Cheukting/mathqa huggingface dataset:
Question (general): consider below info to be a table : amount of bacteria time - amount 1 pm - 10 gms 4 pm - x gms 7 pm - 12.1 gms data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same factor during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 pm ?
Options: a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 12.3 , e ) 11.0
Rationale: let say the factor is x , the at 7 pm quantity = 10 ( i . e . quantity @ 1 pm ) * x ^ 2 = 12.1 = > x ^ 2 = 1.21 or x = 1.1 = > @ 4 pm quantity = 10 x = 10 * 1.1 = 11 . answer e
Answer: e
Question (physics): every day daniel drives 120 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 60 %
Rationale: let ' s test x = 4 . . . . on sunday , daniel drove 120 miles at 4 miles / hour . d = ( r ) ( t ) 120 = ( 4 ) ( t ) 120 / 4 = 30 = t it takes 30 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 88 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 88 = ( 2 ) ( t ) 88 / 2 = 44 = t it takes 44 hours for the second part total time to drive home on monday = 4 + 44 = 48 hours we ' re asked by what percent 48 hours is greater than 30 hours . 48 / 30 = 1.6 , so it is 60 % greater . answer : e
Answer: e
Question (general): how many multiples of 4 are there between 1 and 100 , inclusive ?
Options: a ) 25 , b ) 22 , c ) 23 , d ) 30 , e ) 36
Rationale: "25 multiples of 4 between 1 and 100 inclusive . from 4 * 1 upto 4 * 25 , ( 1,2 , 3,4 , . . . , 25 ) . hence , 25 multiples ! correct option is a"
Answer: a
Question (general): caleb spends $ 66.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 33 , c ) 20 , d ) 40 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 66.50 . by solving the equations y = 33 . ans b ."
Answer: b
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took hours to fill the tank . the leak can drain all the water of the tank in :
Options: a ) 33 , b ) 37 , c ) 76 , d ) 14 , e ) 29
Rationale: explanation : work done by the leak in 1 hour = { \ color { black } \ left ( \ frac { 1 } { 2 } - \ frac { 3 } { 7 } \ right ) = \ frac { 1 } { 14 } } { \ color { black } \ therefore } leak will empty the tank in 14 hrs answer : d ) 14 hours
Answer: d
Question (geometry): rectangular tile each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 900 cm by 600 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "area of tile = 90 * 30 = 2700 area of floor = 900 * 300 = 270000 no of tiles = 270000 / 2700 = 100 so , the no of tile = 100 answer : e"
Answer: e
Question (general): a merchant has selected two items to be placed on sale , one of which currently sells for 45 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 100 % , b ) 90 % , c ) 80 % , d ) 70 % , e ) 60 %
Rationale: "expensive item = $ 100 ; cheap item = $ 55 ; we must increase $ 55 to $ 100 , so by $ 45 , which is approximately 80 % increase : ( 100 - 55 ) / 55 = 3 / 7 = ~ 0.81 . answer : c ."
Answer: c
Question (gain): running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 15 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 6300 , c ) 8400 , d ) 50400 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 15 machine produce 560 * 6 * ( 15 / 8 ) in 6 minutes 560 * 6 * 15 / 8 = 6300 answer is b ."
Answer: b
Question (probability): in how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73
Rationale: "number of ways = 2 * 3 ! * 3 ! = 72 answer is d"
Answer: d
Question (general): if 7 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 42 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 7 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 7 = > ( 3 / 20 ) c = 7 = > c = ( 7 * 20 ) / 3 = 46.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 7 = 34.99 + 7 = 41.99 = 42 answer d"
Answer: d
Question (physics): working at constant rate , pump x pumped out half of the water in a flooded basement in 6 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 28 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 28 hours d"
Answer: d
Question (physics): speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 170 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 68 hours , c ) 36 hours , d ) 58 hours , e ) none
Rationale: "sol . speed upstream = 3 kmph ; speed downstream = 15 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 68 hours . answer b"
Answer: b
Question (gain): if the cost price of 17 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 6.25 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 17 articles = rs . 17 . selling price of 16 articles = rs . 17 therefore , selling price of 17 articles is : - = > 17 / 16 ã — 17 = > 18.06 therefore , profit = selling price - cost price . = > 18.06 â ˆ ’ 17 = 1.06 hence , the percentage of profit = profit x 100 / c . p . = > 1.06 / 17 ã — 100 . = > 6.25 % profit . answer : b"
Answer: b
Question (gain): according to a recent student poll , 4 / 5 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 62 / 95 , b ) 52 / 95 , c ) 92 / 95 , d ) 42 / 95 , e ) 32 / 95
Rationale: "16 students are interested , 4 are not interested prob = 1 - 4 c 2 / 20 c 2 = 1 - ( 4 * 3 / ( 20 * 19 ) ) = 1 - 3 / 95 = 92 / 95 answer : c"
Answer: c
Question (general): let p be a prime number . if n = 8 p , how many distinct even divisors does n have ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: "the correct answer is d . there are two : 2 and 2 p . 8 p = 2 * 2 * 2 p = ( 2 * 2 ) * 2 p . since we care only about distinct divisors , we ignore the fact that 2 appears three times ."
