Cheukting/mathqa huggingface dataset:
Question (gain): tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 965 , d ) d ) 1060 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 45 × 9 = 405 . total cost he has to pay = 560 + 405 = 965 . c )"
Answer: c
Question (probability): in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is theprobability that the extracted ball would turn onto be white , if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ?
Options: a ) 3 / 5 , b ) 5 / 8 , c ) 6 / 7 , d ) 7 / 8 , e ) 6 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Question (physics): nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 36 meter head start . if cristina runs at a pace of 6 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 ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 30 seconds , e ) 12 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 36 for cristina = c = 6 * t @ t = 12 , n = 72 c = 72 right answer ans : e"
Answer: e
Question (general): 587 * 999 = ?
Options: a ) 586411 , b ) 586413 , c ) 486411 , d ) 486413 , e ) none of these
Rationale: "explanation : trick : 587 * ( 1000 - 1 ) = 587000 - 587 = 586413 option b"
Answer: b
Question (physics): it takes 35 identical printing presses 12 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "35 printing presses can do 1 / 12 of the job each hour . 30 printing presses can do 6 / 7 * 1 / 12 = 1 / 14 of the job each hour . the answer is a ."
Answer: a
Question (gain): a sum was put at si at certain rate for 2 years . had it been put at 3 % higher rate , it would have fetched rs . 300 more . find the sum
Options: a ) rs 4000 , b ) rs 5000 , c ) rs 6000 , d ) rs 7000 , e ) rs 8000
Rationale: let p be the sum . and x be the interest rate . ( 2 * ( x + 3 ) * p / 100 ) - ( 2 * x * p / 100 ) = 300 therefore 6 p / 100 = 300 p = rs 5000 answer : b
Answer: b
Question (general): 9 people decided to split the restaurant bill evenly . if the bill was $ 314.16 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20
Rationale: this is equivalent to finding the first number that is divisible by 9 that occurs after 31416 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 31416 = 15 and 18 is divisible by 9 . hence , we need to add 3 to this number for it to be divisible by 9 correct option : d
Answer: d
Question (general): 1395 x 1395 = ?
Options: a ) a ) 1951609 , b ) b ) 1946025 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1395 x 1395 = ( 1395 ) 2 = ( 1400 - 5 ) 2 = ( 1400 ) 2 + ( 5 ) 2 - ( 2 x 1400 x 5 ) = 1960000 + 25 - 14000 = 1960025 - 14000 = 1946025 . answer : b"
Answer: b
Question (general): x ÷ 4 × 5 + 10 – 12 = 48 , then x =
Options: a ) 60 , b ) 40 , c ) 100 , d ) 28 , e ) 50
Rationale: follow reverse process 48 + 12 = 60 – 10 = 50 ÷ 5 = 10 × × 4 = 40 option b
Answer: b
Question (general): - 84 x 29 + 365 = ?
Options: a ) 2071 , b ) 2436 , c ) 2801 , d ) - 2801 , e ) - 2071
Rationale: "e given exp . = - 84 x ( 30 - 1 ) + 365 = - ( 84 x 30 ) + 84 + 365 = - 2520 + 449 = - 2071"
Answer: e
Question (gain): 5 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 267 , e ) 6400
Rationale: "( 5 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 20 x = 320 x = 6400 answer : e"
Answer: e
Question (geometry): what is the area of square field whose side of length 25 m ?
Options: a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 287 sq m , e ) 625 sq m
Rationale: "25 * 25 = 625 sq m answer : e"
Answer: e
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 3 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 12 : 15 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 3 - - > e : l = 5 : 3 = 20 : 12 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 12 : 15 . answer : a ."
Answer: a
Question (physics): a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 168 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 168 km time taken = distance / speed = 168 / 28 = 6 hours answer : option d"
Answer: d
Question (general): find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 10 x + 5 = 0 ?
