regisss/math_qa huggingface dataset:
Problem: four horses are tethered at four corners of a square plot of side 63 metres so that they just can not reach one another . the area left ungrazed is :
Options: a ) 675.5 m 2
b ) 780.6 m 2
c ) 785.8 m 2
d ) 850.5 m 2
e ) 950.5 m 2
Rationale: required area = ( 63 * 63 – 4 * 1 / 4 * 22 / 7 * 63 / 2 * 63 / 2 ) = 850.5 m 2 answer : d
Answer: d
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 7 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 5 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 28 x = 4 ( 3 x + 5 ) 16 x = 20 x = 1.25 quantity of alcohol = ( 4 x 1.25 ) litres = 5 litres . answer : c"
Answer: c
Problem: find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ?
Options: a ) 13 / 89 , b ) 15 / 87 , c ) 27 / 89 , d ) 27 / 87 , e ) 89 / 27
Rationale: "1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 c )"
Answer: c
Problem: 18 men can complete a piece of work in 20 days . in how many days can 15 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 20 , d ) 24 , e ) 11
Rationale: "18 * 20 = 15 * x = > x = 24 days answer : d"
Answer: d
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 9000 , brokerage being 1 / 4 % , is :
Options: a ) 113.2 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 9000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 9000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 125 . = market value of rs . 100 stock = rs . 125 - re . 0.25 . = market value of rs . 100 stock = rs . 124.75 . answer : e"
Answer: e
Problem: a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 3 , b ) 3 : 10 , c ) 2 : 3 , d ) 6 : 3 , e ) 10 : 3
Rationale: "explanation : dog : hare = ( 2 * 5 ) leaps of hare : 3 leaps of hare = 10 : 3 answer : e"
Answer: e
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 55 , how much more remains to be paid ?
Options: a ) $ 455 , b ) $ 495 , c ) $ 525 , d ) $ 550 , e ) $ 585
Rationale: "90 % remains to be paid so the remaining amount is 9 * 55 = $ 495 . the answer is b ."
Answer: b
Problem: if two times of the daughter ’ s age in years is included to the mother ’ s age , the total is 70 and if two times of the mother ’ s age is included to the daughter ’ s age , the total is 95 . so the mother ’ s age is ,
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 39
Rationale: b 40 let daughter ’ s age = a and mother ’ s age = b given : 2 a + b = 70 and , a + 2 b = 95 solving b , we will get b = 40 .
Answer: b
Problem: an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many r ways can the assembly line be arranged ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720
Rationale: c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want r = 6 c ! / 2 - > 720 / 2 = 360
Answer: c
Problem: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 140 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 8 : 7 , b ) 7 : 5 , c ) 1 : 3 , d ) 8 : 7 , e ) 9 : 10
Rationale: "explanation : 3 : 4 a = 3 / 7 * 140 = 60 360 : 400 39 : 40 answer : e"
Answer: e
Problem: the difference between the compound interest and simple interest on a certain sum at 10 % per annum for 2 years is $ 631 . find the sum ?
Options: a ) $ 52000 , b ) $ 61000 , c ) $ 71540 , d ) $ 63100 , e ) $ 56210
Rationale: let the sum be $ x c . i . = x ( 1 + 10 / 100 ) ^ 2 - x = 21 x / 100 s . i . = ( x * 10 * 2 ) / 100 = x / 5 c . i . - s . i . = ( 21 x / 100 ) - ( x / 5 ) = x / 100 x / 100 = 631 x = 63100 answer is d
Answer: d
Problem: what is the smallest number which when diminished by 16 , is divisible 4 , 6 , 8 and 10 ?
Options: a ) 136 , b ) 192 , c ) 198 , d ) 122 , e ) 142
Rationale: required number = ( lcm of 4 , 6,8 , and 10 ) + 16 = 120 + 16 = 136 option a
Answer: a
Problem: in a room with 10 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 5 , d ) 5 / 7 , e ) 16 / 21
Rationale: ( 6 / 10 ) ( 7 / 9 ) + ( 5 / 10 ) ( 6 / 9 ) if you choose one of the 6 with one other friend , then you have a 7 / 9 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 9 chance of not picking one of their friends second . add them up . 42 / 90 + 30 / 90 72 / 90 = 4 / 5 c . 4 / 5
Answer: c
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 79 . how tall is the fourth person ?
