MU-NLPC/Calc-aqua_rat huggingface dataset:
The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.
Choose the correct option:
A) 40 yrs
B) 42 yrs
C) 45 yrs
D) 46 yrs
E) 47 yrs

Solution: The average age of 30 boys of a class is equal to 14 yrs:   i.e Sum of all boys:30*14   include class teacher:31 candidates in a class   & avg age is:15 yr   i.e. sum of all:31*15(include class teacher)=465   so,the age of the class teacher:  465-420= 
  465-420 = 45
45yr   answer will be 45 yrs   ANSWER:45 yrs
Answer: C
In how many years, Rs. 150 will produce the same interest at 6% as Rs. 400 produce in 2 years at 4½% ?
Pick one.
A) 4 years B) 6 years C) 8 years D) 9 years E) 12 years

Solution: Explanation :   Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.400 at 4½ % for 2 years   150×6×n/100=400×9/2×2/100   150×6×n=400×9/2×2   150×6×n=400×9   n=4 years   4 yearsnswer : Option 4 years
Answer: A
If P = k^3 – k, where k and P are positive integers, and k is given by the expression k=(10x)n+54k=(10x)n+54, where x and n are positive integers, then what is the remainder when P is divided by 4 ?	Choose the correct choice from the following answers.
A) 0
B) 1
C) 2
D) 3
E) cannot be determined

Solution: p=k^3-k   =k(k^2-1)   =(k-1)k(k+1)   as can be seen, p is a product of three consecutive integers. now k can be both even and odd.   now look into the given expression of k   k=(10x)n+54k=(10x)n+54   5454 will always be odd. and (10x)n(10x)n will always be even   thus k= even + odd =odd   0lso, k =1 is not possible ( because p is a positive integer)   so lets try k=3   p=(3-1)(3)(3+1)   =2*3*4   0NSWER:0
Answer: A
If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?  Choose one
A) 40 B) 60 C) 100 D) 140 E) 160

Solution: Explanation:   Let’s say t = total current inventory of chairs. The first sentence states that 50 + t = (3/2)t. First solve for the current inventory:   50 + t = (3/2)t   50 = (3/2)t − t   50 = (1/2)t   100 = t   The manager wants to increase this by 40%.   40% of 100 is 40, so the new inventory will be 140.   Answer: (140).
Answer: D
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent Q of the distribution is less than m +d ?	Choose the correct answer: A) 16% B) 32% C) 48% D) 84% E) 92%

Solution: D   The prompt says that 68% of the population lies between m-d and m+d.   Thus, 32% of the population is less than m-d or greater than m+d.   Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.   Thus, Q=(68+16)% or (100-16)% of the population is less than m+d.
Answer: D
Given 3^n, for any real integer of n, which of the following is a possible resultant?
Choose the correct option.
A) 242	B) 244	C) 243	D) 254	E) 245

Solution: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.   3^1 = 3   3^2 = 9   3^3 = 27   3^4 = 81   3^5 = 243   Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.   Cycle of 4, the answer with last digit 3.   Answer: 243
Answer: C
Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 8, when a # b = 100?  Choose the correct choice from the following answers
A) 5  B) 8  C) 10  D) 13  E) 17

Solution: OFFICIAL SOLUTION:   (B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So   4a² + 4b² + 8ab = 100   We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore   (2a + 2b)² = 100.   (2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 8 = 10/2 + 8= 
10/2 + 8 = 13
13.   The correct answer is 13
Answer: D
How many odd three-digit integers greater than 700 are there such that all their digits are different?
Choose the correct choice from the following options
A) 40 B) 56 C) 72 D) 80 E) 104

Solution: 2 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 144   Now take numbers in the range 700 - 900.   Total numbers where all digits are different = 144 (as before)   [highlight]Number of odd numbers = 2 * 8 * 5= 
2 * 8 * 5 = 80
80[/highlight] (now there are 5 possibilities for the unit's digit)   80
Answer: D
The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?  Choose the correct choice from the following options:
A) 5 B) 4 C) 1/2 D) 1/5 E) 1/8

Solution: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5.   The answer is 1/5.
Answer: D
The months of the calendar have been coded in the following ways:
January = 1071
February = 682
March = 1353
April = 154
May = 1335
June = 1046
July = 1047
August = 168
Using the same coding method, can you find out how to code September  Select:  A) 19|9|9  B) 19|9|8  C) 19|9|7  D) 19|9|6  E) 19|9|5

