regisss/math_qa huggingface dataset:
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 3 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 4.0 , b ) 3.8 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 3 and 6 = 12 . upstream time = 12 / 6 = 2 hrs downstream time = 12 / 3 = 4 hrs total time = 6 hrs total distance = 24 average speed = 24 / 6 = 4.0 km / hr"
Answer: a
Problem: abcd is a square where ab = â ˆ š 4008 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2004 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4008 / 2 = 2004 . correct answer b"
Answer: b
Problem: a man swims downstream 72 km and upstream 45 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 1.7 , b ) 2.8 , c ) 3.6 , d ) 2.7 , e ) 1.1
Rationale: "72 - - - 5 ds = 14.4 ? - - - - 1 45 - - - - 5 us = 9 ? - - - - 1 s = ? s = ( 14.4 - 9 ) / 2 = 2.7 answer : d"
Answer: d
Problem: two numbers are in the ratio 1 : 2 , if 7 is added to both , their ratio changes to 3 : 5 . the greatest number is
Options: a ) 24 , b ) 26 , c ) 28 , d ) 32 , e ) 44
Rationale: "let the numbers be x and 2 x then , ( x + 7 ) / ( 2 x + 7 ) = 3 / 5 x = 14 there fore answer is 28 answer c 28"
Answer: c
Problem: what is 82 % of 3 / 4 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.615
Rationale: "82 % * ( 3 / 4 ) = 0.82 * 0.75 = 0.615 answer : e"
Answer: e
Problem: points x , y , and z lie , in that order , on a straight railroad track . the distance from point x to point y is twice the distance from point y to point z . a train traveled from point x to point z without stopping . the train ' s average speed when traveling from point x to point y was 300 miles per hour and the train ' s average speed when traveling from point y to point z was 100 miles per hour . what was the train ' s average speed , in miles per hour , when traveling from point x to point z ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 180 , e ) 260
Rationale: average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 300 speed y - z = 100 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 300 ) + ( d / 100 ) 3 d / ( 2 d / 300 ) + ( 3 d / 300 ) 3 d / ( 5 d / 300 ) 900 d / 5 d average speed = 180 answer : d
Answer: d
Problem: a 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 270 / 9 = 500 / 9 = > x + 270 = 500 = > x = 230 so the length of the train is 230 meters option c"
Answer: c
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 20000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 1000
Rationale: "30 sec approach - solve it using approximation 20000 sheet at full price , 5 cent = 1000 20000 sheet at max discount price , 4 cent = 800 your ans got to be between these two . ans d it is ."
Answer: d
Problem: there is rain at a rate of 12 centimeters per hour all over new jersey . somewhere downtown in new jersey a group of students are waiting for the rain to stop . if the rain filled a tank the with a base area of 250 square centimeters and a depth of 6 centimeters , how long did the students wait for the rain to stop ?
Options: a ) 8 hours
b ) 4 hours 25 minutes
c ) 3 hours 15 minutes
d ) 6 hours
e ) 2 hours
Rationale: answer is : e , 4 hours and 30 mins the volume of the tank is irrelevant and only height matters since rain fell all over the city . thus , it takes only . 12 / 6 = 2 hours of rain to fill the tank .
Answer: e
Problem: if a and b are positive integers , and a = 3 b + 12 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 3 , c ) 2 , d ) 5 , e ) 4
Rationale: "if b is 1 , 2 , 3 , or 4 , then gcd of a and b is 1 , 2 , 3 , and 4 respectively . so , by poe the answer must be d . still : if b is a multiple of 5 , then a is 12 greater than a multiple of 5 , so not a multiple of 5 , so both of them can not be divisive by 5 . answer : d ."
Answer: d
Problem: during a sale , the price of a pair of shoes is marked down 14 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 16 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 86 price after sale = 100 percent increase = 14 / 86 * 100 = 16 % approx . correct option : d"
Answer: d
Problem: two trains of length 60 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 17 sec , d ) 20 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 60 + 280 = 400 m . the time required = d / s = 340 / 20 = 20 sec . answer : c"
Answer: c
Problem: one 100 gallons of fuel are purchased at $ 0.70 per gallon . the fuel is consumed at a rate of $ 0.40 worth of fuel per hour . at this rate , how many hours are required to consume the 100 gallons of fuel ?
