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: We need to count how many letters remain after replacing:

• Multiples of 5 → symbols
• Multiples of 7 → digits

Step 1:Total letters in English alphabet: \[ 26 \]
Step 2:Find multiples of 5 within 1 to 26: \[ 5, 10, 15, 20, 25 \quad (5 \text{ numbers}) \]
Step 3:Find multiples of 7: \[ 7, 14, 21 \quad (3 \text{ numbers}) \]
Step 4:Check for common multiples (LCM of 5 and 7 = 35).
No common multiples within 26.
Step 5:Total replaced positions: \[ 5 + 3 = 8 \]
Step 6:Remaining letters: \[ 26 - 8 = 18 \]
Step 7:Final Answer: \[ 18 \]