Options: a ) 85 , b ) 87 , c ) 89 , d ) 91 , e ) 93
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 79 ) = 316 x = 75 and the fourth person has a height of 75 + 10 = 85 inches the answer is a ."
Answer: a
Problem: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 17 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 5 : 34 pm . the correct answer is b .
Answer: b
Problem: if both 5 ^ 3 and 3 ^ 4 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ^ 2 ) , what is the smallest possible positive value of n ?
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) has two appearances of 3 ( in 12 ^ 2 ) and two appearances of 5 ( in 10 ^ 2 ) . thus n must include at least 3 ^ 2 * 5 = 45 the answer is b ."
Answer: b
Problem: the profit earned by selling an article for 812 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 945 , e ) none of these
Rationale: "let the profit or loss be x and 812 – x = 448 + x or , x = 364 ⁄ 2 = 182 \ cost price of the article = 812 – x = 448 + x = 630 \ sp of the article = 630 × 150 ⁄ 100 = 945 answer d"
Answer: d
Problem: if w is 40 percent less than e , e is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 e , e = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Problem: what is the angle between the minute hand and the hour hand when the time is 1540 hours ?
Options: a ) 150 , b ) 160 , c ) 140 , d ) 130 , e ) none
Rationale: solution : the total angle made by the minute hand during an hour is 360 o . if it takes 360 o for an hour , it will take ( 40 / 60 ) * 360 = 240 o . the angle between the hour hand the minute hand will therefore , be somewhere between 240 - 90 = 150 o , as the hour hand is between 3 and 4 . the angle made by the hour hand when it moves from say 3 to 4 will be 30 o . that is the hour hand makes 30 o during the course of an hour . the hour hand will therefore , move ( 40 / 60 ) * 30 = 20 o . therefore , the net angle between the hour hand and the minute hand will be 150 - 20 = 130 o . answer d
Answer: d
Problem: what is the sum of the multiples of 3 from 33 to 60 , inclusive ?
Options: a ) 465 , b ) 470 , c ) 452 , d ) 450 , e ) 460
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 60 / 3 ) - ( 33 / 3 ) + 1 multiply these together so what we show average * total numbers = sum ( 33 + 60 ) / 2 * ( 60 / 3 ) - ( 33 / 3 ) + 1 = sum 93 / 2 * 10 = 465 a"
Answer: a
Problem: 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 15 , 25 and 30 , what is the minimum possible range in scores of the 3 test - takers ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 15 , e ) 10
Rationale: i simply looked at the 3 different possible scores for each individual test : 15 , 30,25 we have to find the minimum range : 30 - 15 = 15 30 - 25 = 5 25 - 15 = 10 the find the minimum range , you have to make the set of the 5 scores as small as possible . which means that 4 of the 5 scores of each individual person is zero . 5 * 5 = 25 . answer : a
Answer: a
Problem: a goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 250 m , c ) 643 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 270 / 26 = 20 x + 270 = 520 x = 250 . answer : b"
Answer: b
Problem: rebecca ' s annual income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?
Options: a ) 7000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: total rebecca = x + 15000 ; total = x + 15000 + 18000 x + 15000 / x + 33000 = 50 / 100 therefore x = 3000 e
Answer: e
Problem: a cubic object 3 ' ' x 3 ' ' x 3 ' ' is painted blue on all the outside surfaces , including the top and bottom . if the cube is cut into 27 cubes of 1 ' ' x 1 ' ' x 1 ' ' , how many 1 ' ' cubes do have any painted surfaces ?
Options: a ) 15
b ) 22
c ) 26
d ) 33
e ) 44
Rationale: c 26 only the box in the very centre of the stack will not suffer the strokes of the paint brush , whereas all the other 26 boxes will have at least one side painted .
Answer: c
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of charlie 10 years from now ?
