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
(A) 141 is a prime number. Incorrect. Its digit sum, \(1+4+1=6\), is divisible by 3, so \(141=3\times47\); it has factors other than 1 and itself.
(B) 2984234 is divisible by 11. Correct. A number is divisible by 11 when the sums of its alternate digits differ by 0 or a multiple of 11. Counting from the right, the digits in the odd places add to \(4+2+8+2=16\) and those in the even places to \(3+4+9=16\); the difference is 0.
(C) 39552 is divisible by 18. Incorrect. Since \(18=2\times9\), the number must be even and divisible by 9. 39552 is even, but its digit sum \(3+9+5+5+2=24\) is not divisible by 9.
(D) The sum of the face values of 3 and 5 in 36251 is 8. Correct. The face value of a digit is the digit itself, wherever it stands, so the sum is \(3+5=8\). (Their place values would be 30000 and 50.)