Options: a ) 6 , b ) 42 , c ) 24 , d ) 18 , e ) 95
Rationale: a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 10 / 1 = - 10 ab = 5 / 1 = 5 hence a / b + b / a = [ ( - 10 ) 2 - 2 ( 5 ) ] / 5 = 90 / 5 = 18 . d )
Answer: d
Question (gain): jim is able to sell a hand - carved statue for $ 750 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 555.56 , d ) $ 574.90 , e ) $ 588.20
Rationale: "750 = 1.35 * x x = 750 / 1.35 = 555.5555556 . . . which rounds to $ 555.56 , which is ( c ) ."
Answer: c
Question (general): in a fuel station the service costs $ 4.25 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 309.85 $
Rationale: "service cost of 3 van and 2 truck = 4.25 * ( 3 + 2 ) = 21.25 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.6 = 288.6 total cost = fuel + service = 288.6 + 21.25 = 309.85 answer is e"
Answer: e
Question (physics): a cistern is normally filled in 10 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 60 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 10 - 1 / x = 1 / 12 , solving 1 / x = 1 / 60 so in 60 hours full cistern will be empty . answer : c"
Answer: c
Question (general): to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 795 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 199 , c ) 193 , d ) 212 , e ) 213
Rationale: total movies submitted are 795 . as per question we need to take 1 / 4 of 795 to be considered for top 10 movies = 198.75 approximate the value we 199 . imo option b is the correct answer . . .
Answer: b
Question (general): a man can swim in still water at 9 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.9 , c ) 3 , d ) 1.5 , e ) 1.2
Rationale: "m = 9 s = x ds = 9 + x us = 9 - x 9 + x = ( 9 - x ) 2 9 + x = 18 - 2 x 3 x = 9 x = 3 answer : c"
Answer: c
Question (general): the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 6 ) , how many units is p from the y - axis ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 10.5 , e ) 12
Rationale: "the x - axis is 6 units from the point p . thus the y - axis is 12 units from the point p . the answer is e ."
Answer: e
Question (physics): a can do a piece of work in 24 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 9 , b ) 77 , c ) 66 , d ) 55 , e ) 12
Rationale: "8 / 24 + 6 / x = 1 x = 9 days answer : a"
Answer: a
Question (gain): milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this to 2 % ?
Options: a ) 5 litres , b ) 7 litres , c ) 15 litres , d ) can not be determined , e ) none of these
Rationale: "here required quantity of pure milk = 10 × ( 5 − 2 ) / 2 = 10 × 3 / 2 = 15 litres . answer c"
Answer: c
Question (gain): 40 percent of the members of a study group are women , and 20 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.2 , b ) 0.08 , c ) 0.16 , d ) 0.14 , e ) 0.15
Rationale: "say there are 100 people in that group , then there would be 0.4 * 0.20 * 100 = 8 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 8 / 100 . answer : b"
Answer: b
Question (physics): two goods trains each 750 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 ) 72 , b ) 45 , c ) 48 , d ) 51 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : option a"
Answer: a
Question (gain): the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . the present worth is :
Options: a ) rs . 608 , b ) rs . 6076 , c ) rs . 600 , d ) rs . 602 , e ) rs . 601
Rationale: "t . d . = b . g . x 100 = rs . 24 x 100 = rs . 120 . rate x time 10 x 2 p . w . = 100 x t . d . = rs . 100 x 120 = rs . 600 . rate x time 10 x 2 answer : c"
Answer: c
Question (physics): a rectangular plot measuring 90 metres by 60 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 60 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 60 ) = 300 m . ∴ number of poles = [ 300 / 5 ] = 60 m answer c"
Answer: c
Question (physics): a 1200 m long train crosses a tree in 80 sec , how much time will i take to pass a platform 1000 m long ?
Options: a ) 288 , b ) 146.66 , c ) 188 , d ) 180 , e ) 12
Rationale: "l = s * t s = 1200 / 80 s = 15 m / sec . total length ( d ) = 2200 m t = d / s t = 2200 / 15 t = 146.66 sec answer : b"
Answer: b
Question (general): simplify : ( 7 + 2 ) – ( 5 + 3 + 1 ) - 1 .
