Institution: Bangladesh Bank Exam: Officer (General) |-Sonali | Janata | Bangladesh Krishi_Bangladesh Development bank ২৪.০৫.২০১৯ ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To understand why the correct answer is 7, let's analyze the problem step by step.

We have a number \( N \) that when divided by 7 gives a remainder of 0. This means that \( N \) is a multiple of 7, which we can express as \( N = 7k \) for some integer \( k \).

Next, we consider what happens when \( N \) is divided by 14. Since 14 is \( 2 \times 7 \), if \( N \) is a multiple of 7, the possibilities for the remainder when dividing by 14 must lie between 0 and 13 (the possible remainders in modular arithmetic).

The specific condition given states that the remainder is not 0 when \( N \) is divided by 14. Thus, \( N \) cannot be a multiple of 14.

The multiples of 7 are \( 0, 7, 14, 21, 28, \) etc. The number 0 and multiples of 14 (like 14, 28,...) will give a remainder of 0 when divided by 14. Therefore, valid candidates from the multiples of 7 that are not multiples of 14 are numbers like 7, 21, etc.

When we divide these candidates by 14, we find that:
- \( 7 \div 14 \) gives a remainder of 7.
- \( 21 \div 14 \) gives a remainder of 7.

Since 7 is the only number within the range 0 to 13 that works alongside our conditions, the correct answer is 7.