Cheukting/mathqa huggingface dataset:
Question (general): ( 69842 x 69842 - 30158 x 30158 ) / ( 69842 - 30158 ) = ?
Options: a ) 100000 , b ) 69842 , c ) 39684 , d ) 30158 , e ) none
Rationale: answer given expression = [ ( 69842 ) 2 - ( 30158 ) 2 ] / [ ( 69842 - 30158 ) ] = [ ( 69842 - 30158 ) ( 69842 + 30158 ) ] / ( 60842 - 30158 ) = 100000 correct option : a
Answer: a
Question (physics): two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 6 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 120 m , d ) 135 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 6 ) m = 135 m . answer d"
Answer: d
Question (physics): a train running at the speed of 20 km / hr crosses a post in 10 seconds . what is the length of the train ?
Options: a ) 150 , b ) 250 , c ) 415 , d ) 200 , e ) 312
Rationale: "speed = ( 20 x 5 / 18 ) = 50 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 9 x 10 m = 200 m . answer : d"
Answer: d
Question (general): 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 69 % , e ) 75 %
Rationale: initially 92 % and 8 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 92 so , the required % is [ ( 3 / 4 ) ∗ 92 / 100 ] ∗ 100 = 69 % answer : d
Answer: d
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 20 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 160 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,16 r = x / 100 * 0.1 r answer b"
Answer: b
Question (physics): suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 750 ( before payroll deductions ) ?
Options: a ) 1600 , b ) 1625 , c ) 1650 , d ) 1655 , e ) 1675
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 760 x = 260 / 0.16 = 1625 the answer is b ."
Answer: b
Question (general): 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened to fillthe tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs
Rationale: 1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c
Answer: c
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 354
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 15 ) . larger number = ( 23 x 15 ) = 345 . answer : option d"
Answer: d
Question (general): an assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the time to produce the first 60 cogs is 60 / 15 = 4 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 5 hours = 24 cogs per hour . the answer is c ."
Answer: c
Question (other): 210 students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Question (geometry): the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 19 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?
Options: a ) 36 , b ) 4 , c ) 16 , d ) 38 , e ) 40
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 19 ^ 2 / 2 - 17 ^ 2 / 2 = 72 / 2 = 36 ans a ."
Answer: a
Question (gain): increasing the original price of a certain item by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 44.0
Rationale: "we ' re told that the original price of an item is increased by 20 % and then that price is increased by 20 % . . . . if . . . . starting value = $ 100 + 20 % = 100 + . 20 ( 100 ) = 120 + 20 % = 120 + . 20 ( 120 ) = 120 + 24 = 144 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 44 / 100 = 44 % final answer : e"
Answer: e
Question (geometry): the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 112 ) * 63 = 27 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 63 will have a volume a little more than 24 , that is 27 answer : a"
Answer: a
Question (geometry): if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 266 m , what is its area ?
Options: a ) 4290 , b ) 2535 , c ) 2530 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 266 m ⇒ breadth = 55 m length = 55 + 23 = 78 m area = 78 × 55 = 4290 m 2 answer is a ."
Answer: a
Question (probability): the chance of rain on any given day in tel - aviv is 50 % . what is the probability z that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days z = 15 / 64 ans a it is ."
Answer: a
Question (general): if a ^ 2 is divisible by 240 what is the least possible value of integer a ?
Options: a ) 120 , b ) 30 , c ) 90 , d ) 60 , e ) 12
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d"
Answer: d
Question (general): little john had $ 7.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
Options: a ) $ 4.85 , b ) $ 4.15 , c ) $ 4.65 , d ) $ 4.55 , e ) $ 4.05
Rationale: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 7.10 - 3.05 = $ 4.05 answer : e"
Answer: e
Question (general): in a class of 32 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 15
Rationale: "total # of students = 32 avg # of books per student = 2 total # of books = 32 * 2 = 64 # of student borrowed at least 3 books = 32 - 2 - 12 - 10 = 8 # of books borrowed by above 8 students = 60 - ( 12 * 1 ) + ( 10 * 2 ) = 32 considering that 7 out of above 8 students borrowed only 3 books , # of books borrowed = 7 * 3 = 21 so maximum # of books borrowed by any single student = 32 - 21 = 11 option d"
Answer: d
Question (general): the average of 10 numbers is calculated as 21 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 21 + 36 – 26 = 220 = > 220 / 10 = 22 d )"
Answer: d
Question (general): - 45 * 29 + 108 = ?