Options: a ) 17 , b ) 25 , c ) 45 , d ) 47 , e ) 50
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of charlie = 7 * 5 = 35 charlie ' s age 10 years hence = 35 + 10 = 45 answer = c"
Answer: c
Problem: how many of the positive factors of 17 are not factors of 34 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 17 - 1 , 17 factors of 34 - 1 , 2 , 17 , 34 , comparing both , we have three factors of 17 which are not factors of 34 - no factors the answer is a"
Answer: a
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 3
b ) 9 / 5
c ) 9 / 25
d ) 3 / 5
e ) 25 / 9
Rationale: the area of rectangle a is ab . c = 5 a / 3 and d = 5 b / 3 . the area of rectangle b is cd = 25 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 9 ) = 9 / 25 . the answer is c .
Answer: c
Problem: j is faster than p . j and p each walk 24 km . sum of the speeds of j and p is 7 kmph . sum of time taken by them is 14 hours . then j speed is equal to
Options: a ) 22 , b ) 14 , c ) 6 , d ) 8 , e ) 16
Rationale: given j > p j + p = 7 , only options are ( 6 , 1 ) , ( 5 , 2 ) , ( 4 , 3 ) from the given options , if j = 4 the p = 3 . times taken by them = 244 + 243 = 14 answer : b
Answer: b
Problem: 2 ^ 8 × 39 + 31 = ?
Options: a ) 34545 , b ) 65657 , c ) 65567 , d ) 45677 , e ) 56782
Rationale: "256 * 39 + 31 65567 c"
Answer: c
Problem: a river 5 m deep and 35 m wide is flowing at the rate of 2 kmph , calculate the amount of water that runs into the sea per minute ?
Options: a ) 5832.75 , b ) 5839.75 , c ) 5837.75 , d ) 5222.75 , e ) 5835.75
Rationale: "rate of water flow - 2 kmph - - 2000 / 60 - - 33.33 m / min depth of river - - 5 m width of river - - 35 m vol of water per min - - 33.33 * 5 * 35 - - - 5832.75 answer a"
Answer: a
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 15 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 11.7 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is a . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,15 x id est x = 11,7 %"
Answer: a
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 23 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 195 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 23 = 345 m . let the length of the platform be x m . then , ( x + 345 ) / 36 = 15 = > x = 195 m . answer : b"
Answer: b
Problem: the area of a square field is 4802 m ( power ) 2 the length of its diagonal is :
Options: a ) 98 m
b ) 102 m
c ) 95 m
d ) 105 m
e ) 96 m
Rationale: let the diagonal be d metres , then 1 / 2 d ( power ) 2 = 4802 d 2 = 9604 d = √ 9604 d = 98 m answer is a .
Answer: a
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.567 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 0 , e ) can not be determined
Rationale: k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . d
Answer: d
Problem: in the faculty of reverse - engineering , 100 second year students study numeric methods , 100 second year students study automatic control of airborne vehicles and 25 second year students study them both . how many students are there in the faculty if the second year students are approximately 50 % of the total ?
Options: a ) 340 , b ) 335 , c ) 370 , d ) 360 , e ) 350
Rationale: "total number of students studying both are 100 + 100 - 25 = 175 ( subtracting the 25 since they were included in the both the other numbers already ) . so 50 % of total is 175 , so 100 % is 350 answer is e"
Answer: e
Problem: the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?
Options: a ) 7 / 30 , b ) 11 / 40 , c ) 17 / 50 , d ) 19 / 60 , e ) 33 / 80
Rationale: let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 3 / 4 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 19 / 60 . hence , the required probability is 19 / 60 . the answer is d .
Answer: d
Problem: a man sitting in a train which is travelling at 60 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 60 ) kmph = 52 kmph . answer a"
Answer: a
Problem: a straight line in the xy - plane has slope 2 . on this line the x - coordinate of the point is 300 and y - coordinate is 900 then what is the y intercept of the plane ?
