Numbers Questions

Given  65×359×113

⇒2×35×5×79×113 

⇒25×35×59×79×113

Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

In case (A), x and y could, for example, both be equal fractions and x/y would be an integer.

On dividing 627349 by 15, we get remainder = 4.
Therefore, the obtained remainder is the least number to be subtracted from the given number so that the the mnumber is divisible by 15.
Here 4 is the least number to be subtracted from 627349 so that it is divisible by 15.

2n+2n22x2n - 2n = 2n1 + 122n(2-1) = 32

   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.

Number = quotient x divisor + remainder;
so, here
number = 138 k + 26
=> (23 x 6k) + (23+3)
=> 23(6k+1)+3
so, remainder is 3.

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.

Every integer is a rational number since Q can be 1.

Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.

Hence, 4 is a rational number in the given options.

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 => 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.