Options: a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 250
Rationale: the fuel is consumed at this rate : $ 0.40 / $ 0.70 = 4 / 7 gallons per hour . the time it takes to consume 100 gallons is : 100 / ( 4 / 7 ) = 175 hours . the answer is b .
Answer: b
Problem: a chemist mixes one liter of pure water with x liters of a 75 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 75 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 75 - 15 ) / ( 15 - 0 ) = 4 / 1 1 / x = 4 / 1 x = 1 / 4 answer : a"
Answer: a
Problem: if 5 % more is gained by selling an article for rs . 600 than by selling it for rs . 580 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 400 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 600 - 580 = 20 x / 20 = 20 = > x = 400 answer : c"
Answer: c
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 5 / 4 = 1 hrs 15 min answer : c"
Answer: c
Problem: a , b , c subscribe rs . 50000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36000 , what will be the amount a receives ?
Options: a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 36000 × 21 / 50 = 15,120 answer is a .
Answer: a
Problem: steve traveled the first 2 hours of his journey at 30 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 30 * 2 = 60 miles . distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles . therefore , total distance covered = 60 + 240 = 300 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 300 / 5 = 60 miles per hour . choice c"
Answer: c
Problem: a train 600 m long can cross an over brdge of 100 m long in 70 sec and then find the speed of the train ?
Options: a ) 79 , b ) 30 , c ) 36 , d ) 66 , e ) 12
Rationale: length = speed * time speed = l / t s = 700 / 70 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph . answer : c
Answer: c
Problem: when sold at a 60 % discount , a sweater nets the merchant a 35 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 70.38 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 35 % . . therefore the wholesale purchase cost = x . . . . 1.35 x = 40 or x = 29.62 . . . marked price was 100 so . . . so answer is 70.38 % . . d"
Answer: d
Problem: from a group of 3 women and 3 girls , 4 are to be randomly selected . what is the probability that equal numbers of women and girls will be selected ?
Options: a ) 3 / 5 , b ) 1 / 5 , c ) 2 / 5 , d ) 4 / 5 , e ) 1
Rationale: using the first example , here is the probability of that exact sequence occurring : wwgg = ( 3 / 6 ) ( 2 / 5 ) ( 3 / 4 ) ( 2 / 3 ) = 36 / 360 = 1 / 10 each of the other 5 options will yield the exact same probability . . . . wgwg = ( 3 / 6 ) ( 3 / 5 ) ( 2 / 4 ) ( 2 / 3 ) = 36 / 360 = 1 / 10 so we have 6 different options that each produce a 1 / 10 chance of occurring . 6 ( 1 / 10 ) = 6 / 10 = 3 / 5 final answer : a
Answer: a
Problem: what is the sum of natural numbers between 50 and 100
Options: a ) 4800 , b ) 4860 , c ) 3825 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 50 and 100 numbers = 51 = > 100 - 50 = 50 + 1 = 51 sn = 51 / 2 ã — 150 = 51 ã — 75 = 3825 answer : c"
Answer: c
Problem: an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 2 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 1 ) to be divisible by 2 either n or n + 1 must be a multiples of 2 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 2 , or 3 . thus , the overall probability is 2 / 3 . answer : d ."
Answer: d
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 30,000 loan he has taken . the bank charges him a quarterly compound rate of 10 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 40 % . here you find per quarter rate as ( 40 / 4 ) % = 10 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 10 % quarterly rate . so the bank charges 10 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 10 % of 30,000 = $ 12000 as our answer . but since , the interest is compounded , it will be a bit more than $ 12000 . option ( e ) looks correct ."
Answer: e
Problem: the s . i . on a certain sum of money for 4 years at 12 % per annum is half the c . i . on rs . 6000 for 2 years at 15 % per annum . the sum placed on s . i . is ?
