Question

If the positions corresponding to the multiples of 5 in the English alphabet are replaced by symbols and that of multiples of 7 by digits, how many letters will be left?

• A. 15
• B. 17
• C. 18
• D. 21

Hint:

When dealing with multiples, always check for \textbf{overlap using LCM} to avoid double counting.

Answer 1

The Correct Option is C

Concept: This problem involves eliminating certain alphabet positions based on divisibility rules and counting the remaining valid letters. Step 1:Total number of letters in the English alphabet:
\[ 26 \]
Step 2:Identify multiples of 5 between 1 and 26:
\[ 5, 10, 15, 20, 25 \quad (5 \text{ numbers}) \]
Step 3:Identify multiples of 7 between 1 and 26:
\[ 7, 14, 21 \quad (3 \text{ numbers}) \]
Step 4:Check for overlap.
The least common multiple of 5 and 7 is 35, which lies outside the range 1–26, so there are no common elements.
Step 5:Total eliminated positions:
\[ 5 + 3 = 8 \]
Step 6:Remaining letters:
\[ 26 - 8 = 18 \]
Final Answer: 18