Options: a ) 1197 , b ) 1897 , c ) - 1197 , d ) - 1900 , e ) none of these
Rationale: "= > - 45 * ( 30 - 1 ) + 108 ; = > - ( 45 * 30 ) + 45 + 108 ; = > - 1350 + 153 = - 1197 . correct option : c"
Answer: c
Question (general): in a family gathering , there is a basket in which there are oranges , bananas and apples . half of the people in the family eat oranges , half of the other half eat bananas and the rest eat apples . if the number of people who eat oranges are 10 less than the total number of people , find the number of people in the gathering .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: let the number of people who eat oranges be x . then , total number of people = x + ( x / 2 ) + ( x / 2 ) = 2 x = > 2 x - 10 = x = > x = 10 = > total number of people were 2 x = 20 option d
Answer: d
Question (general): excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 15 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 77 , d ) 20 , e ) 45
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 15 km with stoppages . stoppage time = time take to travel ( 60 - 15 ) km i . e 45 km at 60 km / hr . stoppage time = 45 / 60 hrs = 45 min . answer : e"
Answer: e
Question (physics): in a garment industry , 12 men working 9 hours per day complete a piece of work in 10 days . to complete the same work in 12 days , working 15 hours a day , the number of men required is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 9 : : 12 : x = > 12 x 15 x x = 10 x 8 x 12 = > x = 10 x 9 x 12 / ( 12 x 15 ) = > x = 7 answer : d"
Answer: d
Question (physics): laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 20 kmph and prasanna moves southward at a speed of 30 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 28 , d ) 27 , e ) 18
Rationale: explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 20 kmph x 1 hr = 20 km total southward prasanna ' s distance = 30 kmph x 1 hr = 30 km total distance between prasanna and laxmi is = 20 + 30 = 50 km . answer : b
Answer: b
Question (physics): there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 4 / 5 th of the speed of the train . how many kilometers will the car cover in 7 hours ?
Options: a ) 375 , b ) 425 , c ) 475 , d ) 525 , e ) 575
Rationale: the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 5 ) / 4 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 7 hours is 75 × 7 = 525 km the answer is d .
Answer: d
Question (general): ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a then what is the units digit for a / ( ( 13 ! ) ^ 4 ) =
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a solving it , we get a / ( ( 13 ! ) ^ 4 ) = ( ( 13 ! ) ^ 4 - 1 ) last digit of ( 13 ! ) ^ 4 will be 0 . so last digit of ( ( 13 ! ) ^ 4 - 1 ) will be 9 . answer : c
Answer: c
Question (general): vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6358 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2200 , c ) 2000 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6358 = x = 6358 / 2.89 = 2200 therefore , amount invested by raghu is rs . 2200 . answer : b"
Answer: b
Question (general): jacob is 16 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 24
Rationale: "j = 16 ; j = 2 b ; b = 16 / 2 = 8 ; twice as old so b = 8 ( now ) + ( 8 ) = 16 ; jacob is 16 + 8 = 24 answer : e"
Answer: e
Question (general): a bag of potatoes weighs 50 lbs divided by half of its weight . how much does the bag of potatoes weigh ?
Options: a ) 10 lb , b ) 20 lb , c ) 30 lb , d ) 40 lb , e ) 50 lb
Rationale: "a 10 lb 50 ÷ 5 = 10 ."
Answer: a
Question (general): in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors a ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have a = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Question (general): the payment per hour for a daily - wages employee is increased by 33.33 and the working time is reduced by 33.33 % . what is the percentage change in the employee ' s income ?
Options: a ) rs . 0.7889 , b ) rs . 0.8889 , c ) rs . 0.9889 , d ) rs . 1.8889 , e ) rs . 2.8889
Rationale: if payment per hr is increased by 33.33 % , then 11.11 % decrease in income if earlier he is getting rs 1 hr per hr and working for 1 hr , income = rs 1 now he is getting rs 1.3333 per hr and working for 0.66667 hrs , income = rs . 0.8889 answer : b
Answer: b
Question (other): the sub - duplicate ratio of 16 : 64 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 4
Rationale: "root ( 16 ) : root ( 64 ) = 4 : 8 = 2 : 4 answer : e"
Answer: e
Question (general): there are 38 students in a certain geometry class . if two thirds of the students are boys and 3 fourths of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 6 , b ) 12 , c ) 19 , d ) 24 , e ) 27
Rationale: 38 * 2 / 3 * 3 / 4 = 19 answer : c
Answer: c
Question (general): a boat crossed a lake from north to east at the speed of 7 km / h , entered a river and covered twice as much distance going upstream at 6 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "one way of solving this is : speed of boat on still water ( lake ) = 7 kmph speed upstream = 6 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 7 + 1 = 8 kmph ans is e"
Answer: e
Question (physics): a bullet train 120 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 4 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 15 sec , c ) 12 sec , d ) 8 sec , e ) 16 sec
Rationale: "d 8 sec speed of the bullet train relative to man = ( 50 + 4 ) kmph = 54 * 5 / 18 m / sec = 45 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 120 m at ( 45 / 3 ) m / sec = ( 120 * 3 / 45 ) sec = 8 sec"
Answer: d
Question (general): a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 8 is
Options: a ) 189 , b ) 197 , c ) 221 , d ) 227 , e ) 230
Rationale: "in that case , the sophie prime numbers greater than 8 are 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be a ."
