 0.128 } } = > x = 187.5 so time will be approx 188 seconds answer : d"
Answer: d
Problem: the perimeter of one face of a cube is 20 cm . its volume will be :
Options: a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 20 / 4 = 5 cm volume = a * a * a = 5 * 5 * 5 = 125 cm cube option a"
Answer: a
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 84 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 32 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 84 a = 32 the answer is d ."
Answer: d
Problem: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 18 inches and the width of the wall is 32 inches , what is the length of the wall , in inches ?
Options: a ) 15.25 , b ) 18.25 , c ) 19.25 , d ) 20.25 , e ) 21.25
Rationale: "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 18 ^ 2 = 324 . area of rectangle is double of that 2 * 324 = 648 . now a = lw and we need find w so a / l = w ; 648 / 32 = 20.25 answer ! answer is d"
Answer: d
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 50 paisa and z gets 40 paisa . if the share of x is rs . 30 , what is the total amount ?
Options: a ) 67 , b ) 55 , c ) 62 , d ) 47 , e ) 57
Rationale: "x : y : z = 100 : 50 : 40 10 : 5 : 4 10 - - - 30 19 - - - ? = > 57 answer : e"
Answer: e
Problem: the product of two numbers is 276 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 29 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 276 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 276 ) = 841 x + y = 29 . option a"
Answer: a
Problem: how many kilograms of sugar costing rs . 9 per kg must be mixed with 27 kg of sugar costing rs . 7 per kg so that there may be gain of 10 % by selling the mixture at rs . 9.24 per kg ?
Options: a ) 60 kg , b ) 63 kg , c ) 50 kg , d ) 77 kg , e ) none of these
Rationale: "explanation : let the rate of second quality be rs x per kg . step 1 : s . p of 1 kg of mixture = rs . 9.24 gain = 10 % c . p of 1 kg of mixture = [ 100 / ( 100 + 10 ) × 9.24 ] . = > rs . 8.40 . thus , the mean price = rs . 8.40 . step 2 : c . p of 1 kg of sugar of 1 st kind = 900 p c . p of 1 kg of sugar of 2 nd kind = 700 p mean price = 840 p by the rule of alligation , we have : c . p . of 1 kg of c . p . of 1 kg of sugar of 1 st sugar of 2 nd kind ( 900 p ) kind ( 700 p ) \ / mean price ( 840 p ) / \ 840 - 700 : 900 - 840 ( 140 ) ( 60 ) = > required ratio = 140 : 60 = 7 : 3 . step 3 : let , x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind , then = > 7 : 3 = x : 27 . = > 7 / 3 = x / 27 . = > x = ( 7 / 3 ) x 27 . = > x = 63 . answer : b"
Answer: b
Problem: at a loading dock , each worker on the night crew loaded 1 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 5 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 6
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 1 / 4 * 4 / 5 x = 1 / 5 x % loaded by day crew = x / ( x + 1 / 5 x ) = 5 / 6 answer e"
Answer: e
Problem: a train speeds past a pole in 15 seconds and a platform 150 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 205 , b ) 215 , c ) 225 , d ) 235 , e ) 245
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 150 = 25 * ( x / 15 ) 10 x = 2250 x = 225 meters the answer is c ."
Answer: c
Problem: a jeep takes 7 hours to cover a distance of 420 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 52 kmph , c ) 40 kmph , d ) 63 kmph , e ) 65 kmph
Rationale: "time = 7 distance = 420 3 / 2 of 7 hours = 7 * 3 / 2 = 10.5 hours required speed = 420 / 10.5 = 40 kmph c )"
Answer: c
Problem: the end of a blade on an airplane propeller is 5 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 300 π , d ) 480 π , e ) 150 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 5 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 5 / 5280 = 150 π e is the answer"
Answer: e
Problem: what will be the cost of building a fence around a square plot with area equal to 144 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 2784 , b ) 2287 , c ) 2977 , d ) 2668 , e ) 1298
Rationale: "let the side of the square plot be a ft . a 2 = 144 = > a = 12 length of the fence = perimeter of the plot = 4 a = 48 ft . cost of building the fence = 48 * 58 = rs . 2784 . answer : a"
Answer: a
Problem: what is the 36 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 3 rd , 6 th , 9 th , . . . ) to the right of the decimal point is 7 , thus 36 th digit to the right of the decimal point is also 7 . answer : d ."
