Question

In a 4-digit number 2 digits are repeated, not consecutively. If the value of 5 at the hundreds place is subtracted from the value of the digit at the thousands place, the result is 6,500. Determine the number. (More than one correct answer)

• A. Seven thousand five hundred fifty-seven
• B. Seven thousand five hundred seventy-five
• C. 7,575
• D. 7,557

Answer 1

Answer: (B), (C)

7,575

Detailed step-by-step solution:
1. The number is a 4-digit number. (WB1)
2. In a 4-digit number 2 digits are repeated, not consecutively.
3. The value of 5 at the hundreds place in the number will be $5\times 100=500.\left(WB1\right)$
4. This 500 is subtracted from the value of the digit at the thousands place and gives 6,500.
5. The value at the thousands place should be 500 + 6,500 = 7,000. (WB3)
6. So the digit at the thousands place is 7 and our other digit is 5.
7. Let us form the 4-digit number in which 5 and 7 will not repeat consecutively. (WB4)
8. The only way in which 5 and 7 will not repeat consecutively is 7,575.
9. The word form of 7,575 is seven thousand five hundred seventy-five. (WB5)
10. Options A and D are correct.

WB:

Q: Why have we not selected 7,755 and 7,557?

A: For the numbers 7,755 and 7,557, at least one digit is repeated.