Answer: d
Question (gain): a candidate who gets 30 % of the marks fails by 30 marks . but another candidate who gets 45 % marks gets 15 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 371 marks , e ) 120 marks
Rationale: "30 % - - - - - - - - - - - - 30 45 % - - - - - - - - - - - - 15 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 45 30 % - - - - - - - - - - - - - - ? 90 + 30 = 120 marks answer : e"
Answer: e
Question (general): in a forest 190 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,900 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 190 tagged deers comprise 10 % of total # of deers - - > total # of deers = 190 * 10 = 1,900 . answer : d ."
Answer: d
Question (general): a person ' s present age is two - fifth of the age of his mother . after 6 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) a ) 25 , b ) b ) 40 , c ) c ) 32 , d ) d ) 45 , e ) e ) 30
Rationale: "let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 6 = 1 / 2 ( x + 6 ) 2 ( 2 x + 30 ) = 5 ( x + 6 ) x = 30 answer is e"
Answer: e
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 20 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 ) 22 , b ) 88 , c ) 48 , d ) 99 , e ) 72
Rationale: "relative speed = 20 + 30 = 50 km / hr . 50 * 5 / 18 = 125 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 125 = 72 sec answer : e"
Answer: e
Question (geometry): find the circumference and area of radius 11 cm .
Options: a ) 124 cm ² , b ) 144 cm ² , c ) 380 cm ² , d ) 284 cm ² , e ) 394 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 11 × 11 cm ² = 154 cm ² answer : c"
Answer: c
Question (general): the average of marks obtained by 120 boys was 37 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 37 24 x = 4440 - 1800 = > x = 2640 / 24 x = 110 . hence , the number of boys passed = 110 . answer : b
Answer: b
Question (general): a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 105 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 220 , b ) 250 , c ) 280 , d ) 300 , e ) 340
Rationale: "let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 105 x = 300 therefore there are a total of 300 ounces in the drink . the answer is d ."
Answer: d
Question (general): find the least number which when divided by 5 , 6,7 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Options: a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584
Rationale: "explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a"
Answer: a
Question (physics): it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she does yoga for 25 minutes , how much time will she spend in the gym ?
Options: a ) 35 min , b ) 5 min , c ) 15 min , d ) 25 min , e ) 20 min
Rationale: "the ratio is 2 : 3 = yoga : exer , so ( 25 ) ( 3 / 2 ) = 37.5 minutes for exercise , and 2 : 3 = gym : ride , and ( 2 / 3 ) ( 37.5 ) = 25 minutes in the gym . answer : d"
Answer: d
Question (gain): find the compound interest accrued on an amount of rs . 14,800 at 13.5 % p . a at the end of two years . ( round off your answer to nearest integer ?
Options: a ) 2828 , b ) 2338 , c ) 377 , d ) 4266 , e ) 288
Rationale: "ci = 14800 { [ 1 + 13.5 / 100 ] 2 - 1 } = 14800 { [ 1 + 27 / 200 ] 2 - 1 = 14800 { 2 + 27 / 200 } { 27 / 200 } = ( 74 ) [ 2 + 27 / 200 ] ( 27 ) = 1998 [ 2 + 27 / 200 ] = 3996 + 269.73 = rs . 4266 . answer : d"
Answer: d
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 150 2 l ^ 2 / 3 = 150 l ^ 2 = 225 l = 15 cm the answer is a ."
Answer: a
Question (geometry): how many odd numbers between 10 and 1500 are the squares of integers ?
Options: a ) 11 , b ) 14 , c ) 17 , d ) 20 , e ) 23
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is c ."