Options: a ) 2019.625 , b ) 2017.625 , c ) 2013.625 , d ) 2015.625 , e ) 2011.625
Rationale: c . i . = [ 6000 * ( 1 + 15 / 100 ) 2 - 6000 ] = ( 6000 * 23 / 20 * 23 / 20 - 6000 ) = rs . 1935 . sum = ( 967.5 * 100 ) / ( 4 * 12 ) = rs . 2015.625 answer : d
Answer: d
Problem: what is the greatest positive integer x such that 2 ^ x is a factor of 8 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "8 ^ 10 = ( 2 ^ 3 ) ^ 10 = 2 ^ 30 answer : e"
Answer: e
Problem: of the 80 people in a room , 1 / 4 are women . if 3 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "women = 1 / 4 * 80 = 20 married = 3 / 4 * 80 = 60 unmarried = 20 max ( un - married women ) = 20 answer a"
Answer: a
Problem: the ratio of the volumes of two cubes is 125 : 1000 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 9 : 11 , c ) 729 : 1331 , d ) 1 : 4 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 125 : â ³ â ˆ š 1000 = 5 : 10 ratio of surface areas = 5 ^ 2 : 10 ^ 2 = 25 : 100 = 1 : 4 answer : d"
Answer: d
Problem: if the mean of numbers 12 , x , 42 , 78 and 104 is 62 , then what is the mean of 128 , 255 , 511 , 1023 and x ?
Options: a ) 395 , b ) 275 , c ) 355 , d ) 415 , e ) 398.2
Rationale: "the mean of numbers 12 , x , 42 , 78 and 104 is 62 : 12 + x + 42 + 78 + 104 = 62 * 5 - - > x = 74 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 74 ) / 5 = 398.2 . answer : e ."
Answer: e
Problem: if the perimeter of square region q and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of q
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pq ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pq = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Problem: the ratio of the present ages of ramesh and mahesh is 2 : 5 . 10 years hence , the ratio of their ages will be 10 : 15 . find the difference in their present ages ?
Options: a ) 7.5 , b ) 6 , c ) 5.5 , d ) 6.5 , e ) 5
Rationale: let the present ages of ramesh and mahesh be 2 x and 5 x years respectively . ( 2 x + 10 ) / ( 5 x + 10 ) = 10 / 15 6 x + 30 = 10 x + 20 = > x = 2.5 difference in their ages will be the same at all times . this difference = difference of their present ages = > 5 x - 2 x = 3 x = > 7.5 years answer : a
Answer: a
Problem: what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?
Options: a ) 1 or 7
b ) 3 or 21
c ) 4 or 28
d ) 2 or 14
e ) 5 or 14
Rationale: since the chord length = 2 sqrrt ( r ^ 2 - d ^ 2 ) chord length = 32 , r = 20 then we get d = 12 chord length = 24 , r = 20 then we get d = 16 then we add / subtract we get option c ) 4 or 28 answer : c
Answer: c
Problem: one boss decided to increase the salary of an employee by 5 % . how much will he get if his salary was rs . 2000 ?
Options: a ) 2200 , b ) 2000 , c ) 2100 , d ) 2300 , e ) none
Rationale: solution : actual salary is 2000 rupees 5 % of 2000 = 2000 * 5 / 100 = 100 so 100 rupees increased = 2000 + 100 = 2100 he will get salary of 2100 answer c
Answer: c
Problem: a ratio between two numbers is 7 : 9 and their l . c . m . is 189 . the second number is
Options: a ) 35 , b ) 25 , c ) 20 , d ) 27 , e ) none
Rationale: "sol . let the required numbers be 7 x and 9 x . then , their l . c . m . is 63 x . ∴ 63 x = 189 ⇔ x = 3 . hence , the second number is 27 . answer d"
Answer: d
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 80 % , what was the average score for the entire class ?
Options: a ) 64 % , b ) 66 % , c ) 68 % , d ) 70 % , e ) 72 %
Rationale: 70 % of the class scored 60 % and 30 % of the class scored 80 % . the difference between 60 % and 80 % is 20 % . the average will be 60 % + 0.3 ( 20 % ) = 66 % . the answer is b .
Answer: b
Problem: if p ( 32 , 6 ) = kc ( 32 , 6 ) , then what is the value of k ?
