regisss/math_qa huggingface dataset:
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 6 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 60000
Rationale: "perimeter = distance covered in 6 min . = 12000 x 6 m = 1000 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1000 or x = 100 . length = 300 m and breadth = 200 m . area = ( 300 x 200 ) m 2 = 60000 m 2 . e"
Answer: e
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of e ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . e * 23 + 39 = 25 * ( e + 1 ) e = 7 ans . ( a )
Answer: a
Problem: the present age of a father is 3 years more than 3 times the age of his son . 3 years hence , father as age will be 8 years more than twice the age of the son . find the present age of the father .
Options: a ) 88 , b ) 77 , c ) 33 , d ) 44 , e ) 27
Rationale: explanation : let the present age be ' x ' years . then father ' s present age is 3 x + 3 years . three years hence ( 3 x + 3 ) + 3 = 2 ( x + 3 ) + 8 x = 8 hence father ' s present age = 3 x + 3 = [ ( 3 x 8 ) + 3 ] = 27 years . answer : e
Answer: e
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 2500 ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 2500 , then the greatest possible length of integer z is 11 . the answer is c ."
Answer: c
Problem: in measuring the sides of a rectangle , one side is taken 6 % in excess , and the other 5 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.8 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 53 / 50 ) x ( 19 / 20 ) y = ( 144 / 143 ) ( xy ) error in measurement = ( 144 / 143 ) xy - xy = ( 1 / 143 ) xy error percentage = [ ( 1 / 143 ) xy ( 1 / xy ) 100 ] % = ( 7 / 10 ) % = 0.7 % . answer is b ."
Answer: b
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.95 ?
Options: a ) 980 , b ) 1170 , c ) 1530 , d ) 1720 , e ) 1960
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.95 - $ 0.65 = $ 1.30 the charge for the next 1200 grams is $ 1.20 which leaves a charge of $ 0.10 the weight is somewhere between 1450 and 1550 . the answer is c ."
Answer: c
Problem: if the diameter of circle r is 50 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 35 % , b ) 25 % , c ) 20 % , d ) 15 % , e ) 10 %
Rationale: "let diameter of circle r , dr = 50 and diameter of circle s , ds = 100 radius of circle r , rr = 25 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 25 / 50 ) ^ 2 = ( 5 / 10 ) ^ 2 = 25 % answer : b"
Answer: b
Problem: a can do a piece of work in 9 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 54 , e ) 12
Rationale: "8 / 9 + 6 / x = 1 x = 54 days answer : d"
Answer: d
Problem: john ' s bank ' s saving amount is decreased 50 % due to loan payment and current balance is rs . 50000 . find the actual balance before deduction ?
Options: a ) 100000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000
Rationale: "50 % decreased 50 % balance = 50000 100 % = 50000 / 50 * 100 = 100000 answer : a"
Answer: a
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 192 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 12
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 192 - $ 120 = $ 72 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 72 / $ 6 = 12 ans is e"
Answer: e
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 294 , what is the least possible value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "294 = 2 * 3 * 7 * 7 , so n must be at least 14 . the answer is d ."
Answer: d
Problem: excluding stoppages , the speed of a train is 55 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 16 , c ) 12 , d ) 82 , e ) 18
Rationale: "explanation : t = 15 / 55 * 60 = 16 answer : option b"
Answer: b
Problem: a train travels 210 km in 3 hours and 270 km in 4 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 69 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 210 + 270 = 480 km thus , total speed = 7 hrs or , average speed = 480 / 7 or , 69 kmph . answer : b"
Answer: b
Problem: 15 - 2 + 4 ÷ 1 / 2 × 8 = ?
Options: a ) 272 , b ) 77 , c ) 168 , d ) 56 , e ) 59
Rationale: explanation : 15 - 2 + 4 ÷ 1 / 2 × 8 = 15 - 2 + 4 × 2 × 8 = 15 - 2 + 64 = 77 answer : option b
Answer: b
Problem: the difference between the compound interest and simple interest on a certain sum at 20 % per annum for 2 years is $ 500 . find the sum ?
