In the subtraction below, some single digits (not necessarily distinct) are…

2026

In the subtraction below, some single digits (not necessarily distinct) are represented by letters. Find the value of 2 × A + 2 × B + 4 × C × D.

   A9C5
−   2B79
--------
   633D

  1. A.

    50

  2. B.

    52

  3. C.

    66

  4. D.

    48

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Show answer & explanation

Correct answer: A

Solution:
Deduce each digit column-wise from A9C5 − 2B79 = 633D.

1. Units column: 5 − 9 needs a borrow, so 15 − 9 = 6. Hence, D = 6.
2. Tens column: after giving that borrow, C becomes C − 1. To get result digit 3, borrow from the hundreds column: (C − 1 + 10) − 7 = 3, so C = 1.
3. Hundreds column: after the borrow to the tens column, 9 becomes 8. Then 8 − B = 3, so B = 5.
4. Thousands column: A − 2 = 6, so A = 8.

Now compute:
2 × A + 2 × B + 4 × C × D
= 2 × 8 + 2 × 5 + 4 × 1 × 6
= 16 + 10 + 24
= 50

Answer: 50.

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