Answer: c
Question (general): gold is 11 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 11 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 11 w + 5 wx = x + 1 * 8 w 11 + 5 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"
Answer: b
Question (physics): if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 30 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 34 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 24 and 30 ) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 30 * t 3 = 8 hrs t = t 1 + t 2 + t 3 = 21 hrs d = rt ( 240 * 3 ) = r * 21 r = 34 answer : e"
Answer: e
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 63 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 25 sec , d ) 14.3 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 63 * 5 / 18 = 17.5 mps t = 250 / 17.5 = 14.3 sec answer : d"
Answer: d
Question (general): a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase i in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase i = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Question (other): income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 15000 , then find his savings ?
Options: a ) 3600 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3000
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 15000 = > x = 3000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3000 . answer : e"
Answer: e
Question (general): salesperson a ' s compensation for any week is $ 280 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 5000 , b ) $ 7000 , c ) $ 9000 , d ) $ 11,000 , e ) $ 13,000
Rationale: "280 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 220 x = $ 11,000 the answer is d ."
Answer: d
Question (physics): rashmi walks to her bus stop at 5 kmph and reaches there late by 10 minutes . on the next day , she increases her speed to 6 kmph and reaches the bus stop 10 minutes early . how far is the bus stop ?
Options: a ) 13 , b ) 12 , c ) 11 , d ) 10 , e ) 9
Rationale: let the distance to the bus stop is ` ` d ' ' km time taken by her ( at 5 kmph ) = d / 5 hour , and time taken by her ( at 6 kmph ) = d / 6 hour as per given condition , d / 5 - d / 6 = 20 / 60 d = 10 kms answer : d
Answer: d
Question (gain): the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 2 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 8820 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 2 = rs 8820 answer : c"
Answer: c
Question (physics): a cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 , b ) 50 , c ) 53.5 , d ) 55 , e ) 57
Rationale: "explanation : area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 6 x 1.25 ) + 6 x 4 ] m 2 = 49 m 2 answer : a"
Answer: a
Question (general): all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 152 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1216 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 152 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 152 = 3 k + 152 = > 2 k = 304 = > k = 152 the initial quantity of milk in a = 8 k = 8 * 152 = 1216 liters .
Answer: a
Question (general): the average expenditure of a labourer for 7 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 70.11 , b ) 72.02 , c ) 86.5 , d ) 78.2 , e ) none of the above
Rationale: "income of 7 months = ( 7 × 85 ) – debt = 595 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 865 average monthly income = 865 ÷ 10 = 86.5 answer c"
Answer: c
Question (physics): a man leaves a point p at 6 a . m . and reaches the point q at 10 a . m . another man leaves the point give at 8 a . m . and reaches the point p at 12 noon . at what time do they meet ?
Options: a ) 2 a . m , b ) 6 a . m , c ) 9 a . m , d ) 5 a . m , e ) 1 a . m
Rationale: 9 a . m . answer : c
Answer: c
Question (general): 35 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 35 % of companies which offer wireless internet also offer snacks . the answer is b ."
Answer: b
Question (general): the batting average of a particular batsman is 59 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 156 , b ) 208 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 59 * 46 = 2714 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2714 – 2552 = 162 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 162 2 x = 312 x = 156 runs answer a"
Answer: a
Question (gain): find the simple interest on $ 3000 for 3 years at 10 % per annum ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 3000 * 3 * 10 / 100 = $ 900 answer is a"
Answer: a
Question (general): if 9 ^ y = 3 ^ 12 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e"
Answer: e
Question (physics): during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 150 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 400 , e ) 480
Rationale: "easy 400 is the answer . 3 / 4 ( x / 2 ) = 150 x = 150 * 8 / 3 = 400 . answer d"
Answer: d
Question (physics): with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 1 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 120 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 1 2 x / 15 - x / 8 = 1 = > x = 120 km . answer : d"
Answer: d
Question (other): the ratio of the present age of sandy to that of molly is 7 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42
Rationale: "let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 8 ) / ( 2 x + 8 ) = 5 / 2 4 x = 24 x = 6 six years ago , sandy ' s age was 7 ( 6 ) - 6 = 36 the answer is d ."
Answer: d
Question (general): the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 420 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 600 , c ) 287 , d ) 780 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 420 = 3780 salary of the new supervisor = 3780 â ˆ ’ 3000 = 780 answer : d"
Answer: d
Question (general): the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.6 , while the average of the other 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.6 * 2 ) + ( 3.85 * 2 ) ] = 8.8 . required average = ( 8.8 / 2 ) = 4.4 . b"
Answer: b
Question (physics): two trains 121 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 55 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.17 , c ) 7.62 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 121 + 165 ) / ( 80 + 55 ) * 18 / 5 t = 7.62 answer : c"
Answer: c