Cheukting/mathqa huggingface dataset:
Question (other): at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 11 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 5 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 11 k waiters . the new ratio is 1 : 5 which equals 3 : 15 . 15 k = 11 k + 12 k = 3 there are 9 cooks . the answer is c ."
Answer: c
Question (gain): on a certain day , tim invested $ 600 at 10 percent annual interest , compounded annually , and lana invested 1,000 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5.5 , b ) $ 15.5 , c ) $ 23.5 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 600 ( 1.10 ) ^ 2 = 600 ( 1.21 ) = 726 and lana would have 1,000 ( 1.05 ) ^ 2 = 1,000 ( 1.1025 ) = 1102.5 thus , tim earned 126 dollars , while lana earned 102.5 dollars the difference is $ 23.5 and the answer is c ."
Answer: c
Question (general): john has 10 pairs of matched socks . if he loses 9 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 4 pairs ( 8 socks ) out of 10 pairs 1 sock from the 5 th pair . thus the no of matching socks pair remaining = 10 - 5 = 5 answer c"
Answer: c
Question (gain): a $ 500 investment and a $ 1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 8.5 ) = ( 500 ∗ 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 9 % ( option a ) answer : a"
Answer: a
Question (gain): a trader bought a car at 30 % discount on its original price . he sold it at a 70 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 18 % , b ) 13 % , c ) 12 % , d ) 32 % , e ) 19 %
Rationale: "original price = 100 cp = 70 s = 70 * ( 170 / 100 ) = 119 100 - 119 = 19 % answer : e"
Answer: e
Question (general): in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 5 ohms ?
Options: a ) 7 / 9 , b ) 20 / 9 , c ) 7 / 20 , d ) 9 / 20 , e ) 11 / 20
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 5 = 9 / 20 r = 20 / 9 the answer is b ."
Answer: b
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 14 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 23.56 , b ) 23.59 , c ) 23.55 , d ) 18.86 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 14 + 10 ) = 48 cm parameter of the square = 48 cm i . e . 4 a = 48 a = 12 diameter of the semicircle = 12 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 12 ) = 1 / 2 ( 22 / 7 ) ( 12 ) = 264 / 14 = 18.86 cm to two decimal places answer : d"
Answer: d
Question (gain): a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 6 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 6 / 100 x 12000 ) = rs . 720 . answer d"
Answer: d
Question (physics): calculate the circumference of a circular field whose radius is 5 centimeters .
Options: a ) 30 π cm
b ) 80 π cm
c ) 70 π cm
d ) 50 π cm
e ) 10 π cm
Rationale: circumference c is given by c = 2 π r = 2 π * 5 = 10 π cm correct answer e
Answer: e
Question (gain): two friends plan to walk along a 43 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 15 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ?
Options: a ) 21 , b ) 21.5 , c ) 22 , d ) 22.5 , e ) 23
Rationale: "if q complete x kilometers , then p completes 1.15 x kilometers . x + 1.15 x = 43 2.15 x = 43 x = 43 / 2.15 = 20 then p will have have walked 1.15 * 20 = 23 km . the answer is e ."
Answer: e
Question (other): the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 588 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 3468 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 588 : n & there n = 289 x 588 / 49 = rs . 3468 answer : d"
Answer: d
Question (physics): a person travels equal distances with speeds of 4 km / hr , 8 km / hr , 12 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 600 mts , d ) 2 km , e ) 1200 mts
Rationale: let the each distance be x km total distance = 3 x then total time , ( x / 4 ) + ( x / 8 ) + ( x / 12 ) = 11 / 60 x = 0.4 total distance = 3 * 0.4 = 1.2 km = 1200 meters correct option is e
Answer: e
Question (physics): a man drives at a speed of 40 miles / hr . his wife left 30 mins . late with 50 miles / hr speed . when will they meet ?