Options: a ) $ 10000 , b ) $ 50000 , c ) $ 15200 , d ) $ 12500 , e ) $ 15000
Rationale: "let the sum be $ x c . i . = x ( 1 + 20 / 100 ) ^ 2 - x = 35 x / 100 s . i . = ( x * 20 * 2 ) / 100 = 2 x / 5 c . i . - s . i . = ( 35 x / 100 ) - ( 2 x / 5 ) = 5 x / 100 5 x / 100 = 500 x = 10000 answer is a"
Answer: a
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 432 square meters , then what is the width of the rectangular garden ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the width of the garden . 3 x ^ 2 = 432 x ^ 2 = 144 x = 12 the answer is e ."
Answer: e
Problem: the mean of 50 observations was 39 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 39 × 50 + 48 – 23 ) = 1975 . therefore correct mean = 1975 / 50 = 39.5 . answer e"
Answer: e
Problem: when positive integer n is divided by 2 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 10 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 2 , the remainder is 1 i . e . , n = 2 x + 1 values of n can be one of { 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17,19 , . . . . . . . . . . . . . . 31 , 33,35 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , 47 , 54 , 61 . . . . . . . . } combining both the sets we get n = { 19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 21 or 21 x in case of n = 5 p = 5 so for min value of p , we take min value of n . c is the answer ."
Answer: c
Problem: how many odd factors does 160 have ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 160 = 2 * 5 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 } plus 1 to each = { 2 } product = 2 therefore , there are 2 odd factors of 160 . answer : a ."
Answer: a
Problem: the length of a rectangle is doubled while its width is tripled . what is the % change in area ?
Options: a ) 250 %
b ) 300 %
c ) 500 %
d ) 650 %
e ) 700 %
Rationale: the original area is l * w the new area is 2 l * 3 w = 6 * l * w = l * w + 5 * l * w the area increased by 500 % . the answer is c .
Answer: c
Problem: there were totally 100 men . 81 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 - 81 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 19 - 25 - 15 - 30 = 100 - 89 = 11 answer : a"
Answer: a
Problem: nicky and cristina are running a 400 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 40 , b ) 25 , c ) 35 , d ) 30 , e ) 50
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . d"
Answer: d
Problem: a mixture of 70 liters of wine and water contains 10 % water . how much water must be added to make water 12 ½ % of the total mixture ?
Options: a ) 12 liters , b ) 10 liters , c ) 4 liters , d ) 2 liters , e ) 3 liters
Rationale: "70 * ( 10 / 100 ) = 7 wine water 87 1 / 2 % 12 1 / 2 % 87 1 / 2 % - - - - - - - 63 12 1 / 2 % - - - - - - - ? = > 9 - 7 = 2 answer : d"
Answer: d
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 35 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 17.5 minutes . , b ) 35 minutes . , c ) 52.5 minutes . , d ) 70 minutes . , e ) 105 minutes .
Rationale: "danny ' s time is 35 minutes . the time to reach halfway is 17.5 minutes . steve ' s time is 70 minutes . the time to reach halfway is 35 minutes . the time difference is 35 - 17.5 = 17.5 minutes the answer is a ."
Answer: a
Problem: a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 40 % 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 ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 28 % .
Rationale: "20 % of 2 litres = 0.4 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.8 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 28 % answer : e"
Answer: e
Problem: in a kilometer race , a beats b by 60 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 199 sec , b ) 156.7 sec , c ) 726 sec , d ) 127 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 60 = 166.7 sec . time taken by a = 166.7 - 10 = 156.7 sec . answer : b"
Answer: b
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 120 metres ?
Options: a ) 18 , b ) 24 , c ) 17 , d ) 12 , e ) 13
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 120 m = 120 / 5 = 24 seconds . answer : b"
Answer: b
Problem: the perimeter of one face of a cube is 24 cm . its volume will be :
Options: a ) 216 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 24 / 4 = 6 cm volume = a * a * a = 6 * 6 * 6 = 216 cm cube option a"
Answer: a
Problem: when a train moves at an average speed of 100 kmph it reaches its destination on time . when its average speed becomes 80 kmph , then it reaches its destination 20 minutes late . find the length of journey rounded to two decimal places .