Answer: d
Problem: if a ( a - 2 ) = 2 and b ( b - 2 ) = 2 , where a ≠ b , then a + b =
Options: a ) − 1 , b ) − 2 , c ) 4 , d ) 46 , e ) 48
Rationale: "i . e . if a = - 1 then b = 2 or if a = 2 then b = - 1 but in each case a + b = - 1 + 2 = - 1 answer : option a"
Answer: a
Problem: if an object travels 400 feet in 4 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 68 , b ) 54 , c ) 87 , d ) 96 , e ) 15
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 400 feet in 4 sec then it travels 400 / 4 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 100 feet in 1 hour = 360000 feet in 1 hr = 360000 / 5280 miles in 1 hour = 36000 / 528 miles / hr ~ 68 miles / hr answer - a"
Answer: a
Problem: if the sum and difference of two numbers are 10 and 19 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 190
Rationale: let the numbers be x and y . then , x + y = 10 and x - y = 19 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 19 = 190 . answer : e
Answer: e
Problem: if 14 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 56
Rationale: let x be the number of students in the school . 0.14 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.14 x / 0.25 = 0.56 x students went to the camping which is 56 % . the answer is e
Answer: e
Problem: cole drove from home to work at an average speed of 80 kmh . he then returned home at an average speed of 120 kmh . if the round trip took a total of 3 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 85 , e ) 108
Rationale: "first round distance travelled ( say ) = d speed = 80 k / h time taken , t 2 = d / 80 hr second round distance traveled = d ( same distance ) speed = 120 k / h time taken , t 2 = d / 120 hr total time taken = 3 hrs therefore , 3 = d / 80 + d / 120 lcm of 80 and 120 = 240 3 = d / 80 + d / 120 = > 3 = 3 d / 240 + 2 d / 240 = > d = 240 * 2 / 5 km therefore , t 1 = d / 80 = > t 1 = ( 240 * 3 ) / ( 5 x 80 ) = > t 1 = ( 9 x 60 ) / 5 - - in minutes = > t 1 = 108 minutes . e"
Answer: e
Problem: the reciprocal of the hcf and lcm of two are 1 / 16 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 208 , e ) 266
Rationale: "reciprocal of the hcf and lcm of two are 1 / 16 and 1 / 312 so , hcf = 16 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 16 * 312 / 24 = 208 answer : d"
Answer: d
Problem: 360 metres long yard , 31 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "31 trees have 30 gaps between them , required distance ( 360 / 30 ) = 12 b"
Answer: b
Problem: a test has 120 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 120 . thus 5 c < = 280 and so c < = 56 . then 40 < = c < = 56 and c can have 17 possible values . the answer is d ."
Answer: d
Problem: a = 2 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 1 different values and answer is b . . . ."
Answer: b
Problem: a train running at the speed of 80 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 227 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 200 m
Rationale: "speed = 80 * 5 / 18 = 200 / 9 m / sec length of the train = speed * time = 200 / 9 * 9 = 200 m answer : e"
Answer: e
Problem: a train 180 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 2 , e ) 4
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 180 * 3 / 55 = 10 sec . answer b"
Answer: b
Problem: what is the difference between 38 % of 80 nd 12 % of 160 .
Options: a ) 11.3 , b ) 12.4 , c ) 12.7 , d ) 11.2 , e ) 10.3
Rationale: "( 38 / 100 ) * 80 â € “ ( 12 / 100 ) * 160 30.4 - 19.2 = 11.2 answer : d"
Answer: d
Problem: paul completes a piece of work in 80 days , rose completes the same work in 120 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 80 × 120 / 200 = 48 days answer is d
Answer: d
Problem: in a certain pond , 100 fish were caught , tagged , and returned to the pond . a few days later , 100 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 100 ) * 100 = 2 % so , x * 2 % = 50 x = 2500 ans . d"
Answer: d
Problem: the manufacturing cost of a shoe is rs . 210 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 222 , b ) s 216 , c ) s 258 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 210 + ( 500 / 100 ) = 215 . gain = 20 % = > sp = 1.2 cp = 1.2 x 215 = 258 answer : c"
Answer: c
Problem: a vessel of capacity 2 litre has 40 % of alcohol and another vessel of capacity 6 litre had 60 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 44 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "40 % of 2 litres = 0.8 litres 60 % of 6 litres = 3.6 litres therefore , total quantity of alcohol is 4.4 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 44 % b"
Answer: b
Problem: 65 % of x = 20 % of 422.50 . find the value of x ?
Options: a ) 100 , b ) 130 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 422.50 then , 65 / 100 * x = 20 / 100 * 4225 / 10 x = 845 / 10 * 100 / 65 = 130 answer is b"
Answer: b
Problem: on increasing the number of lines in a page by 80 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 20 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: explanation : number of pages increased = 80 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 80 = 160 % increase in the number of pages in the book = 80 160 x 100 % = 50 % c
Answer: c
Problem: a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 55 % , d ) 65 % , e ) 70 %
Rationale: number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b
Answer: b
Problem: in a group of 86 students , each student is registered for at least one of 3 classes – history , math and english . 20 - 8 students are registered for history , 20 - 3 students are registered for math , and forty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?
