# Numbers Questions

Q:

How many numbers with distinct digits are possible product of whose digits is 18?

 A) 12 B) 8 C) 6 D) 4

Explanation:

Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92.

Three-digit numbers: The three digits can be 1, 2 and 9$\inline&space;\small&space;\Rightarrow$ 3! Or 6 possibilities.

We cannot have three digits as (3, 3, 2) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

4 124
Q:

The difference between the squares of two consecutive odd integers is always divisible by ?

 A) 8 B) 2 C) 6 D) 4

Explanation:

Let the two consecutive odd integers be (2x + 1) and (2x + 3)

Then,

(2x + 3)2 - (2x + 1)2

= (2x + 3 + 2x + 1) (2x + 3 - 2x - 1)

= (4x + 4)(2)
= 8 (x + 1), which is always divisible by 8

4 123
Q:

If x is a whole number, then x²(x² - 1) is always divisible by ?

 A) 4 B) 8 C) 12 D) None

Explanation:

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.

2 109
Q:

Find the next number in the series 141,137,146,130,155,119,...

 A) 147 B) 168 C) 162 D) 182

Explanation:

The pattern is -4, +9,-16, +25, -36

The next number=119+49=168

4 101
Q:

What should be the maximum value of B in the following equation?
8A9 – 6B2 + 4C6 = 723

 A) 4 B) 1 C) 5 D) 7

Explanation:

1 1
8 A 9
+ 4 C 6
-  6 B 2
7 2 3
We may represent the given sum, as shown below:

1 + A + C - B = 12
A + C - B = 11

Now,giving the maximum values to A and C, i.e.

A = 9 and C = 9, we get B = 7.