Options: a ) 200 , b ) 250 , c ) 100 , d ) 300 , e ) 220
Rationale: "eq of line = y = mx + c m = 2 x = 300 y = 300 * 2 + c , substitute y by 900 as given in question . 900 = 600 + c , c = 200 correct option is a"
Answer: a
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,200 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2100 , c ) 3600 , d ) 3200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 11200 = > 7 x = 11200 = > x = 1600 total number of motorcycles = 2 x = 2 * 1600 = 3200 answer d"
Answer: d
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifth of its present ?
Options: a ) 62.5 , b ) 65 , c ) 61 , d ) 64 , e ) 60
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 25 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 25 x ) / ( 2 x / 5 ) = ( 25 x ) x 5 / 2 x = 125 / 2 = 62.5 answer is a ."
Answer: a
Problem: the walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the walker continues to walk at her constant rate , how many minutes must the cyclist wait until the walker catches up ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 4 / 3 miles to meet the waiting cyclist . the hiker will need 1 / 3 hours or 20 mins to cover the remaining 4 / 3 miles . so the answer is c .
Answer: c
Problem: a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 94 miles per hour , what is the value of y ?
Options: a ) 98 , b ) 84 , c ) 90 , d ) 120 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 94 solving for d and y , 15 y = 11 y + 480 5 y = 480 y = 98 answer a"
Answer: a
Problem: what is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 1000 = 2 ^ 3 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000 . we then need to eliminate the 100 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 995 . there are a total of 500 - 100 = 400 such numbers between 1 and 1000 . the answer is d ."
Answer: d
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 13000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 180000 , c ) rs . 436800 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 13000 * 112 / 100 = rs . 14560 b ' s monthly income = 2 parts - - - - > rs . 14560 a ' s monthly income = 5 parts = 5 / 2 * 14560 = rs . 36400 a ' s annual income = rs . 36400 * 12 = rs . 436800 answer : c"
Answer: c
Problem: 3 * 13 + 3 * 14 + 3 * 17 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 143 , e ) 151
Rationale: "3 * 13 + 3 * 14 + 3 * 17 + 11 = 39 + 42 + 51 + 11 = 143 the answer is d ."
Answer: d
Problem: in mrs . susna ' s class , 1 / 4 of her students are getting an a , 1 / 2 are getting a b , 1 / 8 are getting a c , 1 / 12 are getting a d , and 1 / 24 are getting a f . what fraction of mrs . susna ' s class getting a passing grade of c or higher .
Options: a ) 5 / 6 , b ) 3 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 1 / 2
Rationale: if mrs . susna ' s class has 24 students , the number of students receiving as , bs , or cs , are 6 , 12 , and 3 respectively . that means 21 / 24 of her students are receiving passing grades or 7 / 8 . ( answer : c )
Answer: c
Problem: the area of the house of a hall is 20 m 2 that of a longer wall 10 m 2 and of the shorter wall 8 m 2 , find the edge of the new cube ?
Options: a ) 45 m 3
b ) 40 m 3
c ) 60 m 3
d ) 600 m 3
e ) 300 m 3
Rationale: lb = 20 ; lh = 10 ; fh = 8 ( lbh ) 2 = 20 * 10 * 8 = > lbh = 40 m 3 answer : b
Answer: b
Problem: there is a 45 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 45 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 45 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , and 43 . the total is 10 . the answer is e ."
Answer: e
Problem: the present population of a town is 4032 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2800 , c ) 3500 , d ) 3600 , e ) 2050
Rationale: "p = 4032 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4032 / ( 1 + 20 / 100 ) ^ 2 = 4032 / ( 6 / 5 ) ^ 2 = 2800 ( approximately ) answer is b"
Answer: b
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 2 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 240 , c ) 289 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 2 = 240 answer : b"
Answer: b
Problem: the present population of a town is 10000 . population increase rate is 10 % p . a . find the population of town after 2 years ?
Options: a ) 10000 , b ) 11100 , c ) 15000 , d ) 12100 , e ) 14520
Rationale: "p = 10000 r = 10 % required population of town = p ( 1 + r / 100 ) ^ t = 10000 ( 1 + 10 / 100 ) ^ 2 = 10000 ( 11 / 10 ) ^ 2 = 12100 answer is d"
Answer: d
Problem: john has taken 4 ( 4 ) tests that have an average of 82 . in order to bring his course grade up to a ‘ b ’ , he will need to have a final average of 86 . what will he need to average on his final two tests to achieve this grade ?
