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Pig vs Hive

Out of four choices, you are requested to select the best possible answer(s).

1. A boy has several colored balls in his bag - 12 white, 15 orange and 25 pink. The lights are out and it is totally dark. Now, how many balls he must take out to make sure that he has a pair of each color?

A. 40

B. 42

C. 6

D. 12

**Answer : ****42**

In this problem, the worst case scenario will be as follows.

**Step 1:** He picks all of same colored balls of the largest group. The largest group is pink.
Therefore, he will be picking all 25 pink balls first.

**Step 2:** Then he picks all of same colored balls of the next largest group. The second
largest group is Orange. Therefore, he will be picking 15 orange balls.

**Step 3:** Now, if he starts picking the remaining balls which are white, he could very well
stop at 2 balls as he would be having a pair of white ball anyway.

Therefore total picks = 25 + 15 + 2 = 42.

**Shortcut:**

If confused, for these kinds of problems you have to add higher values first + 2, leaving the least group. Here least group is white.

Therefore our answer will be 25 pink + 15 orange + 2 = 42

Hence the answer is **42**.

2. Two dice are tossed. The probability that the total score is a prime number is

A. 1 / 6

B. 5 / 12

C. 1 / 2

D. 7 / 9

**Answer : ****5 / 12**

The event “Total score is a prime number when two dice are tossed” occurs in the following 15 ways :

(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6),(6, 1), (6, 5).

Total ways when two dice are thrown = 36

Thus, Required probability = 15 / 36 = 5 / 12

3. A square garden has fourteen posts along each side at equal interval. Find how many posts are there in all four sides:

A. 52

B. 56

C. 60

D. 62

**Answer : ****52**

Since each corner is shared by two sides,

Total posts = 56 - 4 corner posts.

Total posts =52.

4. If a number selected at random from a set which contains only 2 digit numbers, find the probability that the selected number will be a multiple of "8".

A. 1/10

B. 4/45

C. 1/15

D. None of these

**Answer : ****4/45**

There are 90 two digit numbers. (From 10 to 99)

Therefore, the set contains 90 numbers.

We know that the first two digit number that is a multiple of 8 is 16 and every 8th number from 16 will be a multiple of 8.

Therefore, there are 11 (integral value of 90/8 = 11) of those numbers that are divisible by "8".(alternatively the two digit multiples of 8 are 16,24,32,40,48,56,64,72,80,88 and 96)

Then, the required probability is 8/90 = 4/45

5. What is the probability that a number selected at random from the set of 3 digit numbers will be a multiple of "9" and a divisor of 900 ?

A. 1/450

B. 5/36

C. 1/180

D. 7/900

**Answer : ****1/180**

The three digit numbers are 100,101,102,...,999

There are a total of 900 three digit numbers.

We know that the number 99 preceded by 100 is divisible by 9 and then every nine-th number from 101 will be divisible by "9".

Therefore, there are (900/9) 100 of those numbers that are divisible by 9.

Now, the 3 digit divisors of 900 are 900/1, 900/2, 900/3, 900/4, 900/5, 900/6 and 900/9.

i.e., the 3 digit divisors of 900 are 900, 450, 300, 225, 180, 150 and 100. Here, except 150 and 100 other numbers are multiple of 9.

The remaining 5 numbers are both multiple of 9 and a divisor of 900.

Hence, the required ratio = 5/900 = 1/180.