Options: a ) 99.33 km , b ) 133.33 km , c ) 125.33 km , d ) 156.66 km , e ) none
Rationale: sol . difference between timings = 20 min = 1 / 3 hr . let the length of journey be x km . then , x / 80 - x / 100 = 1 / 3 â ‡ ” 5 x - 4 x = 133.33 â ‡ ” x = 133.33 km . answer b
Answer: b
Problem: a certain bacteria colony doubles in size every day for 20 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 19
Rationale: "simultaneous grow = same amount of time in 20 days we should expect to have p ( 2 ) ^ 20 so if we have two things doing the job of getting us there then ; 2 ^ x + 2 ^ x = 20 2 ( 2 ) ^ x = 2 2 ^ ( x + 1 ) = 2 ^ 20 x + 1 = 20 x = 19 ; answer : e"
Answer: e
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 126 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 6 yearned with the compound interest is the percent yearned on percent . so , $ 6 is yearned on $ 60 , which means that the interest = 10 % . this on the other hand means that half of the savings = 60 * 10 = $ 600 . twice of that = $ 1,200 . answer : d ."
Answer: d
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1234 , b ) 1540 , c ) 1650 , d ) 1632 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Problem: joan and karl each bought a sofa and the sum of their purchases was $ 600 . if twice of what joan paid was $ 90 more than what karl paid , what did joan pay for her sofa ?
Options: a ) $ 190 , b ) $ 210 , c ) $ 230 , d ) $ 250 , e ) $ 270
Rationale: j + k = 600 so k = 600 - j 2 j = k + 90 2 j = ( 600 - j ) + 90 3 j = 690 j = 230 the answer is c .
Answer: c
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 36 , b ) 40 , c ) 45 , d ) 51 , e ) 56
Rationale: "the total number of ways to choose 5 managers is 8 c 5 = 56 we need to subtract the number of groups which include the two managers , which is 6 c 3 = 20 . 56 - 20 = 36 the answer is a ."
Answer: a
Problem: a reduction of 18 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 1080 , what is the reduced price for kg ?
Options: a ) 72.15 , b ) 27.24 , c ) 24.25 , d ) 28.46 , e ) 20.9
Rationale: "1080 * ( 18 / 100 ) = 194 - - - - 8 ? - - - - 1 = > rs . 24.25 answer : c"
Answer: c
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 38 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 152 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 38 = > 4 / x = 1 / 38 x = 38 ∗ 4 = 152 mins option d"
Answer: d
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 6 ) = 4 x . the fraction of sensors which have been upgraded is x / ( x + 4 x ) = x / 5 x = 1 / 5 the answer is b ."
Answer: b
Problem: a copy machine , working at a constant rate , makes 30 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 4,500 , d ) 2,550 , e ) 324,000
Rationale: "together the two machines make 30 + 55 = 85 copies per minute . so , in half an hour they will make 85 * 30 = 2,550 copies . answer : d ."
Answer: d
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 5 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 5 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 2 = 10 . thus there are 160 - 10 = 150 such numbers . answer : b ."
Answer: b
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 450 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 495 , e ) 510
Rationale: let no . of non - officers be x 15 * 450 + x * 110 = ( x + 15 ) 120 x = 495 d
Answer: d
Problem: there are 15 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 105 , d ) 60 , e ) 90
Rationale: 15 players are there . two players play one game with one another . so 15 c 2 = 15 x 14 / 2 = 105 so option c is correct
Answer: c
Problem: two heavily loaded sixteen - wheeler transport trucks are 855 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 135 , d ) 320 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 855 - 90 = 765 k ratio of speeds 9 : 8 - > 765 / 17 = 45 truck a = 90 + 45 * 9 = 495 truck b = 45 * 8 = 360 delta = 135 km answer c"
Answer: c
Problem: 5357 x 51 = ?
Options: a ) 273232 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273207
Rationale: "5357 x 51 = 5357 x ( 50 + 1 ) = 5357 x 50 + 5357 x 1 = 267850 + 5357 = 273207 e )"
Answer: e
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 300 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 750 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 300 = 750 answer : b"
Answer: b
Problem: a student is ranked 16 th from right and 6 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 16 , from left 6 total = 16 + 6 - 1 = 21 answer : d"
Answer: d
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum w of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : w = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Problem: if a number x is 10 % less than another number y and y is 10 % more than 125 , then x is equal to
Options: a ) 143 , b ) 150 , c ) 123.75 , d ) 140.55 , e ) none
Rationale: solution y = 125 + 10 % of 125 = 125 + 12.50 = 137.50 . x = 137.50 - 10 % of 137.50 = 137.50 - 13.75 = 123.75 . answer c
Answer: c
Problem: 575.104 x 15.98 ã · 9.001 + 21.25 = ?
