Institution: AGRANI BANK LTD Exam: Agrani bank Ltd - Senior Officer - 12.08.2011
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To find how many numbers between 1 and 100 are of the form \( 7x + 5 \) where \( x \) is a positive integer, we start with the equation:

\[
y = 7x + 5
\]

where \( y \) is the number we’re interested in. The next step is to determine the possible integer values of \( x \) that keep \( y \) within the range of 1 to 100.

First, we set up the inequality:

\[
1 \leq 7x + 5 \leq 100
\]

Subtracting 5 from all parts of the inequality gives us:

\[
-4 \leq 7x \leq 95
\]

Dividing the entire inequality by 7 results in:

\[
-\frac{4}{7} \leq x \leq \frac{95}{7}
\]

Calculating \( \frac{95}{7} \approx 13.57 \), we can see that \( x \) can take positive integer values from 1 to 13 (since \( x \) must be a positive integer, we ignore the negative part).

Thus, the possible positive integer values of \( x \) are \( 1, 2, 3, \ldots, 13 \). This means there are 13 valid integers for \( x \), leading to 13 different numbers of the form \( 7x + 5 \) within the range of 1 to 100. Hence, the correct answer is **B) 13**.