Options: a ) 87 , b ) 90 , c ) 92 , d ) 94 , e ) 97
Rationale: traditional method : total scored till now 82 * 4 = 328 total score to avg 86 in 6 tests = 86 * 6 = 516 total to be scored on 2 tests = 516 - 328 = 188 avg on 2 tests = 188 / 2 = 94 answer : d
Answer: d
Problem: find the surface area of a 8 cm x 4 cm x 2 cm brick .
Options: a ) 136 cu cm , b ) 112 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) none
Rationale: "sol . surface area = [ 2 ( 8 x 4 + 4 x 2 + 8 x 2 ) ] = ( 2 x 56 ) = 112 cu cm answer b"
Answer: b
Problem: a car started running at a speed of 38 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 47 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: a 47 km the total distance covered by the car in the first 10 hours = 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 + 56 = sum of 10 terms in ap whose first term is 30 and last term is 56 = 10 / 2 [ 38 + 56 ] = 470 km .
Answer: a
Problem: 3 containers a , b and c are having mixtures of milk and water in the ratio of 1 : 5 and 3 : 5 and 5 : 7 respectively . if the capacities of the containers are in the ratio of all the 3 containers are in the ratio 5 : 4 : 5 , find the ratio of milk to water , if the mixtures of all the 3 containers are mixed together .
Options: a ) 53 : 115 , b ) 55 : 115 , c ) 115 : 55 , d ) 5 : 115 , e ) 115 : 53
Rationale: assume that there are 500400 and 500 liters respectively in the 3 containers . then , we have , 83.33 , 150 and 208.33 liters of milk in each of the three containers . thus , the total milk is 441.66 liters . hence , the amount of water in the mixture is 1400 - 441.66 = 958.33 liters . hence , the ratio of milk to water is 441.66 : 958.33 = > 53 : 115 ( using division by . 3333 ) the calculation thought process should be ( 441 * 2 + 2 ) : ( 958 * 3 + 1 ) = 1325 : 2875 dividing by 25 = > 53 : 115 . answer a 53 : 115
Answer: a
Problem: the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 15 % , b ) 20 % , c ) 28 % , d ) 35 % , e ) 40 %
Rationale: "sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28 % c"
Answer: c
Problem: if 5 x = 7 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?
Options: a ) 25 / 6 , b ) 42 / 25 , c ) 6 / 5 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 7 y = > x / y = 7 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 7 / 5 ) * ( 6 / 5 ) = 42 / 25 ans : b"
Answer: b
Problem: if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 67 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.66 , e ) none of the above
Rationale: "50 * 10 = 500 67 * 5 = 335 835 / 15 = 55.66 answer : d"
Answer: d
Problem: the sum of first 45 natural numbers is :
Options: a ) 1035 , b ) 1040 , c ) 1042 , d ) 1045 , e ) 1050
Rationale: "let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . shorcut method : sn = n ( n + 1 ) = 45 ( 45 + 1 ) = 1035 . 2 2 a"
Answer: a
Problem: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 226 m , what is its area ?
Options: a ) 2510 , b ) 2535 , c ) 3060 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 226 m ⇒ breadth = 45 m length = 45 + 23 = 68 m area = 68 × 45 = 3060 m 2 answer is c ."
Answer: c
Problem: there is a 30 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 42 % , b ) 48 % , c ) 54 % , d ) 60 % , e ) 66 %
Rationale: p ( china and not malaysia ) = 0.3 * 0.4 = 0.12 p ( malaysia and not china ) = 0.6 * 0.7 = 0.42 total probability = 0.12 + 0.42 = 0.54 = 54 % the answer is c .
Answer: c
Problem: mike earns $ 14 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "let it be x % less , then = 14 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 14 x = 350 / 14 x = 25 % answer : a"
Answer: a
Problem: the total price of a basic computer and printer are $ 2500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 6 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 6 of that new total price : p = 1 / 6 * $ 3,000 = $ 500 . plug this value in the first equation : c + 500 = $ 2,500 - - > c = $ 2000 answer : e .
