# Numbers Questions

Q:

Find the remainder when 1234 x 1235 x 1237 is divided by 8.

 A) 4 B) 2 C) 0 D) 6

Explanation:

When we divide 1234 by 8, remainder is 2

When we divide 1235 by 8, remainder is 3

When we divide 1237 by 8, remainder is 5

$\inline \fn_jvn \small \Rightarrow 2\times 3\times 5=30$

As 30 will not be the remainder because it is greater than 8,

when 30 divided by 8, remainder = 6.

Filed Under: Numbers - Quantitative Aptitude - Arithmetic Ability
Exam Prep: CAT
Job Role: Bank PO

6 369
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

4 367
Q:

What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

 A) 2 B) 3 C) 4 D) 5

Explanation:

By trial and error method, we get
2880/3 = 960 is not a perfect square
2880/4 = 720 is not a perfect square
2880/5 = 576 which is perfect square of 24
Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

4 353
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.

4 294
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.