Options: a ) 3 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: a u b u c = a + b + c - ab - bc - ac + abc 86 = 28 + 23 + 44 - ab - bc - ac + 3 = > ab + bc + ac = 12 exactly two classes = ab + bc + ac - 3 abc = 12 - 3 * 3 = 3 hence a
Answer: a
Problem: a man can row his boat with the stream at 24 km / h and against the stream in 10 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 24 us = 10 s = ? s = ( 24 - 10 ) / 2 = 7 kmph answer : c"
Answer: c
Problem: there were totally 100 men . 82 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 82 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 18 - 25 - 15 - 30 = 100 - 88 = 12 answer : b"
Answer: b
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 900 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 .
b ) 40 .
c ) 42 .
d ) 44 .
e ) 45 .
Rationale: let the width = x x * 4 x = 900 x ^ 2 = 225 x = 15 length = 4 * 15 = 60 difference = 60 - 15 = 45 e is the answer
Answer: e
Problem: sachin is younger than rahul by 18 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.5 , b ) 63 , c ) 65 , d ) 36 , e ) 24.19
Rationale: "explanation : if rahul age is x , then sachin age is x - 18 , so , 9 x - 162 = 7 x 2 x = 162 x = 81 so sachin age is 81 - 18 = 63 answer : b ) 63"
Answer: b
Problem: average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 590 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 1170 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 590 x 3 rs . = 1170 rs . correct option : c"
Answer: c
Problem: two numbers are less than third number by 32 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 14 %
Rationale: "let the third number is x . then first number = ( 100 - 32 ) % of x = 68 % of x second number is ( 63 x / 100 ) difference = 68 x / 100 - 63 x / 100 = x / 20 so required percentage is , difference is what percent of first number ( x / 20 * 100 / 68 x * 100 ) % = 14 % answer : e"
Answer: e
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 100 at the end of 2 years and further to $ 200 at the end of another 4 years . what was the rate of interest in which he invested his sum ?
Options: a ) 50 % , b ) 25 % , c ) 10 % , d ) 30 % , e ) 18 %
Rationale: "explanatory answer initial amount invested = $ x amount at the end of year 2 = $ 100 amount at the end of year 6 ( another 4 years ) = $ 200 therefore , the interest earned for the 4 year period between the 2 rd year and 6 th year = $ 200 - $ 100 = $ 100 as the simple interest earned for a period of 4 years is $ 100 , interest earned per year = $ 25 . therefore , interest earned for 2 years = 2 * 25 = $ 50 . hence , initial amount invested x = amount after 2 years - interest for 2 years = 100 - 50 = $ 50 . rate of interest = ( interest per year / principal ) * 100 = 25 / 50 * 100 = 50 % correct choice is a"
Answer: a
Problem: two nascar stock cars take off from the starting line at the exact same time , heading in opposite directions . the budweiser car travels at 145 miles per hour , while the stella artois car travels at 150 miles per hour . at this rate , and ignoring other variable , how long will the cars have to drive in order to be 500 miles , in total , from each other ?
Options: a ) 1.5 hours , b ) 1.27 hours , c ) 1.73 hours , d ) 2 hours , e ) 1.69 hours
Rationale: the cars travel ( 145 + 150 = 295 ) miles in one hour . 500 miles / 295 miles / hour = 1.69 hours answer is e
Answer: e
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 2 / 3 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 8
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 2 x / 3 ) ( 3 y / 4 ) = xy / 2 the total number of boxes is xy + xy / 2 = 3 xy / 2 the fraction loaded by the day crew is xy / ( 3 xy / 2 ) = 2 / 3 the answer is b ."
Answer: b
Problem: convert 400 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 643736
Rationale: "1 mile = 1609.34 meters 400 mile = 400 * 1609.34 = 643736 meters answer is e"
Answer: e
Problem: find the average of all numbers between 6 and 36 which are divisible by 7
Options: a ) 20 , b ) 15 , c ) 25 , d ) 30 , e ) 35
Rationale: explanation : average = ( 7 + 14 + 21 + 28 + 35 ) / 7 = 105 / 7 = 15 option b
Answer: b
Problem: in how many ways 3 boys and 3 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 36 , d ) 256 , e ) none
Rationale: "solution : let the arrangement be , b g b g b g b 34 boys can be seated in 3 ! ways . girl can be seated in 3 ! ways . required number of ways , = 3 ! * 3 ! = 36 . answer : option c"
Answer: c
Problem: if you multiply all the numbers on your mobile phone except 0 , what is the answer ?