Options: a ) 6 , b ) 32 , c ) 120 , d ) 720 , e ) 820
Rationale: solution since 32 p 6 = k 32 c 6 ⇒ 32 ! / ( 32 - 6 ) ! = k 32 ! / ( 32 - 6 ) ! ⇒ k = 6 ! = 720 . answer d
Answer: d
Problem: for how many values of q , is | | | q - 5 | - 10 | - 5 | = 2 ? ( those ls are mods )
Options: a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8
Rationale: i think its 8 | | | q - 5 | - 10 | - 5 | = 2 let | q - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; q has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d
Answer: d
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts three hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 6 , d ) d ) 5.5 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 3 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 3 + t ) = 40 * t t = 9 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 9 / 60 = 6 hrs time taken by a = 3 + t = 3 + 9 = 12 hrs time taken by k = 6 hrs so k starts 12 - 6 = 6 hrs after a . ( answer c )"
Answer: c
Problem: at joes steakhouse the hourly wage for a chef is 25 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 3.19 , e ) $ 5.40
Rationale: "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 25 % greater than dishwasher wages - - > 25 % of $ 4.25 = ( 25 * ( $ 4.25 ) ) / 100 - - > ( $ 106.25 ) / 100 - - > $ 1.06 therefore , chef wages per hour = $ 4.25 + $ 1.06 = = > $ 5.31 difference of wages between manager and chef = $ 8.50 - $ 5.31 = = > $ 3.19 answer : d"
Answer: d
Problem: a manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18 % . the wholesaler sells the same to retailer at a profit of 20 % . the retailer in turn sells them to a customer for rs . 30.09 , there by earning a profit of 25 % . the cost price for the manufacturer is ?
Options: a ) 33 , b ) 29 , c ) 17 , d ) 10 , e ) 16
Rationale: "explanation : let the cost price for the manufacturer be rs . x . then , 125 % of 120 % of 118 % of x = 30.09 . 125 / 100 * 120 / 100 * 118 / 100 * x = 3009 / 100 177 / 100 x = 3009 / 100 = > x = 17 answer : c"
Answer: c
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 11 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 477 , b ) 384 , c ) 279 , d ) 276 , e ) 291
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 11 + 21 = 32 t = 12 d = 32 * 12 = 384 . answer : b"
Answer: b
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is ?
Options: a ) 39 yr , b ) 42 yr , c ) 45 yr , d ) 32 yr , e ) 50 yr
Rationale: "let b ' s present age = x years then a ' s present age = x + 9 years x + 9 + 10 = 2 ( x - 10 ) x + 19 = 2 x - 20 x = 39 years answer is a"
Answer: a
Problem: if 89 / 99 = 0.898 , what is the 83 rd digit to the right of the decimal point of the fraction ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 7 , e ) 9
Rationale: "we are not concerned what 89 / 99 means . . we have to look at the decimal . . 0.898 means 0.898989 . . . . so right of decimal , all odd numbered are 8 and all even numbered are 9 . . here 83 is odd , so ans is 8 answer is c"
Answer: c
Problem: little krish had $ 200.50 . he spent $ 35.25 on sweets and gave to his two friends $ 25.20 each . how much money was left ?
Options: a ) $ 220.85 , b ) $ 214.85 , c ) $ 114.85 , d ) $ 314.85 , e ) $ 104.85
Rationale: krish spent and gave to his two friends a total of 35.25 + 25.20 + 25.20 = $ 85.65 money left 200.50 - 85.65 = $ 114.85 correct answer is c ) $ 114.85
Answer: c
Problem: pat , kate , and mark charged a total of 117 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 65
Rationale: "65 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 117 = > x = 13 26 : 13 : 78 78 - 13 = 65 answer e"
Answer: e
Problem: what is the probability of getting at least one six in a single throw of three unbiased dice ?
Options: a ) 1 / 6 , b ) 125 / 216 , c ) 1 / 36 , d ) 81 / 216 , e ) 91 / 216
Rationale: "find the number of cases in which none of the digits show a ' 6 ' . i . e . all three dice show a number other than ' 6 ' , 5 * 5 * 5 = 125 cases . total possible outcomes when three dice are thrown = 216 . the number of outcomes in which at least one die shows a ' 6 ' = total possible outcomes when three dice are thrown - number of outcomes in which none of them show ' 6 ' . = 216 - 125 = 91 . the required probability = 91 / 216 . answer : e"
Answer: e
Problem: in the coordinate plane a slope of the line k is 3 / 2 times the x - intercept of the line k . what is the y - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) 1 / 4 , e ) 2 / 3
Rationale: as 3 / 2 y = mx + c , from 3 / 2 y = 0 + m we get y = 2 / 3 . hence , the correct answer choice is e .
