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 nineth 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.

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