Options: a ) 1 hours , b ) 2 hours , c ) 3 hours , d ) 4 hours , e ) 5 hours
Rationale: in 30 minutes the man would have droven 20 miles , when his wife starts . now both are driving in the same direction . so speed of wife related to man is 10 ( 50 - 40 ) miles / hr . so wife will cover 20 miles in 2 hours to meet the man . answer : b
Answer: b
Question (physics): a and b together can complete work in 8 days . a alone starts working and leaves it after working for 6 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 5 , d ) 12 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 8 now a does half of the work in 6 day so a can complete the whole work in 12 days a ’ s one day work = 1 / 12 b ’ s one day work = 1 / 8 - 1 / 12 = 1 / 24 b alone can complete the work in 24 days so half of the work in 12 days answer : option d"
Answer: d
Question (gain): in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 63 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 450 , c ) 150 , d ) 35 , e ) 350
Rationale: since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 63 , so 0.14 * { total } = 63 - - > { total } = 450 . answer : b .
Answer: b
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 78 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 19 , c ) 14 , d ) 18 , e ) 26
Rationale: the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 78 / 3 = 26 kmph . answer : e
Answer: e
Question (physics): angelina walked 960 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 13 , c ) 24 , d ) 36 , e ) 42
Rationale: "let the speed be x . . . so time taken from home to grocery = 960 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 960 / x - 240 / x = 40 . . 720 / x = 40 . . x = 18 m / secs . . so grocery to gym = 2 * 18 = 36 m / s . . . d"
Answer: d
Question (gain): money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 3500 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 31,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 3500 triples to $ 10500 , in 28 years , it will again triple to $ 10500 * 3 = $ 31,500 answer e"
Answer: e
Question (general): the ratio of the ages of 3 people is 4 : 6 : 7 . 8 years ago , the sum of their ages was 44 . find their present ages .
Options: a ) 28 , 42,49 , b ) 24 , 36,42 , c ) 20 , 30,35 , d ) 16 , 24,28 , e ) 12 , 18,21
Rationale: let the present ages be 4 x , 6 x , 7 x . ( 4 x - 8 ) + ( 6 x - 8 ) + ( 7 x - 8 ) = 44 17 x = 68 x = 4 their present ages are 16 , 24 , and 28 . the answer is d .
Answer: d
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 72 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 25 sec , d ) 18 sec , e ) 12.5 sec
Rationale: "d = 100 + 150 = 250 s = 72 * 5 / 18 = 20 mps t = 250 / 20 = 12.5 sec answer : e"
Answer: e
Question (general): a meal cost $ 35.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 35.5 ) = 3.55 15 % ( 35.5 ) = 5.325 total amount could have been 35.5 + 3.55 and 35.5 + 5.325 = > could have been between 39.05 and 40.625 = > approximately between 39 and 41 answer is b ."
Answer: b
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 10 cm long , and the distance between them is 10 cm .
Options: a ) 187 cm 2 , b ) 185 cm 2 , c ) 150 cm 2 , d ) 185 cm 2 , e ) 195 cm 2
Rationale: "explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 10 ) * ( 10 ) = 150 cm 2 answer : option c"
Answer: c
Question (geometry): a rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 3900 , c ) s . 3228 , d ) s . 4200 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 90 + 60 – 10 ) 10 = > 1400 m 2 1400 * 3 = rs . 4200 answer : d"
Answer: d
Question (gain): a soccer team played 158 games and won 40 percent of them . how many games did it win ?
Options: a ) 84 , b ) 63.2 , c ) 104 , d ) 50.8 , e ) 15.8
Rationale: 40 % of 158 = x 0.40 * 158 = x 63.2 = x answer : b
Answer: b
Question (physics): the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 70 kmph its consumption is 1 litre per hour . if each litre costs $ 70 and other expenses per hous is $ 70 , then what would be the minimum expenditure required to cover a distance of 700 km ?