Options: a ) 983.578 , b ) 1043.65 , c ) 1033.65 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 575.104 x 15.98 ã · 9.001 + 21.25 â ‰ ˆ ( 575.104 x 16 / 9 ) + 21.25 â ‰ ˆ 1022.40 + 21.25 â ‰ ˆ 1043.65 answer : option b"
Answer: b
Problem: if a car had traveled 30 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 90 km , at what speed did it travel ?
Options: a ) 35 kmh , b ) 45 kmh , c ) 60 kmh , d ) 75 kmh , e ) 90 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 90 / x - 90 / ( x + 30 ) = 1 / 2 substitute the value of x from the options . - - > x = 60 - - > 90 / 60 - 90 / 90 = 3 / 2 - 1 = 1 / 2 answer : c"
Answer: c
Problem: the length and width of a rectangle are integer values . what is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer
Options: a ) 12
b ) 45
c ) 36
d ) 48
e ) 60
Rationale: if we consider all pythagorean triplets with integral values , we have the following results : - ( 3 , 4,5 ) , ( 6 , 8,10 ) . . . . . . . . the diameter of the circle is 5 in the 1 st case and 10 in the 2 nd . but the question says that radius of the circle is also an integer hence the 1 st triplet will be ruled out . we are left with the 2 nd triplet where radius of the circle = 5 , hence the sides of the rectangle are 6 and 8 making the area = 45 . b
Answer: b
Problem: if the selling price of 8 articles is same as the cost price of 12 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 50 % gain , d ) 50 % loss , e ) 60 % loss
Rationale: "explanation : let the c . p of each article be re 1 . then , s . p of 8 articles = c . p of 12 articles = rs . 12 / - now , c . p of 8 articles = rs . 8 / - , s . p of 8 articles = rs 12 / - gain = rs ( 12 - 10 ) = rs 4 / - . gain % = ( 4 / 8 * 100 ) % = 50 % gain answer : option c"
Answer: c
Problem: janet invited her boy and girl friends to her party at the ratio of 3 : 7 . if 30 % of the boys and 70 % of the girls will be coming for the party from texas , how many janet invited friends will be coming from texas .
Options: a ) 62 % , b ) 52 % , c ) 57 % , d ) 56 % , e ) 58 %
Rationale: let total no of janet invited friends be 100 , boys 30 and girls 70 , so total number of janet ' s invited guests coming from texas for both boys and girls respectively 30 * 30 / 100 = 9 and 70 * 70 / 100 = 49 so total 58 of janet ' s invited guest out of the 100 invited guests will be coming from texas . . so required % is 58 % answer : e
Answer: e
Problem: david works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 500 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 13,500 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 6500 , b ) 3500 , c ) 2500 , d ) 4500 , e ) 2000
Rationale: "let the rate be x , then population of the bacteria after each hour can be given as 500,500 x , 500 ( x ^ 2 ) , 500 ( x ^ 3 ) now population at 4 pm = 13,500 thus we have 500 ( x ^ 3 ) = 13,500 = 27 thus x = 3 therefore population at 3 pm = 500 ( 9 ) = 4,500 answer : d"
Answer: d
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 3 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 3 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 . b ' s 1 hour ' s work = ( 7 / 12 - 1 / 3 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"
Answer: e
Problem: 2 , 5 , 10 , 17 , . .
Options: a ) 5 , b ) 8 , c ) 26 , d ) 7 , e ) 12
Rationale: "explanation : numbers are ( 1 * 1 ) + 1 = 2 ( 2 * 2 ) + 1 = 5 ( 3 * 3 ) + 1 = 10 ( 4 * 4 ) + 1 = 17 ( 5 * 5 ) + 1 = 26 answer : c"
Answer: c
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent of the original cost ?
Options: a ) 200 , b ) 600 , c ) 800 , d ) 1600 , e ) 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Problem: 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 17 , 28 and 35 , 45 what is the minimum possible range in scores of the 3 test - takers ?