Answer: e
Problem: find the average of first 4 multiples of 9 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 9 + 18 + 27 + 36 ) / 4 = 22.5 answer is c"
Answer: c
Problem: company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . the two companies merge , every employee stays with the resulting company , and no new employees are added . if the resulting company í s workforce consists of 25 percent managers , what percent of the workforce originated from company a ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 75 %
Rationale: let say company a has x employes and b has y employees . now they merge and total no of employees = x + y employees . per the question company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . we translate it into equation as follows : . 1 x + . 3 y = . 25 ( x + y ) = > x + 3 y = 2.5 ( x + y ) = > . 5 y = 1.5 x = > y = 3 x . now we know total employee = x + y . we need to find % age of x in total ( x + y ) ie x / ( x + y ) x 100 % = > x / ( 3 x + x ) [ substitute y = 3 x ] = > x / 4 x x 100 % = > . 25 x 100 % = > 25 % . answer : c
Answer: c
Problem: how many positive integers less than 100 are neither multiples of 5 or 6 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 32 , d ) d ) 33 , e ) e ) 67
Rationale: "to answer this q we require to know 1 ) multiples of 5 till 100 = 100 / 5 = 20 2 ) multiples of 6 till 100 = 100 / 6 = 16.66 = 16 add the two 20 + 16 = 36 ; subtract common terms that are multiple of both 5 and 6 . . lcm of 5 and 6 = 30 multiples of 30 till 100 = 100 / 30 = 3.3 = 3 so total multiples of 2 and 3 = 36 - 3 = 33 ans = 100 - 33 = 67 e"
Answer: e
Problem: a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 12 : 00 p . m . ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 20
Rationale: "sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour . hence , they cross each other 20 times before 12 : 00 p . m . answer e"
Answer: e
Problem: if n is a positive integer and n ^ 3 is a multiple of 550 , what is the least possible value of n ?
Options: a ) 8 , b ) 27 , c ) 81 , d ) 110 , e ) 125
Rationale: "cube of a number entails having 3 copies of the original prime factors . since 550 is a factor of n ^ 3 the least possible value of n is 5 ( 11 ) 2 = 110 the answer is d ."
Answer: d
Problem: two goods trains each 375 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 51 , e ) 36
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 375 + 375 = 750 m . required time = 750 * 6 / 125 = 36 sec . answer : option e"
Answer: e
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 300 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 307.50 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 15,000 . now , put the value of x = 3000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 3000 + 5 % of 3000 = 3150 . 2 nd year , amount = 3150 + 5 % of 3150 = 3307.50 . we can see after 2 years interest = 3307.50 - 3000 = 307.50 . hence , it satisfies the question . hence e is the correct answer"
Answer: e
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 25 % . staff are allowed a further 20 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.6 d , b ) 0.7 d , c ) 0.5 d , d ) 0.8 d , e ) 0.9 d
Rationale: "effective discount = a + b + ab / 100 = - 25 - 20 + ( - 25 ) ( - 20 ) / 100 = - 40 sale price = d * ( 1 - 40 / 100 ) sale price = . 6 * d answer ( a )"
Answer: a
Problem: what is the normal price of an article sold at $ 108 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 130 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 170
Rationale: "0.8 * 0.9 * cost price = $ 108 cost price = $ 150 the answer is c ."
Answer: c
Problem: kim has 8 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 16 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 15
Rationale: "total pairs = 16 c 2 = 120 ; same color pairs = 8 c 1 * 1 c 1 = 8 ; prob = 1 / 15 ans e"
Answer: e
Problem: how many factors does 16 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 4 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 2 * 2 = 4 answer c ."
Answer: c
Problem: there are 14 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 91 , b ) 98 , c ) 105 , d ) 112 , e ) 119
Rationale: "14 c 2 = 91 the answer is a ."