Answer: e
Problem: a wooden box of dimensions 8 m x 10 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 5 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 4000000 , e ) none of these
Rationale: explanation : number = ( 800 * 1000 * 600 ) / 4 * 5 * 6 = 4000000 answer : d
Answer: d
Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of both the cards being kings ?
Options: a ) 1 / 15 , b ) 25 / 57 , c ) 35 / 256 , d ) 1 / 221 , e ) 2 / 15
Rationale: "let s be the sample space . then , n ( s ) = 52 c 2 = ( 52 x 51 ) / ( 2 x 1 ) = 1326 . let e = event of getting 2 kings out of 4 . n ( e ) = 4 c 2 = ( 4 x 3 ) / ( 2 x 1 ) = 6 . p ( e ) = n ( e ) / n ( s ) = 6 / 1326 = 1 / 221 . option d"
Answer: d
Problem: a school has 4 section of chemistry in class x having 65 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.25 , b ) 52.25 , c ) 51.95 , d ) 53.25 , e ) none of the above
Rationale: required average marks = 65 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 65 + 35 + 45 + 42 = 3250 + 2100 + 2475 + 1890 / 187 = 9715 â  „ 187 = 51.95 answer c
Answer: c
Problem: the speed at which a girl can row a boat in still water is 75 kmph . if he rows downstream , where the speed of current is 15 kmph , what time will he take to cover 300 metres ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "speed of the boat downstream = 75 + 15 = 90 kmph = 90 * 5 / 18 = 25 m / s hence time taken to cover 400 m = 400 / 25 = 16 seconds . answer : a"
Answer: a
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 16 , b ) 3 / 11 , c ) 13 / 20 , d ) 3 / 10 , e ) 1 / 10
Rationale: "p ( x is prime ) = 1 / 4 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 4 * 1 / 4 = 1 / 16 the answer is a ."
Answer: a
Problem: what would be the perimeter of the square whose side is equal to the diameter of the circle whose perimeter is 52.5 cm ?
Options: a ) 52.5
b ) 60.2
c ) 66.8
d ) 74.25
e ) 80.12
Rationale: diameter of the circle = perimeter / ï € = 52.5 x 7 / 22 = 16.70 perimeter of the square = 16.70 x 4 = 66.8 cm answer : c
Answer: c
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: if 1430 is divisible by anyone of the answer choices . a . 1430 / 20 = 143 / 2 b 1430 / 21 = 1430 / 21 c 1430 / 22 = 65 if 1430 apple was divided among 65 people , each would have received 22 . after addition of 45 people the answer should be 13 . 1430 / 110 = 13 . c is the answer .
Answer: c
Problem: a merchant purchased a jacket for $ 42 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 6 , d ) $ 12 , e ) $ 15
Rationale: actual cost = $ 42 sp = actual cost + mark up = actual cost + 30 % sp = 42 * 100 / 70 on sale sp = 80 / 100 ( 42 * 100 / 70 ) = 48 gross profit = $ 6 answer is c
Answer: c
Problem: if two positive numbers are in the ratio 1 / 9 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: "given ratio = 1 / 9 : 1 / 5 = 5 : 9 let first number be 5 x and the second number be 9 x . the second number is more than first number by 4 x . required percentage = 4 x / 5 x * 100 = 80 % . answer : e"
Answer: e
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 25 million in sales of and then $ 9 million in royalties on the next $ 130 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 25 million in sales to the next $ 130 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 35 % , d ) 42 % , e ) 56 %
Rationale: "( 9 / 130 ) / ( 3 / 25 ) = 15 / 26 = 57.7 % it means that 9 / 130 represents only 57.7 % . therefore a decrease of 42 % . answer d"
Answer: d
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 5 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 30 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 30 days to doing 5 w widgets . answer : d"
Answer: d
Problem: two employees x and y are paid a total of rs . 616 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 300
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 616 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 616 ⇒ y [ 12 / 10 + 1 ] = 616 ⇒ 22 y / 10 = 616 ⇒ 22 y = 6160 ⇒ y = 6160 / 22 = 560 / 2 = rs . 280 b"
Answer: b
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 22 , d ) 15 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 8 w = 120 = > w = 15 answer d"
Answer: d
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 546 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 546 = > x = ( 546 * 100 ) / 65 = 840 answer d"
Answer: d
Problem: jacob is now 14 years younger than michael . if 9 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 9 , d ) 21 , e ) 25
Rationale: "jacob = x years , michael = x + 14 years 9 years from now , 2 ( x + 9 ) = x + 23 2 x + 18 = x + 23 x = 5 x + 4 = 9 years answer c"
Answer: c
Problem: a bag consists of 60 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 11 / 12 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: bag consists of 60 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 60 - 5 - 9 = 46 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 60 + 46 / 60 = 55 / 60 = 11 / 12 hence , answer will be a .