Options: a ) a 17 , b ) b ) 28 , c ) c ) 35 , d ) d ) 45 , e ) e ) 80
Rationale: it is finding the minimum range between all their scores , if all test taker scores are between 0 and maximum range we will have : a - 0 and 17 b - 0 and 28 c - 0 and 35 d - 0 and 45 therefore the minimum range is 45 , it cant be any lower however you play with the numbers . d
Answer: d
Problem: a sum of money is distributed among a , b , c , d in the proportion of 5 : 3 : 2 : 3 . if a gets $ 1000 more than b , what is the c ' s share ?
Options: a ) $ 2000 , b ) $ 5000 , c ) $ 8000 , d ) $ 1500 , e ) $ 1000
Rationale: "let the shares of a , b , c , d are 5 x , 3 x , 2 x , 3 x 5 x - 3 x = 1000 x = 500 c ' s share = 2 x = $ 1000 answer is e"
Answer: e
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 15 seconds . the speed of the train is :
Options: a ) 22 , b ) 50 , c ) 99 , d ) 35 , e ) 12
Rationale: speed of the train relative to man = ( 125 / 15 ) m / sec = ( 25 / 3 ) m / sec . [ ( 25 / 3 ) * ( 18 / 5 ) ] km / hr = 30 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 30 = = > x = 35 km / hr . answer : d
Answer: d
Problem: two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction . what time will they take to be 32 km apart ?
Options: a ) 18 , b ) 16 , c ) 19 , d ) 15 , e ) 34
Rationale: "explanation : relative speed = 7.5 - 5.5 = 2 kmph ( because they walk in the same direction ) distance = 32 km time = distance / speed = 32 / 2 = 16 hr answer : b"
Answer: b
Problem: two thirds of the roads from a to b are at least 5 miles long , and 1 / 2 of the roads from b to c are at least 5 miles long . if you randomly pick a road from a to b and then randomly pick a road from b to c , what is the probability that at least one of the roads you pick is at least 5 miles long ?
Options: a ) 5 / 6 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 11 / 12
Rationale: "so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 2 = 5 / 6 . answer : a ."
Answer: a
Problem: the difference between a number and its two - fifth is 510 . what is 15 % of that number ?
Options: a ) 152.01 , b ) 85 , c ) 76 , d ) 168.2 , e ) 127.5
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 15 % of 850 = 127.5 . answer : e"
Answer: e
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 42 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 18000 x 7 ) + 6000 ( x - 7 ) x = 42 answer c"
Answer: c
Problem: a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . the share of c is ?
Options: a ) 23 , b ) 87 , c ) 84 , d ) 26 , e ) 19
Rationale: given total sum = rs . 427 and given that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . = > 3 a = 4 b = 7 c but given = > a + b + c = 427 now express a and b in terms of c i . e = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c
Answer: c
Problem: if x and t are integers and 2 x – t = 11 , then 4 x + t can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - t = 11 . . . . t = 2 x - 11 4 x + t = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Problem: excluding stoppages , the speed of a bus is 40 kmph and including stoppages , it is 30 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 12 min , c ) 18 min , d ) 15 min , e ) 20 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 40 x 60 ) min = 15 min answer : d"
Answer: d
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 54 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 15 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: answer : a 54 ° divided by 360 ° equals 0.15 , therefore the sector is equal to 15 % of the total
Answer: a
Problem: nicky and cristina are running a 100 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 25 , e ) 60
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . a"
Answer: a
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 55 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 3 , d ) 8 , e ) 9
Rationale: "going down = 20 m going up = 10 - - > total = 30 going down = 10 - - > total = 40 going up = 5 - - > total = 45 going down = 5 - - > total = 50 going up = 2.5 - - > total = 52.5 going down = 2.5 - - > total = 55 ( caught ) no of bouncing = 3 answer : c"
Answer: c
Problem: find the value of 582964 x 99999 = m ?
Options: a ) 58210607666 , b ) 58310607896 , c ) 58295817036 , d ) 58591650836 , e ) 58310692816
Rationale: "582964 x 99999 = 582964 x ( 10000 - 1 ) = 582964 x 100000 - 582964 x 1 = 58296400000 - 582964 = 58295817036 c"
Answer: c
Problem: a big container is 30 % full with water . if 18 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 18 liters of water is added , the container becomes 75 % full . hence these 18 liters account for 45 % of the container , which means that the capacity of it is 18 / 0.45 = 40 liters . or : if the capacity of the container is x liters then : 0.3 x + 18 = 0.75 x - - > x = 40 liters . answer : b ."