Answer: a
Problem: a technology company made a $ 5 million profit on its first $ 15 million in sales and a $ 12 million profit on its next $ 30 million in sales . by what percent did the ratio of profit to sales increase from the first $ 15 million in sales to the next $ 30 million in sales ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: solution : this is a percent increase problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first 15 million in sales , and the second ratio will be for the next 30 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 15 million profit / sales = 5 / 15 = 1 / 3 next 30 million profit / sales = 12 / 30 = 2 / 5 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 15 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 15 million royalties / sales = ( 1 / 3 ) x 15 = 5 next 30 million royalties / sales = ( 2 / 5 ) x 15 = 6 we can plug 5 and 6 into our percent change formula : ( new – old ) / old x 100 [ ( 6 – 5 ) / 5 ] x 100 1 / 5 x 100 , so a 20 % increase . answer b .
Answer: b
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 63 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 63 2 x = 12 = > x = 6 answer : b"
Answer: b
Problem: a bag holds 4 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 4 / 14 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 4 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 4 red and 3 green marbles after one red has been picked , we need to pick 1 red from a total of 3 red and 3 green marbles . p ( both red ) = ( 4 / 7 ) * ( 3 / 6 ) = 4 / 14 option a"
Answer: a
Problem: a train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 seconds . its length in meters is :
Options: a ) 60 m , b ) 70 m , c ) 100 m , d ) 120 m , e ) 150 m
Rationale: "let the length of the train be x metres and its speed be y metres / sec . then x / y = 15 y = x / 15 x + 100 / 25 now , ( x + 100 ) / 25 = x / 15 x = 150 m answer : e"
Answer: e
Problem: a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 500 , b ) $ 650 , c ) $ 420 , d ) $ 375 , e ) $ 625
Rationale: "avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 400 + 500 ) / 5 = 420 answer is c"
Answer: c
Problem: if 12401 is divided by any no . then quotient is 76 and remainder is 13 . what is divisor ?
Options: a ) 154 , b ) 124 , c ) 153 , d ) 163 , e ) 183
Rationale: divisor = ( dividend - remainder ) / quotient = ( 12401 - 13 ) / 76 = 12388 / 76 = 163 divisor = 163 answer d
Answer: d
Problem: in a games hour 4 different types of players came to the ground ? cricket 12 , hokey 17 , football 11 , softball 10 . how many players are present in the ground ?
Options: a ) 70 , b ) 50 , c ) 62 , d ) 49 , e ) 50
Rationale: "total number of players = 12 + 17 + 11 + 10 = 50 answer is b"
Answer: b
Problem: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 55 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 2200 , e ) none of these
Rationale: explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 55 = rs . 150 cp on 40 metres = 150 x 40 = rs . 6000 profit earned on 40 metres cloth = rs . 8200 – rs . 6000 = rs . 2200 . answer : option d
Answer: d
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 20 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 20 + 11 - - > { bike } = 55 - - > # those who have bike only is { bike } - { both } = 55 - 20 = 35 . answer : b ."
Answer: b
Problem: what is the units digit of 32 ! + 50 ! + 2 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 2 + 4 = 6 the units digit is 6 . the answer is d ."
Answer: d
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 60,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 480,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 60,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 60000 * 2 ^ 3 = 480000 hence , the answer is d ."