Options: a ) 1000 , b ) 1500 , c ) 1240 , d ) 1630 , e ) 1400
Rationale: "70 kmph consumption is 1 lt / hr so 700 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 70 so 10 lt costs $ 700 extra expenses for 1 hr - $ 70 10 hrs - $ 700 total expense - $ 700 + $ 700 = $ 1400 answer : e"
Answer: e
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 80 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 76.6
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover this distance at regular speed is 45 + 2 = 47 seconds = 47 / 3,600 hours = 5 / 383 hours ; so , we get that to cover 1 kilometer 1 / ( 5 / 383 ) hours is needed - - > regular speed 76.6 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"
Answer: e
Question (gain): 15 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 18 = 50 / 3 = 16.67 % answer is a"
Answer: a
Question (gain): total number of people attending a party is 600 . 70 % of the men are wearing black shirt and rest are wearing red . if 60 % of the total people are women then how many men are wearing red shirts ?
Options: a ) 168 , b ) 72 , c ) 56 , d ) 170 , e ) 60
Rationale: number of woman in the party = 0.60 * 600 = 360 number of men in the party = 600 - 360 = 240 % of men wearing red shirts = 100 - 70 = 30 % number of men wearing red shirt = 0.30 * 240 = 72 . b is the correct answer
Answer: b
Question (physics): the mall charges 60 cents for the first hour of parking and $ 4 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 2 per hour . if edward parked his car in the mall for 7 hours and 30 minutes , how much is he going to pay ?
Options: a ) $ 25.2 , b ) $ 22 . , c ) $ 13 . , d ) $ 14.5 . , e ) $ 15.5
Rationale: "0.60 + 4 * 4 + 2 * 4 + 0.60 = $ 25.2 answer : $ 25.2"
Answer: a
Question (general): suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 650 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 760 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) $ 2.50 , b ) $ 5.00 , c ) $ 5.50 , d ) $ 7.50 , e ) $ 15.00
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 650 . . . eq 1 8 x + 32 y = 760 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1300 8 x = 760 . 36 x = 540 = > x = 15 . sub x in eq 2 . . . . we get 120 + 32 y = 760 . . . then we get 32 y = 640 then y = 20 difference between x and y is 5 . answer : option b is correct answer ."
Answer: b
Question (general): ( 17 ) 5.5 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 5.5 * ( 17 ) x = 178 . then , ( 17 ) 5.5 + x = ( 17 ) 8 . ∴ 5.5 + x = 8 ⇔ x = ( 8 - 5.5 ) ⇔ x = 2.5 answer e"
Answer: e
Question (general): in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case .
Options: a ) 627 , b ) 528 soldiers , c ) 626 , d ) 657 , e ) 673
Rationale: assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = ( 1200 ) ( 30 ) ( 3 ) kg . also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) k as the same provisions are available = > ( 1200 ) ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ ( 1200 ) ( 30 ) ( 3 ) ] / ( 25 ) ( 2.5 ) - 1200 = > x = 528 . answer : b
Answer: b
Question (general): what least value should be replaced by * in 483 * 4312 so the number become divisible by 6
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , last digit is 2 so it is dividable by 2 so ( 4 + 8 + 3 + * + 4 + 3 + 1 + 2 ) = 25 + * should be divisible by 6 , 15 + will be divisible by , so that least number is 2 . answer : option d"
Answer: d
Question (general): calculate the standard deviation of each data set { 10 , 1010 , 1010 }
Options: a ) 8.05 , b ) 9 , c ) 10 , d ) 15 , e ) 15.5
Rationale: standard deviation data set a = √ [ ( ( 9 - 10 ) 2 + ( 10 - 10 ) 2 + ( 11 - 10 ) 2 + ( 7 - 10 ) 2 + ( 13 - 10 ) 2 ) / 5 ] = 2 standard deviation data set b = √ [ ( ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 + ( 10 - 10 ) 2 ) / 5 ] = 0 standard deviation data set c = √ [ ( ( 1 - 10 ) 2 + ( 1 - 10 ) 2 + ( 10 - 10 ) 2 + ( 19 - 10 ) 2 + ( 19 - 10 ) 2 ) / 5 ] = 8.05 option a
Answer: a
Question (other): the ratio of three numbers is 3 : 4 : 7 and their product is 18144 . the numbers are
Options: a ) 9 , 12,21 , b ) 15 , 20,25 , c ) 18 , 24,42 , d ) 24 , 15,17 , e ) 30 , 12,7
Rationale: "let the numbers be 3 x , 4 x and 7 x 3 x x 4 x x 7 x = 18144 x 3 = 216 x = 6 the numbers are 18 , 24,42 answer c 18 , 24,42"
Answer: c
Question (gain): john and david can finish a job together in 3 hours . if john can do the job by himself in 4 hours , what percent of the job does david do ?