Answer: a
Problem: if 6 women can color 360 m long cloth in 3 days , then 5 women can color 100 m long cloth in ?
Options: a ) 2 days , b ) 3 days , c ) 2.5 days , d ) 4 days , e ) 1 day
Rationale: "the length of cloth painted by one woman in one day = 360 / 6 × 3 = 20 m no . of days required to paint 100 m cloth by 5 women = 100 / 5 × 20 = 1 day answer : e"
Answer: e
Problem: when a certain number x is divided by 95 , the remainder is 31 . what is the remainder when x is divided by 19 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 15 , e ) 17
Rationale: "let possible value of x is 126 least possible value of x / 19 is 126 / 19 = > 6 quotient with remainder 12 thus answer is ( c ) 12"
Answer: c
Problem: ram sold two bicycles , each for rs . 990 . if he made 10 % profit on the first and 10 % loss on the second , what is the total cost of both bicycles ?
Options: a ) 2000 , b ) 2888 , c ) 2667 , d ) 2999 , e ) 2122
Rationale: ( 10 * 10 ) / 100 = 1 % loss 100 - - - 99 ? - - - 1980 = > rs . 2000 answer : a
Answer: a
Problem: the simple form of the ratio 7 / 6 : 3 / 2 is ?
Options: a ) 5 : 8 , b ) 7 : 9 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 1
Rationale: "7 / 6 : 3 / 2 = 7 : 9 answer : b"
Answer: b
Problem: a company produces 72000 bottles of water everyday . if a case can hold 9 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 9 . number of cases required to hold 72000 bottles = 72000 / 9 = 8000 cases . so the answer is d = 8000"
Answer: d
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 135 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 20 , d ) 15 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 135 6 x + 15 = 135 6 x = 120 x = 20 answer : c"
Answer: c
Problem: on average , activated yeast cells divide once every 120 minutes ; that is , each individual cell divides into two individual cells over that time span . given that a certain yeast colony consisted of 310000 cells two hours ago , approximately how many cells will be populating the colony 12 hours from now ?
Options: a ) 77500 , b ) 1 , 860000 , c ) 2 , 480000 , d ) 3 , 720000 , e ) 39 , 680000
Rationale: 310000 × 2 × 2 × 2 × 2 x 2 × 2 × 2 = 310000 × 128 = e
Answer: e
Problem: the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 1 years ?
Options: a ) 5100 , b ) 5120 , c ) 7200 , d ) 5400 , e ) 5500
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 = 7200 answer : c"
Answer: c
Problem: the average ( arithmetic mean ) of 10 , 30 , and 50 is 8 more than the average of 20 , 40 , and x . what is x ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the average of 10 , 30 , and 50 is 30 . the average of 20 , 40 and x is 22 . then 20 + 40 + x = 66 . x = 6 . the answer is c ."
Answer: c
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 7 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 7 + 1 ) / ( 7 - 1 ) = 8 / 6 = 4 / 3 answer : a"
Answer: a
Problem: what is the square root of 625 , divided by 5 ?
Options: a ) 9 , b ) 36 , c ) 5 , d ) 6 , e ) 1
Rationale: square root is a number times itself square root of 625 = 25 , 25 / 5 = 5 ( c ) 5
Answer: c
Problem: find the simple interest on rs . 350 for 10 months at 5 paisa per month ?