Answer: a
Question (general): how many digits will be there to the right of the decimal point in the product of 89.635 and . 02218 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : sum of decimal places = 3 + 5 = 8 the last digit to the extreme right is zero ( since 5 x 8 = 40 ) hence , there will be 7 significant digits to the right of the decimal point . answer : option c"
Answer: c
Question (general): 70,76 , 74,85 , 90,105 , 105,130 , 130,130 the list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . if the standard deviation of the 10 running times is 22.4 , rounded to the nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: how many of the 10 running times are more than one sd below the meanmeans how many data points from given 10 are less thanmean - 1 sd . we are given that sd = 22.4 , so we should find mean - - > mean = 100 - - > there are only 3 data points below 100 - 22.4 = 77.6 , namely 70 75 , and 74 . answer : c .
Answer: c
Question (gain): if the cost price of 60 articles is equal to the selling price of 40 articles , then what is the percent profit ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 40 y = 60 x y = 1.5 x the answer is c ."
Answer: c
Question (gain): john is the owner of a company and for thanksgiving he wants to give a turkey to each employee to celebrate the holiday . each turkey cost him $ 25 . if he has 85 employees , how much would john need to spend ?
Options: a ) $ 2125 , b ) $ 1320 , c ) $ 2000 , d ) $ 1580 , e ) $ 2000.75
Rationale: answer is ( a ) . if john wants to give each of his employees a turkey to help celebrate the thanksgiving holiday and each one costs him $ 25 multiplied by the number of employees ( 85 ) , he would have to pay a total of $ 2125 .
Answer: a
Question (general): set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 5 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 5
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is e"
Answer: e
Question (general): there are 28 balls which are red , blue or green . if 12 balls are green and the sum of red balls and green balls is less than 24 , at most how many red balls are there ?
Options: a ) 10 , b ) 12 , c ) 11 , d ) 13 , e ) 14
Rationale: r + g + b = 28 g = 12 r + g < 24 = > r + 12 < 24 = > r < 12 = > at most 11 red balls answer : c
Answer: c
Question (gain): a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 480 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 4000 , d ) 2800 , e ) 2791
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 480 = > 36 x / 100 - 24 x / 100 = 480 = > 12 x / 100 = 480 = > x = 4000 . answer : c"
Answer: c
Question (gain): what is 66.67 % of 804 ?
Options: a ) 587.69 , b ) 536 , c ) 627 , d ) 300.87 , e ) 567.67
Rationale: "66.67 % = 2 / 3 2 / 3 of 804 = 2 / 3 * 804 = 536 . . . . ans - b"
Answer: b
Question (geometry): a 7 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ?
Options: a ) 4 / 5 , b ) 6 / 7 , c ) 5 / 8 , d ) 7 / 9 , e ) 9 / 10
Rationale: "the longer wire will form a square with an area more than 1 if the wire is cut at a point within three meters of either end . the probability of this is 6 / 7 . the answer is b ."
Answer: b
Question (physics): a train 200 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 987 , b ) 271 , c ) 72 , d ) 27 , e ) 36
Rationale: "length = speed * time speed = l / t s = 200 / 20 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e"
Answer: e
Question (probability): a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ?
Options: a ) 1 / 16 , b ) 5 / 16 , c ) 2 / 5 , d ) 13 / 16 , e ) 27 / 32
Rationale: fair coin is tossed 5 times . hence total number of outcomes = 2 ^ 5 = 32 . problem asks for probability of getting atleast heads twice . hence if we calculate probability of getting heads exactly once and probability of not getting heads at all and subract it from the total probability of the event which is 1 ( as total probability of certain event will be always 1 ) we can get the probability of getting atleast heads twice . probability of getting exactly one head and no heads = ( number of possible outcomes [ htttt , thttt , tthtt , tttht , tttth , ttttt ] = 6 ) / ( total possible outcomes = 32 ) = > 6 / 32 = 3 / 16 hence probability of getting atleast heads twice = 1 - ( 3 / 16 ) = 13 / 16 = > choice [ d ]
Answer: d
Question (gain): there are 50 students in a class . if 6 % are absent on a particular day , find the number of students present in the class .
Options: a ) 47 , b ) 36 , c ) 28 , d ) 12 , e ) 11
Rationale: "number of students absent on a particular day = 6 % of 50 i . e . , 6 / 100 × 50 = 3 therefore , the number of students present = 50 - 3 = 47 students . answer : a"
Answer: a