Solution: Solution:   19|9|9   Explanation:   This is simple. All the months have been coded with a distinctive way.   Let's see about January:   January = 1071 = 10|7|1   10 is the position of J, the first letter of January in alphabetical order.   7 is the number of letters used in forming the word January.   1 is the position of January in the calendar.   For February:   February = 682 = 6|8|2   6 is the position of F, the first letter of February in the alphabetical order.   8 are the number of letters used in forming the word.   2 is the position of February in the calendar.   Similarly, September = 19|9|9   19 is the position of S, the first letter of September in the alphabetical order.   9 are the number of letters used in forming the word.   9 is the position of September in the calendar.   19|9|9nswer 19|9|9
Answer: A
The price of a certain painting increased by 10% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
Choose one:  A) 102%  B) 105%  C) 95%  D) 93.5%  E) 90%

Solution: Easiest thing to do: Assume that price is 100   Price at the end of yr 1: 100+ 10 = 110   Price at the end of year 2 = 110 - 110*0.15 = 110*0.85= 
110*0.85 = 93.5
93.5   Hence required answer= (93.5/100)*100= 
(93.5/100)*100 = 93.5
93.5%   Answer is 93.5%.
Answer: D
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Pick:
A) 1877 ways B) 1440 ways C) 1678 ways D) 1976 ways E) 1286 ways

Solution: In the word, "MATERIAL" there are three vowels A, I, E.   If all the vowels are together, the arrangement is MTRL'AAEI'.   Consider AAEI as one unit. The arrangement is as follows.   M T R L A A E I   The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.   Number of required ways of arranging the above letters = 5! * 4!/2!   = (120 * 24)/2= 
(120 * 24)/2 = 1_440
1440 ways.   Answer: 1440 ways
Answer: B
total 52 matches are conducted in Knockout match type. How many players will be participated in that tournament?
Choose one
A) 60 B) 51 C) 53 D) 56 E) 50

Solution: 51 players   ANSWER:51
Answer: B
The sum of three numbers is 343. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
Pick one:
A) 20	B) 30	C) 38	D) 105	E) None of these

Solution: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15   and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24   Therefore, A : B : C = 10 : 15 : 24   ∴ A : B : C = 10 : 15 : 24   Let the number be 10x, 15x and 24x.   Then, 10x + 15x + 24x = 343   or 49x = 343 or x = 7   ⇒ Second number = 15x = 15 × 7 = 105   Answer 105
Answer: D
Pipes A and B can fill a tank in 8 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
Choose the correct choice from the following choices: A) 1 13/17 hours B) 2 8/11 hours C) 3 9/17 hours D) 4 4/5 hours E) None

Solution: Solution   Net part filled in 1 hour	= (1/8 + 1/6 -1/12)   = 5/24.   Therefore, the tank will be full in 24/5 hrs.	â€¹=â€º 4 4/5 hrs.   Answer 4 4/5 hours
Answer: D
WHEN A PERSON SELLS TWO ITEMS $1300 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:	Choose the correct answer:
A) no loss no gain B) 2% gain C) 5% gain D) 4% loss E) 1% loss

Solution: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.   Answer : 4% loss
Answer: D
In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 30 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?  Choose one:  A) 64%  B) 66%  C) 72%  D) 76%  E) 80%

Solution: Let in May Lee family's total income =100   in May Mrs Lee's income =60   in May rest of the family's income = 40   In june Mrs Lees income = 60*130/100= 
60*130/100 = 78
78   In june Total income= 78+ 40= 
78+ 40 = 118
118   % of Mrs Lee's income= 72/112 =66.10   (66%)
Answer: B
If you roll 2 dice, what is the probability of rolling a 5?
Answers:
A) 1/9 B) 1/12 C) 1/3 D) 5/12 E) 2/13

Solution: The answer is 1/9, as there are 4/36 ways to add the sum of 5 with 2 dice. 1/9nswer: 1/9
Answer: A
There are 12 red balls, 10 blue balls, 12 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?  Options
A) 10 B) 23 C) 43 D) 40 E) 16

Solution: The worst case scenario would be if we pick 11 red balls, 9 blue balls, 11 (?) balls and 8 black balls. In this case we'll have  11+9+11+8= 
 11+9+11+8 = 39
39 balls and still won't have all the balls of one color. The next 40rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.   Answer: 40
Answer: D
Two poles of height 6 meters and 11 meters stand on a plane ground. If the distance between their feet is 12 meters then find the difference in the distance between their tops:  Choose the correct option.
A) 12m B) 5m C) 13m D) 11m E) 12m