Options: a ) 277 , b ) 175 , c ) 288 , d ) 266 , e ) 121
Rationale: "i = ( 350 * 10 * 5 ) / 100 = 175 answer : b"
Answer: b
Problem: a and b can do a piece of work in 60 days and 60 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 60 + 1 / 60 ] = 10 [ 1 + 1 / 60 ] = 1 / 3 a complete remaining work in 1 / 3 * 60 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 9
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 9 + 2 ^ 9 , which will give you 2 ^ 10 answer b"
Answer: b
Problem: what is the ratio of 4 / 7 to the product 2 * ( 7 / 3 ) ?
Options: a ) 6 : 49 , b ) 1 : 3 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "4 / 7 / 14 / 3 = 6 / 49 . . . imo option a ."
Answer: a
Problem: calculate the sum of first 39 natural numbers .
Options: a ) 780 , b ) 891 , c ) 812 , d ) 847 , e ) 890
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 39 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 39 ) = ( 39 × 40 / 2 ) = 780 . answer a"
Answer: a
Problem: operation # is defined as adding a randomly selected two digit multiple of 14 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 14 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Problem: if the sides of a triangle are 26 cm , 24 cm and 10 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 130 cm 2 , c ) 312 cm 2 , d ) 315 cm 2 , e ) none of these
Rationale: "the triangle with sides 26 cm , 24 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 10 = 120 cm 2 answer : a"
Answer: a
Problem: n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 4,5 and 6 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 1,2 , 3 , 4 , 5 , 6 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 1 and 6 in the hundreds places and reserve them for the tens places now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 265 and 314 ( difference is 49 ) or try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . we get 463 and 512 ( difference is 49 ) b"
Answer: b
Problem: of the 150 people at a party , 70 were women , and 40 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "total people at party = 150 women = 70 so men 150 - 70 = 80 no . of pple who tried appetizer = 150 - 50 ( given info ) = 100 no of women who tried appetizer = 40 so remaining ppl ( men ) who tried the appetizer = 100 - 40 = 60 correct option c"
Answer: c
Problem: the breath of a rectangular landscape is 6 times its length . there is a playground in it whose area is 4200 square mtr & which is 1 / 7 th of the total landscape . what is the breath of the landscape ?
Options: a ) 520 , b ) 420 , c ) 320 , d ) 550 , e ) 450
Rationale: "sol . 6 x * x = 7 * 4200 x = 70 length = 6 * 70 = 420 b"
Answer: b
Problem: it was calculated that 75 men could complete a piece of work in 25 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 28 days . , b ) 30 days . , c ) 37.5 days . , d ) 40 days . , e ) 36 days .
Rationale: "one day work = 1 / 25 one man ’ s one day work = 1 / ( 25 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 25 * 75 ) the total no . of days required to complete the work = ( 75 * 25 ) / 50 = 37.5 answer : c"
Answer: c
Problem: a farmer divides his herd of x cows among his 4 sons so that one son gets one half of the herd , the second gets one - fourth , the third gets one - fifth and the fourth gets 7 cows . then x is equal to
Options: a ) 100 , b ) 140 , c ) 180 , d ) 160 , e ) 120
Rationale: no . of cows : : x 1 st son : x / 2 2 nd son : x / 4 3 rd son : x / 5 4 th son : 7 ( x ) + ( x / 4 ) + ( x / 5 ) + 7 = x = > x - ( 19 x / 20 ) = 7 = > ( 20 x - 19 x ) / 20 = 7 = > x = 140 answer : b
Answer: b
Problem: solve for x and check : x + 5 = 3
Options: a ) 2 , b ) 3 , c ) 1 , d ) - 2 , e ) 4
Rationale: "solution : x + 5 - 5 = 3 - 5 x = - 2 check : x + 5 = 3 - 2 + 5 = 3 3 = 3 answer : d"
Answer: d
Problem: a trained covered x km at 40 kmph and another 4 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 11.33 kmph , b ) 12.33 kmph , c ) 13.33 kmph , d ) 14.33 kmph , e ) 23.33 kmph
Rationale: "total time taken = x / 40 + 4 x / 20 hours = 9 x / 40 hours average speed = 3 x / ( 9 x / 40 ) = 13.33 kmph answer : c"
Answer: c
Problem: a rectangular block 8 cm by 24 cm by 56 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 10 , c ) 15 , d ) 40 , e ) 21
Rationale: "volume of the block = 8 * 24 * 56 = 10752 cm ^ 3 side of the largest cube = h . c . f of 8 , 24,56 = 8 cm volume of the cube = 8 * 8 * 8 = 512 cm ^ 3 number of cubes = 10752 / 512 = 21 answer is e"
Answer: e
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 93 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 93 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 93 * 7 ) = 1350 - ( 609 + 651 ) = 1350 - 1260 = 90 answer b"
Answer: b
Problem: find the compound ratio of ( 2 : 3 ) , ( 5 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 5 : 3
Rationale: "required ratio = 2 / 3 * 5 / 11 * 11 / 2 = 2 / 1 = 5 : 3 answer is e"
Answer: e
Problem: what is the least common multiple of 15 , 18 , and 34 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 360 , e ) 1530
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 18 = 2 * 3 ^ 2 34 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 1530 option e"
Answer: e
Problem: a meeting has to be conducted with 4 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 ) 48 , b ) 55 , c ) 58 , d ) 62 , e ) 70
Rationale: "the total number of ways to choose 4 managers is 8 c 4 = 70 we need to subtract the number of groups which include the two managers , which is 6 c 2 = 15 . 70 - 15 = 55 the answer is b ."