Answer: b
Problem: ( 18.6 x 17.2 ÷ 0.6 ) x 27.5 = ?
Options: a ) 12132 , b ) 14678 , c ) 12708 , d ) 14663 , e ) 15688
Rationale: "explanation : ( 319.92 ÷ 0.6 ) x 27.5 = 533.2 x 27.5 = 14663 answer : option d"
Answer: d
Problem: a 300 m long train crosses a platform in 51 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 277 , e ) 550
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 5 a = 50 / 3 3 x + 900 = 2550 = > x = 550 m . answer : e"
Answer: e
Problem: 16.02 ã — 0.0001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.0001 = 0.001602 the answer is b ."
Answer: b
Problem: at an election 2 candidates are participated and a candidate got 30 % of votes and defeated by 1000 . and 100 votes are invalid . find the total polled votes ?
Options: a ) 2150 , b ) 2600 , c ) 3120 , d ) 1500 , e ) 1895
Rationale: "winner votes = 100 - 30 = 70 polled votes = [ ( 100 * 1000 ) / 2 * 70 - 100 ] + 100 = 2600 answer is b"
Answer: b
Problem: find avrg speed if a man travels at speed of 32 km / hr up and 48 km / hr dawn at an altitude of 230 m .
Options: a ) 25.8 , b ) 26.8 , c ) 38.4 , d ) 34.4 , e ) 29.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 32 * 48 ( 32 + 48 ) = 38.4 answer : c"
Answer: c
Problem: what is the least integer greater than – 1 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 1 ) + ( 0.5 ) = - 0.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 1 to - 0.5 ) . next , the question asks for the least integer that is greater than - 0.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 0.5 is 0 . final answer : c"
Answer: c
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 7 + 16 * 7 ) ] = 15 years . answer : e"
Answer: e
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 500 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 4.76 % , b ) 5.88 % , c ) 6.33 % , d ) 7.75 % , e ) 8.33 %
Rationale: in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 400 - $ 60 = 340 . the interest rate is $ 20 / $ 340 = 1 / 17 which is about 5.88 % the answer is b .
Answer: b
Problem: a doctor prescribed 24 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 50 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 24 c . c % prescribed dosage greater than the typical dosage = ( 24 - 16 / 16 ) * 100 % = ( 8 / 16 ) * 100 % = 50 % answer d"
Answer: d
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent z of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march z = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Problem: how many different positive integers are factors of 324 ?
Options: a ) 9 , b ) 16 , c ) 25 , d ) 36 , e ) 49
Rationale: "18 × 18 = 6 ^ 2 × 3 ^ 2 so total factors = ( 5 + 1 ) ( 5 + 1 ) = 36 answer : d"
Answer: d
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 250 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 5.5
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 250 / 45 = $ 5.5 answer : e ."
Answer: e
Problem: ( 258 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 544
Rationale: "explanation : ? = ( 258 x 1265 / 100 ) ÷ 6 = 326370 / 600 = 544 answer : option e"
Answer: e
Problem: if ( 1 / 5 ) ^ n * ( 1 / 4 ) ^ 18 = 1 / ( 2 * ( 10 ) ^ 35 ) , then n =
Options: a ) 40 , b ) 45 , c ) 35 , d ) 30 , e ) 25
Rationale: ( 1 / 5 ) ^ m ( 1 / 4 ) ^ 18 = 1 / { 2 ( 10 ) ^ 35 } 2 ( 10 ) ^ 35 / 4 ^ 18 = 5 ^ m [ 2 ( 2 ^ 35 ) ( 5 ^ 35 ) ] / [ 2 ^ 36 ] = 5 ^ m 5 ^ 35 = 5 ^ m n = 35 c
Answer: c
Problem: let exp ( m , n ) = m to the power n . if exp ( 10 , m ) = n exp ( 22 ) where m and n are integers then n = ___ ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 10 ^ m = n * ( 2 ^ 2 ) ( 2 * 5 ) ^ m = n * ( 2 ^ 2 ) ( 2 ^ m ) * ( 5 ^ m ) = n * ( 2 ^ 2 ) now equate both side we get m = 2 and ( 5 ^ m ) = n ( 5 ^ 2 ) = n = > n = 25 answer : b
Answer: b
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 5.6 ] + [ 3.4 ] + [ 12.7 ] ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 5.6 ] = - 6.0 [ 3.4 ] = 3.0 [ 12.7 ] = 12.0 therefore , answer is : - 6.0 + 3.0 + 12.0 = 9.0 option d ."