Options: a ) 256485 , b ) 362880 , c ) 125425 , d ) 0 , e ) 125826
Rationale: "we have to multiply 1 to 9 to find the answer . therefore 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 = 362880 answer is b"
Answer: b
Problem: a straight line in the xy - plane has slope 4 . on this line the x - coordinate of the point is 50 and y - coordinate is 300 then what is the y intercept of the plane ?
Options: a ) 150 , b ) 110 , c ) 100 , d ) 200 , e ) 50
Rationale: eq of line = y = mx + c m = 4 x = 50 y = 50 * 4 + c , substitute y by 300 as given in question . 300 = 200 + c , c = 100 correct option is c
Answer: c
Problem: what two - digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 13 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 13 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 99 thus the answer is b
Answer: b
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area q of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Problem: a and b invests rs . 10000 each , a investing for 8 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 25000 , find their shares ?
Options: a ) 22277 , b ) 26782 , c ) 22882 , d ) 15000 , e ) 28761
Rationale: "the ratio of their profits a : b = 8 : 12 = 2 : 3 share of a in the total profit = 2 / 5 * 25000 = rs . 10000 share of a in the total profit = 3 / 5 * 25000 = rs . 15000 answer : d"
Answer: d
Problem: a river 3 m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 2678 , c ) 3600 , d ) 3400 , e ) 2500
Rationale: "( 2000 * 3 * 36 ) / 60 = 3600 m 3 answer : c"
Answer: c
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 20 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 1777 meters , d ) 200 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 20 seconds distance = speed * time 36000 * 20 / 3600 = 200 meters . d is the answer ."
Answer: d
Problem: how many seconds will a 900 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 ) 23 sec , b ) 30 sec , c ) 49 sec , d ) 54 sec , e ) 59 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 = 900 * 3 / 50 = 54 sec . answer : d"
Answer: d
Problem: two airplanes take off from one airfield at noon . one flies due east at 201 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 166 , b ) 332 , c ) 400 , d ) 402 , e ) 566
Rationale: "d in two hours : the plane flying east will be 402 miles away from airport . the other plane will be 566 miles away from airport . 566 / 402 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 402 miles apart . d"
Answer: d
Problem: what is the sum of all the multiples of 10 between 0 and 120 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 780
Rationale: "the multiples of 10 between 0 and 120 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 , 110 and 120 . if these are all added together , the result is 780 . final answer : e"
Answer: e
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 11,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 100,000
Rationale: answer equals c in 48 years . i thought by 50 th year it would reach 95,500 . options should have been separated more widely for clarity .
Answer: c
Problem: the ratio 4 : 20 expressed as percent equals to
Options: a ) 20 % , b ) 25 % , c ) 55 % , d ) 65 % , e ) none of above
Rationale: explanation : actually it means 4 is what percent of 20 , which can be calculated as , ( 4 / 20 ) * 100 = 4 * 5 = 20 answer : option a
Answer: a
Problem: jack takes a loan of $ 120000 with 12 % annual interest : the interest is paid once , at the end of the year . jill takes a loan of $ 120000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to jack ' s loan interest , approximately how much more does jill have to repay ?
Options: a ) zero , b ) $ 81.90 , c ) $ 8190.03 , d ) $ 819.00 , e ) $ 8.19
Rationale: jack ' s interest = $ 120,000 * 0.12 = $ 14400 or $ 1,200 each month . jills ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 120,000 * 0.01 = $ 1,200 ; for the 2 nd month = $ 1,200 + 1 % of 1,200 = $ 1,212 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1,212 + 1 % of 1,212 = ~ $ 1,224 ; for the 4 th month = $ 1,224 + 1 % of 1,224 = ~ $ 1,236 ; . . . for the 12 th month = $ 1,320 + 1 % of 1,320 = ~ $ 1,332 . the difference between jack ' s interest and jill ’ s interest = ~ ( 12 + 24 + . . . + 132 ) = $ 792 . answer : d .
Answer: d
Problem: the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 2.5 , d ) 7 / 3 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 4 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 4 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 4 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 7 / 3 answer : d"
Answer: d
Problem: evaluate 45 / . 05
Options: a ) 700 , b ) 900 , c ) 705 , d ) none of these , e ) 506
Rationale: "explanation : 45 / . 05 = 4500 / 5 = 900 option b"
Answer: b
Problem: how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 1 ?
Options: a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495
Rationale: 510 , 512 , 514 , 516 , and 518 , so total 5 . hence option a .
Answer: a