Answer: b
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 9 is how many times as great as the frequency corresponding to a reading of 3 ?
Options: a ) 40 , b ) 50 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 and if richter scale reading goes from 7 to 8 it will be 10 and if richter scale reading goes from 8 to 9 it will be 10 so it will from 3 to 9 i . e 4,5 , 6,7 , 8,9 = 10 * 10 * 10 * 10 * 10 * 10 = 10 ^ 6 answer is e"
Answer: e
Problem: the contents of a certain box consist of 72 apples and 30 oranges . how many oranges must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 68 , b ) 78 , c ) 88 , d ) 138 , e ) 108
Rationale: "apple = ( apple + orange + x ) * 0.3 72 = ( 30 + 72 + x ) * 0.3 x = 138 answer : d"
Answer: d
Problem: a factory produces 6000 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 1500 toys , c ) 6113 toys , d ) 2354 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 4 days ) by 4 . 6000 / 4 = 1500 toys correct answer b"
Answer: b
Problem: two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 9 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 32 / 9 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 9 combined = 5 / 18 work done in 2 days = 5 / 9 work left = 4 / 9 rate * time = work left 1 / 8 * time = 4 / 9 time = 32 / 9 b"
Answer: b
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box , what is the probability that the sum of the 3 numbers on the balls selected from the box will be odd ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: the sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls ( odd + odd + odd = odd ) or two even numbered balls and one odd numbered ball ( even + even + odd = odd ) ; p ( ooo ) = ( 1 / 2 ) ^ 3 ; p ( eeo ) = 3 * ( 1 / 2 ) ^ 2 * 1 / 2 = 3 / 8 ( you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways : eeo , eoe , or oee ) ; so finally p = 1 / 8 + 3 / 8 = 1 / 2 . answer : c .
Answer: c
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 8 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 33 : 1 , b ) 33 : 7 , c ) 33 : 8 , d ) 33 : 5 , e ) 33 : 2
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 1 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 1 = 33 / 4 = 8.25 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 8.25 : 1.75 = 33 : 7 . answer : b"
Answer: b
Problem: the average age of a class of 39 students is 15 years . if the age of the teacher be included , then the average increases by 3 months . find the age of the teacher .
Options: a ) 20 , b ) 23 , c ) 25 , d ) 21 , e ) 22
Rationale: "total age of 39 persons = ( 39 x 15 ) years = 585 years . average age of 40 persons = 15 yrs 3 months = 61 / 4 years . total age of 40 persons = ( 61 / 4 ) x 40 ) years = 610 years . : . age of the teacher = ( 610 - 585 ) years = 25 years . answer is c ."
Answer: c
Problem: a man can row 5 kmph in still water . when the river is running at 2.3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 2.91 , b ) 3.48 , c ) 2.98 , d ) 3.78 , e ) 4.21
Rationale: "m = 5 s = 2.3 ds = 6.3 us = 2.7 x / 6.3 + x / 2.7 = 1 x = 1.89 d = 1.89 * 2 = 3.78 answer : d"
Answer: d