If ABC x DEED = ABCABC; where A, B, C, D and E are different digits, what are the values of D and E?

Question

Accepted Answer

The equation is ABC x DEED = ABCABC.

We can rewrite ABCABC as ABC x 1000 + ABC, which simplifies to ABC x (1000 + 1) = ABC x 1001.

Substitute this back into the original equation:
ABC x DEED = ABC x 1001

Since ABC is a three-digit number, it is not zero. We can divide both sides by ABC:
DEED = 1001

Now, by comparing the digits of DEED with 1001, we can determine the values of D and E:
D = 1
E = 0
E = 0
D = 1

So, D = 1 and E = 0.

The problem states that A, B, C, D, and E are different digits. Our derived values D=1 and E=0 are different from each other. The remaining digits A, B, C can be chosen from the other available digits (2, 3, 4, 5, 6, 7, 8, 9) to satisfy the condition.

Let's check the options:
A) D = 2, E = 0: DEED would be 2002, not 1001.
B) D = 0, E = 1: DEED would be 0110 (or 110), not 1001.
C) D = 1, E = 0: DEED would be 1001, which matches our derivation. This is correct.
D) D = 1, E = 2: DEED would be 1221, not 1001.

Therefore, the values of D and E are 1 and 0, respectively.

The final answer is C.

Answer

D = 2,E = 0

Answer

D = 0,E = 1

Answer

D = 1,E = 0

Answer

D = 1,E = 2

If ABC x DEED = ABCABC; where A, B, C, D and E are different digits, what are the values of D and E?

Explanation

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