Answer: d
Problem: if a and b are multiples of 3 then which are all the multiples of 3 1 ) a / b 2 ) a ^ b 3 ) a + b 4 ) a - b 5 ) a * b
Options: a ) 13 , b ) 12 , 45 , c ) 1 , 25 , d ) all of these , e ) 12 , 35
Rationale: a * b a ^ b a + b a - b are multiples of 3 except a / b answer : e
Answer: e
Problem: 75 persons major in physics , 83 major in chemistry , 10 not at major in these subjects u want to find number of students majoring in both subjects
Options: a ) 65 , b ) 66 , c ) 67 , d ) 68 , e ) 69
Rationale: consider the number of total students = n ( t ) = 100 number of persons major in physics = n ( p ) = 75 number of persons major in chemistry = n ( c ) = 83 according to the question ; 10 not at major in these subjects = n ( p ' ∩ c ' ) = 10 n ( p ' ∩ c ' ) = n ( p u c ) ' = 10 n ( p u c ) ' = n ( t ) - n ( p u c ) 10 = 100 - n ( p u c ) n ( p u c ) = 90 n ( p u c ) = n ( p ) + n ( c ) - n ( p ∩ c ) 90 = 75 + 83 - n ( p ∩ c ) n ( p ∩ c ) = 158 - 90 n ( p ∩ c ) = 68 number of students majoring in both subjects will be 68 answer : d
Answer: d
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 320 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 47 , c ) 54 , d ) 56 , e ) 240
Rationale: "area = length x breadth 320 = 40 x breadth so , breadth = 8 units fencing required is - breadth + breadth + length 8 + 8 + 40 = > 56 feet answer must be ( d ) 56"
Answer: d
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 4 and the units digit of ( a + 1 ) ^ 2 is 9 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "if the units digit of a ^ 2 is 4 , then the units digit of a is either 2 or 8 . if the units digit of ( a + 1 ) ^ 2 is 9 , then the units digit of a + 1 is either 3 or 7 . to satisfy both conditions , the units digit of a must be 2 . then a + 2 has the units digit of 4 , thus the units digit of ( a + 2 ) ^ 2 will be 6 . the answer is d ."
Answer: d
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 54,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.22598 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 354000 x \ therefore required percentage = \ inline \ frac { 800 x } { 354000 } \ times 100 = 0.22598 a"
Answer: a
Problem: if 15 students in a class average 70 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 78 % , b ) 79 % , c ) 80 % , d ) 81 % , e ) 82 %
Rationale: ( 15 * 70 + 10 * 90 ) / 25 = 78 % the answer is a .
Answer: a
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 87 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 87 thus m = 696 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 696 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 12 answer : e"
Answer: e
Problem: ajith and rana walk around a circular course 115 km in circumference , starting together from the same point . if they walk at speed of 4 and 5 kmph respectively , in the same direction , when will they meet ?
Options: a ) after 20 hours , b ) after 115 hours , c ) after 115 minutes , d ) after 20 minutes , e ) after 30 minutes
Rationale: rana is the faster person . he gains 1 km in 1 hour . so rana will gain one complete round over ajith in 115 hours . i . e . they will meet after 115 hours . answer : b
Answer: b
Problem: two pipes a and b fill at a certain rate . b is filled at 1020 , 4080 ( 10 in 1 hour , 20 in 2 hours , 40 in 3 hrs and so on ) . if 1 / 16 of b is filled in 17 hrs , what time it will take to get completely filled ?
Options: a ) 20 hrs , b ) 21 hrs , c ) 22 hrs , d ) 23 hrs , e ) 24 hrs
Rationale: 1 / 16 in 17 hrs so 1 / 8 in 18 hrs 1 / 4 in 19 hrs 1 / 2 in 20 hrs and complete tank in 21 hrs answer : b
Answer: b
Problem: two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is :
Options: a ) 3 : 5 , b ) 4 : 5 , c ) 5 : 5 , d ) 4 : 3 , e ) 2 : 1
Rationale: "third no is x first no - 120 % of x = 6 x / 5 second no = 150 x / 100 = 3 x / 2 ration of first nos = 6 x / 5 : 3 x / 2 = 12 x : 15 x = 4 : 5 answer b"
Answer: b
Problem: a car is purchased on hire - purchase . the cash price is $ 26 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 603 , b ) $ 624 , c ) $ 625 , d ) $ 626 , e ) $ 627
Rationale: "explanation : cash price = $ 26 000 deposit = 10 % ã — $ 26 000 = $ 2600 loan amount = $ 26000 â ˆ ’ $ 2600 number of payments = 60 = $ 23400 i = p * r * t / 100 i = 14040 total amount = 23400 + 14040 = $ 37440 regular payment = total amount / number of payments = 624 answer : b"
Answer: b
Problem: a certain industrial loom weaves 0.129 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.129 : 15 : : 1 : x = > 0.129 * x = 15 = > x = 15 / 0.129 = > x = 116 answer : c"
Answer: c