Answer: a
Problem: in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "given 150 deers were caught and they are tagged in the first slot . in the second slot , 50 were caught and 5 we tagged then 10 % of them are tagged . given this 10 % approximates the percentage of tagged deer in the forest . . here number is 150 . . then 100 % is 1500 . . is the number of deers population in the forest . . answer : d is correct answer . ."
Answer: d
Problem: the sum of four consecutive even numbers is 84 . what would be the smallest number ?
Options: a ) 33 , b ) 88 , c ) 70 , d ) 123 , e ) 18
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 84 = > x = 11 smallest number is : 2 ( x - 2 ) = 18 . answer : e"
Answer: e
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 52 units per day , what is the value of n ?
Options: a ) 30 , b ) 19 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 52 * ( n + 1 ) - - > n = 19 . or as 40 extra units increased the average for n + 1 days by 2 units per day then 40 / ( n + 1 ) = 2 - - > n = 19 . answer : b ."
Answer: b
Problem: an escalator moves towards the top level at the rate of 8 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 16 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 8 + 2 ) = 16 sec answer : c"
Answer: c
Problem: a photograph is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ?
Options: a ) 76
b ) 65
c ) 59.5
d ) 49
e ) 38.5
Rationale: area covered by photograph = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e
Answer: e
Problem: ( 1000 ) 7 ÷ ( 10 ) 15 = ?
Options: a ) 10 , b ) 100 , c ) 1000000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 15 = ( 10 ) 21 / ( 10 ) 15 = 10 ( 6 ) = 1000000 option c"
Answer: c
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 3000 , then his salary per month in rupees is :
Options: a ) 20000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 3000 , salary = 20000 rs . answer : a"
Answer: a
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 8 : 3 . the sum of numbers is :
Options: a ) 22 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 8 x and 3 x . then , their l . c . m = 24 x . so , 24 x = 48 or x = 2 . the numbers are 16 and 6 . hence , required sum = ( 16 + 6 ) = 22 . answer : a"
Answer: a
Problem: when positive integer e is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation that can be formed e is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b
Answer: b
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.48 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.32 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.48 = 3 * x - - > x = $ 0.32 . answer : d ."
Answer: d
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to decreased by 10 percent , how much would she earn per week ?
Options: a ) rs . 415 , b ) rs . 325 , c ) rs . 352 , d ) rs . 315 , e ) rs . 425
Rationale: "soln : - ( 406 / 116 ) 90 = 315 in this case long division does not take much time . ( 406 / 116 ) = 3.5 3.5 * 90 = rs . 315 answer : d"
Answer: d
Problem: amit , sumit and pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations . after breakfast , each of them boards a different tourist vehicle from the nearest bus - depot . after 3 hours , sumit who had gone to a famous beach , calls on the mobile of pramit and claims that he has observed a shark in the waters . pramit learns from the local guide that at that time of the year , only 8 sea - creatures ( including a shark ) are observable and the probability of observing any creature is equal . however , amit and pramit later recall during their discussion that sumit has a reputation for not telling the truth 5 out of 6 times . what is the probability that sumit actually observed a shark in the waters ?
Options: a ) 1 / 36 , b ) 1 / 30 , c ) 5 / 36 , d ) 1 / 24 , e ) 1 / 28
Rationale: explanation : the probability that sumit actually sees a shark , given that he claimed to have seen one . = > p ( he actually sees the shark and reports truth ) / p ( he claims of seeing a shark ) . = > p ( sees the shark ) p ( reports truth ) / ( p ( he sees a shark ) p ( reports truth ) + p ( does n ' t see ) p ( reports false ) . = > ( 1 / 8 × 1 / 6 ) / ( 1 / 8 × 1.6 + 7 / 8 × 5 / 6 ) = > 1 / 36 . answer : a
Answer: a
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 10 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) s . 8400 , b ) s . 9000 , c ) s . 14000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 10 * 2 ) / 100 = 840 = > 30 x / 100 - 20 x / 100 = 840 = > 10 x / 100 = 840 = > x = 8400 . answer : a"
Answer: a