Solution: distance between their tops = sqrt( 12^2+(11-6)^2) = sqrt 169=13m   ANSWER:13m
Answer: C
One fourth of a solution that was 10 percent salt by weight was replaced by a second solution resulting in a solution that was 16 percent salt by weight. The second solution was what percent salt by weight ?	Choose the correct choice:
A) 34%
B) 24%
C) 22%
D) 18%
E) 8.5%

Solution: EQ can be written as ...   let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of salt in 2nd sol)=34%=34%
Answer: A
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 5x boxes?  Choose the correct choice:
A) 3 minutes  B) 4 minutes  C) 5 minutes  D) 6 minutes  E) 10 minutes

Solution: Rate = Work / Time   Given Rate of Machine A = X / 10 min   Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .   Rate of Machine B = 4x / 10   we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates   let's first find the combined Rate of Machine A and B   Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10   Now combine Time = combine work needs to be done / Combine Rate = 5x/5x * 10 = 10 Min   Ans: 10 minutes5 /5  * 10= 
5 /5  * 10 = 10
10 Min   Ans: 10 minutes
Answer: E
A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone?  Choose the correct choice from the following options:
A) 6 days	B) 8 days	C) 12 days	D) 10 days	E) 5 days

Solution: Explanation:   A and B 1day's work = 1/6   A alone can do 1day's work = 1/12   what time B will take to do the work alone?   B = (A+B) - A = (1/6) - (1/12) = 12 Days   Answer: Option 12 days
Answer: C
28, 26, 21, 19, 14, 12, ?  Options:
A) 3	B) 2	C) 8	D) 7	E) 5

Solution: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....   Answer : 7.
Answer: D
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 8000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college?  Select the correct option:
A) $20000
B) $15000
C) $32000
D) $10000
E) $9000

Solution: Since investment doubles in 70/r years then for r=4 it'll double in 70/4=~18 years (we are not asked about the exact amount so such an approximation will do). Thus in 36 years investment will double twice and become ($8,000*2)*2=$32,000 (after 18 years investment will become $8,000*2=$16,000 and in another 18 years it'll become $16,000*2=$32,000).   Answer: $32000.
Answer: C
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many X such committees are possible? Select the correct option.
A) X=20  B) X=40  C) X=50  D) X=80  E) 120

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=80.   Answer: X=80.
Answer: D
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?  Choose the correct choice from the following.
A) 10
B) 15
C) 21
D) 18
E) 29

Solution: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days   So fodder will be available for  (60 + 8 + 12)= 
 (60 + 8 + 12) = 80
80 cows c 24x60	.0 .   for-^—=18 days.   18
Answer: D
14, 18, x, 20
The median of the list of positive integers above is 16. Which of the following could be the average (arithmetic mean) of the list?	Select the correct option
A) 3  B) 5.5  C) 6.25  D) 16  E) 7.5

Solution: GivenThe median of the list of positive integers above is 16   So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 16   so the sequence will be x 14 18 20   Lets say x = 12, which gives us mean = sum/4 = 16   16 is correct
Answer: D
The price of an article is reduced by 25% in order to
restore the must be increased by ? Choose the correct option.
A) 3/100%
B) 100/3%
C) 6/25%
D) 25/6%
E) 4/75%

Solution: [x/(100-x)]*100 =[25/(100-25)]*100   =(25/75)*100=100/3%   ANSWER 100/3% 100/3%
Answer: B
With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Answers: A) 287 km B) 480 km C) 127 km D) 177 km E) 2698 km

Solution: Let the distance be x km. Then,   x/(7 1/2) - x/8 = 4   2x/15 - x/8 = 4 => x   = 480 km   Answer: 480 km
Answer: B
The salary of a person was reduced by 15%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?  Pick
A) 10%  B) 17.6%  C) 13.7%  D) 15.1%  E) 12.3%

Solution: Let the original salary be $100   New salary = $85   Increase on 85=15   Increase on 100 = 15/85* 100 = 17.6%   Answer is 17.6%
Answer: B
On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 30% 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?	Choose the correct choice from the following options:
A) 10.5%
B) 12.5%
C) 15%
D) 22%
E) 14.28%

Solution: 0.1 M = 0.70 E   => E/M = 1/7 * 100 = 14.28%   So answer is E.   M - # of Motorists   14.28% - # of Motorists exceeding speed
Answer: E
Two numbers are such that the ratio between them is 3:5 but if each is increased by 10, the ratio between them becomes 5 : 7, the numbers are Choose the correct choice from the following options:
A) 3, 5
B) 7, 9
C) 13, 22
D) 15, 25
E) None