Options: a ) 35 % , b ) 28 % , c ) 26 % , d ) 20 % , e ) 25 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 12 donuts which is the job ( i picked this as a smart number ) . john on his own works 12 / 4 = 3 donuts per hour . john and david work 12 / 3 = 4 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 3 hours = 3 donuts per hour . therefore 3 donuts / 12 donuts = 1 / 4 = 25 % answer : e"
Answer: e
Question (physics): the length of the longest tape in cm which can be used to measure exactly , the length 6 m ; 5 m ; and 12 m is :
Options: a ) 200 , b ) 100 , c ) 50 , d ) 1200 , e ) 500
Rationale: the three lengths in cm are 600,500 & 1200 . hcf of 600 , 500 & 1200 is 100 hence , the answer is 100 cm . answer : b
Answer: b
Question (physics): a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 84 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 84 / 21 = 4 hours answer is a"
Answer: a
Question (general): 7.007 / 2.002 =
Options: a ) 3.05 , b ) 3.50035 , c ) 3.501 , d ) 3.5035 , e ) 3.5
Rationale: "7.007 / 2.002 = 7007 / 2002 = 7 ( 1001 ) / 2 ( 1001 ) = 7 / 2 = 3.5 the answer is e ."
Answer: e
Question (general): the average of first 40 prime numbers is ?
Options: a ) 15.41 , b ) 16.41 , c ) 15.61 , d ) 15 , e ) 16.91
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 12 = 197 / 12 = 16.41 ( approx ) answer is b"
Answer: b
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 198 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1650 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 198 . ∴ x 16 x 9 / 12 x 1 / 100 } = 198 or x = 1650 . ∴ p . w . = rs . 1650 . answer c"
Answer: c
Question (general): find the number , difference between number and its 3 / 5 is 56 .
Options: a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 150
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 56 , = > ( 2 / 5 ) x = 56 = > 2 x = 56 * 5 , = > x = 140 answer : option a"
Answer: a
Question (physics): how many seconds will a 600 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 22 , b ) 36 , c ) 99 , d ) 77 , e ) 12
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 600 * 3 / 50 = 36 sec . answer : b"
Answer: b
Question (physics): nicky and cristina are running a 200 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 35 , b ) 30 , c ) 45 , d ) 40 , e ) 50
Rationale: the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . b
Answer: b
Question (physics): a train 200 m long is running with a speed of 54 kmph . in what will it pass a car whose speed at 36 kmph in the direction opposite to that in which the train is going
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 15 sec
Rationale: "explanation : speed of the train relative to man = ( 54 + 36 ) kmph = 90 × 5 / 18 m / sec = 25 m / sec . time taken by the train to cross the car = time taken by it to cover 200 m at 25 m / sec = ( 200 × 1 / 25 ) sec = 8 sec answer : option a"
Answer: a
Question (gain): a sum of 12,500 amounts to 15,500 in 4 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 5 % , e ) 8 %
Rationale: c 6 % s . i . = ( 15500 - 12500 ) = 3000 . rate = ( 100 x 3000 ) / ( 12500 x 4 ) % = 6 %
Answer: c
Question (physics): car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 72 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 12 : 7 , c ) 13 : 7 , d ) 65 : 36 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 65 ã — 8 = 520 km distance travelled by car b = 72 ã — 4 = 288 km ratio = 520 / 288 = 65 : 36 d"
Answer: d
Question (general): jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 85 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 85 * 3 = 255 jerry wants the average to be = 87 hence total score on 4 tests should be = 87 * 4 = 348 score required on the fourth test = 348 - 255 = 93 option d"
Answer: d
Question (general): a number exceeds by 20 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: "x – 3 / 8 x = 20 x = 32 answer : a"
Answer: a