A four-digit odd number ‘A’ whose unit digit is not 5 and when divided by a…
2023
A four-digit odd number ‘A’ whose unit digit is not 5 and when divided by a prime number gives resultant as a three-digit number ‘B’ whose tens place is 0. Sum of digit of A is eight while that of B is 5. Which of the following statement/s is/are correct about A and B.
I. Product of the digits of A is equal to its sum of the digit
II. Difference between the hundred place digit of A and B is 3
III. Sum of A and B is 1624
Answer: E. Only (I) and (III) — The number B has three digits, tens digit 0 and digit sum 5. The valid value that satisfies the prime-division condition is B = 203, and A = 203 x 7 = 1421. A…
- A.
Only (II)
- B.
All of the above
- C.
Only (III)
- D.
Only (I)
- E.
Only (I) and (III)
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Correct answer: E
The number B has three digits, tens digit 0 and digit sum 5. The valid value that satisfies the prime-division condition is B = 203, and A = 203 x 7 = 1421. A is a four-digit odd number, its unit digit is not 5 and its digit sum is 1 + 4 + 2 + 1 = 8. Statement I is true because 1 x 4 x 2 x 1 = 8. Statement II is false because the hundreds digits differ by 2, not 3. Statement III is true because 1421 + 203 = 1624. Therefore only I and III are correct.