Options: a ) - 1 , b ) – 2 , c ) 1 , d ) 2 , e ) 0
Rationale: "solution : ( 7 + 2 ) – ( 5 + 3 + 1 ) - 1 = 9 - 5 - 3 + 1 - 1 = 9 - 8 + 1 - 1 = 2 - 1 = 1 answer : ( c )"
Answer: c
Question (physics): how many shots of 1 cm radius can be prepared from a sphere of 7 cm radius ?
Options: a ) 343 , b ) 388 , c ) 327 , d ) 88 , e ) 99
Rationale: "4 / 3 ï € * 7 * 7 * 7 = 4 / 3 ï € * 1 * 1 * 1 * x x = 343 answer : a"
Answer: a
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 10 % 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 ) 10.5 % , b ) 18 % , c ) 15 % , d ) 22 % , e ) 11.11 %
Rationale: "0.1 m = 0.90 e = > e / m = 1 / 9 * 100 = 11.11 % = e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Question (physics): a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 3 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 4.0 , b ) 3.8 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 3 and 6 = 12 . upstream time = 12 / 6 = 2 hrs downstream time = 12 / 3 = 4 hrs total time = 6 hrs total distance = 24 average speed = 24 / 6 = 4.0 km / hr"
Answer: a
Question (geometry): abcd is a square where ab = â ˆ š 4008 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2004 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4008 / 2 = 2004 . correct answer b"
Answer: b
Question (physics): a man swims downstream 72 km and upstream 45 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 1.7 , b ) 2.8 , c ) 3.6 , d ) 2.7 , e ) 1.1
Rationale: "72 - - - 5 ds = 14.4 ? - - - - 1 45 - - - - 5 us = 9 ? - - - - 1 s = ? s = ( 14.4 - 9 ) / 2 = 2.7 answer : d"
Answer: d
Question (other): two numbers are in the ratio 1 : 2 , if 7 is added to both , their ratio changes to 3 : 5 . the greatest number is
Options: a ) 24 , b ) 26 , c ) 28 , d ) 32 , e ) 44
Rationale: "let the numbers be x and 2 x then , ( x + 7 ) / ( 2 x + 7 ) = 3 / 5 x = 14 there fore answer is 28 answer c 28"
Answer: c
Question (gain): what is 82 % of 3 / 4 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.615
Rationale: "82 % * ( 3 / 4 ) = 0.82 * 0.75 = 0.615 answer : e"
Answer: e
Question (physics): points x , y , and z lie , in that order , on a straight railroad track . the distance from point x to point y is twice the distance from point y to point z . a train traveled from point x to point z without stopping . the train ' s average speed when traveling from point x to point y was 300 miles per hour and the train ' s average speed when traveling from point y to point z was 100 miles per hour . what was the train ' s average speed , in miles per hour , when traveling from point x to point z ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 180 , e ) 260
Rationale: average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 300 speed y - z = 100 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 300 ) + ( d / 100 ) 3 d / ( 2 d / 300 ) + ( 3 d / 300 ) 3 d / ( 5 d / 300 ) 900 d / 5 d average speed = 180 answer : d
Answer: d
Question (physics): a 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 270 / 9 = 500 / 9 = > x + 270 = 500 = > x = 230 so the length of the train is 230 meters option c"
Answer: c
Question (gain): if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 20000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 1000
Rationale: "30 sec approach - solve it using approximation 20000 sheet at full price , 5 cent = 1000 20000 sheet at max discount price , 4 cent = 800 your ans got to be between these two . ans d it is ."
Answer: d
Question (physics): there is rain at a rate of 12 centimeters per hour all over new jersey . somewhere downtown in new jersey a group of students are waiting for the rain to stop . if the rain filled a tank the with a base area of 250 square centimeters and a depth of 6 centimeters , how long did the students wait for the rain to stop ?
Options: a ) 8 hours
b ) 4 hours 25 minutes
c ) 3 hours 15 minutes
d ) 6 hours
e ) 2 hours
Rationale: answer is : e , 4 hours and 30 mins the volume of the tank is irrelevant and only height matters since rain fell all over the city . thus , it takes only . 12 / 6 = 2 hours of rain to fill the tank .
