Question

When 200 is divided by a positive integer x, the remainder is 12. How many values of x are possible?
1. 3
2. 8
3. 6
4. 2

Answer 1

Correct Answer - Option 1 : 3

Given:

On dividing 200 by x, the remainder is 12.

Concept Used:

Dividend = (Divisor × Quotient) + Remainder 

Calculation:

200 is divisible by x, 

Here 200 is dividend and x is a divisor.

And the remainder is 12.

⇒ xp + 12 = 200

Where p is a quotient.

⇒ xp = 200 – 12

⇒ xp = 188

Now the prime factorization of 188,

⇒ 188 = 2 × 94

⇒ 188 = 2 × 2 × 47

188 is divisible by 2, 4, 47, 94, and 188
But the remainder is 12,

So we will need a number which is greater than 12

⇒ The numbers are 47, 98, and 188

∴ The number of values of x is 3.