Question

If ABC × DEED = ABCABC, where A, B, C, D, and E are different digits. The values of D and E are:

• A. D = 2, E = 0
• B. D = 0, E = 1
• C. D = 1, E = 0
• D. D = 1, E = 2

Hint:

In number puzzles with repeating patterns, try converting numbers to digit-based expressions and test values logically.

Answer 1

The Correct Option is C

We're given: \[ \text{ABC} \times \text{DEED} = \text{ABCABC} \] Let: - ABC be a 3-digit number, i.e. \( 100A + 10B + C \) - DEED be a 4-digit number, i.e. \( 1000D + 100E + 10E + D = 1001D + 110E \) So the expression becomes: \[ (100A + 10B + C) \times (1001D + 110E) = 100000A + 10000B + 1000C + 100A + 10B + C \Rightarrow \text{ABCABC} \] We test values via trial and error. Try: - ABC = 123 - DEED = 1001 × 1 + 110 × 0 = 1001 Then: \[ 123 \times 1001 = 123123 = \text{ABCABC} \Rightarrow \boxed{D = 1, E = 0} \]