Answer: e
Question (general): if a and b are positive integers , and a = 3 b + 12 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 3 , c ) 2 , d ) 5 , e ) 4
Rationale: "if b is 1 , 2 , 3 , or 4 , then gcd of a and b is 1 , 2 , 3 , and 4 respectively . so , by poe the answer must be d . still : if b is a multiple of 5 , then a is 12 greater than a multiple of 5 , so not a multiple of 5 , so both of them can not be divisive by 5 . answer : d ."
Answer: d
Question (gain): during a sale , the price of a pair of shoes is marked down 14 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 16 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 86 price after sale = 100 percent increase = 14 / 86 * 100 = 16 % approx . correct option : d"
Answer: d
Question (physics): two trains of length 60 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 17 sec , d ) 20 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 60 + 280 = 400 m . the time required = d / s = 340 / 20 = 20 sec . answer : c"
Answer: c
Question (gain): one 100 gallons of fuel are purchased at $ 0.70 per gallon . the fuel is consumed at a rate of $ 0.40 worth of fuel per hour . at this rate , how many hours are required to consume the 100 gallons of fuel ?
Options: a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 250
Rationale: the fuel is consumed at this rate : $ 0.40 / $ 0.70 = 4 / 7 gallons per hour . the time it takes to consume 100 gallons is : 100 / ( 4 / 7 ) = 175 hours . the answer is b .
Answer: b
Question (gain): a chemist mixes one liter of pure water with x liters of a 75 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 75 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 75 - 15 ) / ( 15 - 0 ) = 4 / 1 1 / x = 4 / 1 x = 1 / 4 answer : a"
Answer: a
Question (gain): if 5 % more is gained by selling an article for rs . 600 than by selling it for rs . 580 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 400 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 600 - 580 = 20 x / 20 = 20 = > x = 400 answer : c"
Answer: c
Question (physics): a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 5 / 4 = 1 hrs 15 min answer : c"
Answer: c
Question (general): a , b , c subscribe rs . 50000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36000 , what will be the amount a receives ?
Options: a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 36000 × 21 / 50 = 15,120 answer is a .
Answer: a
Question (physics): steve traveled the first 2 hours of his journey at 30 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 30 * 2 = 60 miles . distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles . therefore , total distance covered = 60 + 240 = 300 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 300 / 5 = 60 miles per hour . choice c"
Answer: c
Question (physics): a train 600 m long can cross an over brdge of 100 m long in 70 sec and then find the speed of the train ?
Options: a ) 79 , b ) 30 , c ) 36 , d ) 66 , e ) 12
Rationale: length = speed * time speed = l / t s = 700 / 70 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph . answer : c
Answer: c
Question (gain): when sold at a 60 % discount , a sweater nets the merchant a 35 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 70.38 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 35 % . . therefore the wholesale purchase cost = x . . . . 1.35 x = 40 or x = 29.62 . . . marked price was 100 so . . . so answer is 70.38 % . . d"
Answer: d
Question (probability): from a group of 3 women and 3 girls , 4 are to be randomly selected . what is the probability that equal numbers of women and girls will be selected ?
Options: a ) 3 / 5 , b ) 1 / 5 , c ) 2 / 5 , d ) 4 / 5 , e ) 1
Rationale: using the first example , here is the probability of that exact sequence occurring : wwgg = ( 3 / 6 ) ( 2 / 5 ) ( 3 / 4 ) ( 2 / 3 ) = 36 / 360 = 1 / 10 each of the other 5 options will yield the exact same probability . . . . wgwg = ( 3 / 6 ) ( 3 / 5 ) ( 2 / 4 ) ( 2 / 3 ) = 36 / 360 = 1 / 10 so we have 6 different options that each produce a 1 / 10 chance of occurring . 6 ( 1 / 10 ) = 6 / 10 = 3 / 5 final answer : a
Answer: a
Question (general): what is the sum of natural numbers between 50 and 100
Options: a ) 4800 , b ) 4860 , c ) 3825 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 50 and 100 numbers = 51 = > 100 - 50 = 50 + 1 = 51 sn = 51 / 2 ã — 150 = 51 ã — 75 = 3825 answer : c"
Answer: c