Solution: Explanation:   Let the numbers be 3a and 5a   Then 3a+10/5a+10=5/7   ⇒7(3a+10)=5(5a+10)⇒a=5   The numbers are 15 & 25   Correct Option: 15, 25
Answer: D
A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side. Answers.
A) 2 B) 4 C) 6 D) 8 E) 9

Solution: Adjacent sides of parallelogram = 2 cm and 9 cm   Distance between shorter sides = 8 cm   Area of parallelogram = b × h   = 9 × 8 cm²   = 72 cm²   Again, area of parallelogram = b × h   72 = 12 × h   h = 72/12= 
72/12 = 6
6 cm   Therefore, the distance between its longer side= 6 cm.   ANSWER-OPTION 6
Answer: C
A person buys an article at Rs.550. At what price should he sell the article so as to make a profit of 30%?  Select the correct option:	A) 600	B) 715	C) 772	D) 662	E) 521

Solution: Cost price = Rs.550   profit = 30% of 550 = Rs.165   Selling price = Cost price + Profit   = 550 + 165= 
550 + 165 = 715
715   Answer: 715
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:	Options:
A) 12 years B) 14 years C) 15 years D) 20 years E) 11 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   ANSWER 14 years
Answer: B
If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?  Choose one:  A) 3  B) 6  C) 11  D) 22  E) 222

Solution: Maybe there is a faster way to do it but I did it like this:   How many ways can you arrange abc?   abc   acb   bac   bca   cab   cba   which are equivalent to:   100a + 10b + c   100a + 10c + b   100b + 10a + c   100b + 10c + a   100c + 10a + b   100c + 10b + a   if you add them all together you get 222a + 222b + 222c   ANSW222R:222
Answer: E
On Thursday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up C percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of C?
Select:
A) 20%  B) 30%  C) 33 1⁄3%  D) 40%  E) 50%

Solution: Let the original price be 100   discounted Price = 80   New Price = 20 +100= 
20 +100 = 120
120   C=(40/80)*100   Ans:50%
Answer: E
In a group of cows and chickens, the number of legs was 18 more than twice the number of heads. The number of cows was:
Choose the most appropriate option:
A) 5
B) 7
C) 9
D) 12
E) 14

Solution: Let the number of cows be x and their legs be 4x.   Let the number of chicken be y and their legs be 2x.   Total number of legs = 4x + 2y.   Total number of heads = x + y.   The number of legs was 18 more than twice the number of heads.   Therefore, 2 × (x + y) + 18 = 4x + 2y.   or, 2x + 2y + 18 = 4x + 2y.   or, 2x + 18 = 4x [subtracting 2y from both sides].   or, 18 = 4x – 2x [subtracting 2x from both sides].   or, 18 = 2x.   or, x = 9 [dividing by 2 on both sides].   Therefore, the number of cows = 9.   9orrect Answer:9)9
Answer: C
If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers.
Choose one
A) 50  B) 30  C) 125  D) 25  E) None of these

Solution: H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750= 
18750/750 = 25
25.   ANSWER:25
Answer: D
3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?  Choose the correct choice from the following options
A) 40
B) 45
C) 50
D) 35
E) 30

Solution: Work done by 4 men and 6 women in 1 day = 1/8   Work done by 3 men and 7 women in 1 day = 1/10   Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as   4m + 6w = 1/8 ---(1)   3m + 7w = 1/10 ---(2)   Solving equation (1) and (2) , we get m=11/400 and w=1/400   40mount of work 10 women can do in a day = 10 × (1/400) = 1/40   Ie, 10 women can complete the work in 40 days   40nswer is 40.
Answer: A
The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate Y of movement for his trip along the moving walkway?  Choose the correct choice from the following options
A) 2 feet per second B) 2.5 feet per second C) 3 feet per second D) 4 feet per second E) 5 feet per second

Solution: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average Y MUST bebetween3-6 ft per second or the Earth is FLAT!!!.   So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer 5 feet per second as plausible.
Answer: E
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Select:	A) 180 m	B) 240 m	C) 260 m	D) 280 m	E) 380 m

Solution: Speed = 54 x 5/18 = 15 m/s   Length of the train = (15 x 20)m = 300 m.   Let the length of the platform be x metres.   Then, (x + 300)/36 = 15   --> x + 300 = 540   x = 240m.   Answer : 240 m.
Answer: B
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ? Select the correct option.
A) 5/ 19	B) 5/ 12	C) 5/ 27	D) 5/ 18	E) 5/ 11

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9)   =5/ 12   Answer: 5/ 12
Answer: B