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ABC is a three-digit number. When ABC is multiplied by a single-digit number X, the product is 2634. In the three-digit number ABC, the digit in the tens place is equal to half of X. Which of the following statements is/are correct about ABC? (i) The unit digit of ABC is 9 (ii) ABC is a prime number (iii) The sum of the digits of ABC is 16

1. Only (i) and (iii)
2. Only (i) and (ii)
3. Only (iii)
4. All (i), (ii) and (iii)

Correct answer: All (i), (ii) and (iii)

Solution

From 2634, the only suitable single-digit factor satisfying the tens-digit condition leads to ABC = 439 and X = 6. Then the unit digit is 9, 439 is prime, and the digit sum is 4+3+9 = 16.

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