Question

If x is the least positive integer satisfying 100 ≡ x(mod 6), then (2x+1) is equal to :

• A. 7
• B. 5
• C. 9
• D. 11

Answer 1

The Correct Option is C

To solve for the least positive integer \( x \) satisfying the congruence \( 100 \equiv x \pmod{6} \), we need to understand what this modulus operation implies. The expression \( 100 \equiv x \pmod{6} \) means that when 100 is divided by 6, the remainder is \( x \).

First, perform the division of 100 by 6:

100 ÷ 6 = 16 remainder 4

So, \( x = 4 \) as 4 is the remainder when 100 is divided by 6. This makes \( x \) the least positive integer satisfying the condition.

Next, substitute \( x = 4 \) into the expression \( 2x + 1 \):

\( 2x + 1 = 2(4) + 1 = 8 + 1 = 9 \)

Therefore, when calculating \( (2x+1) \) with \( x \) found, the result is 9.

The correct answer is: 9