Consider the following statements
(A) 141 is a prime number.
(B) 2984234 is divisible by 11.
(C) 39552 is divisible by 18.
(D) The sum of the face values of 3 and 5 in 36251 is 8.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (B) and (D) only
Evaluation of Each Statement:
(A) 141 is a prime number. False. 141 is composite because it is divisible by 3 (sum of digits: 1 + 4 + 1 = 6, divisible by 3) and 47 (141 = 3 × 47).
(B) 2984234 is divisible by 11. True. Using the divisibility rule for 11 (alternating sum or difference of sums in odd/even positions from left): Digits: 2, 9, 8, 4, 2, 3, 4 Odd positions: 2 + 8 + 2 + 4 = 16 Even positions: 9 + 4 + 3 = 16 Difference: 16 - 16 = 0 (divisible by 11). Direct check: 2984234 ÷ 11 = 271294 (exact integer).
(C) 39552 is divisible by 18. False. For divisibility by 18, the number must be divisible by both 2 and 9.
- It is even (ends in 2), so divisible by 2.
- Sum of digits: 3 + 9 + 5 + 5 + 2 = 24 (not divisible by 9, since 24 ÷ 9 = 2.666...). Direct check: 39552 ÷ 18 ≈ 2197.333 (not an integer).
(D) The sum of the face values of 3 and 5 in 36251 is 8. True. Face value of a digit is the digit itself (independent of place value): 3 + 5 = 8.
Thus, only statements (B) and (D) are correct.