**Substitution (Plugging In)**

Sometimes instead of making up numbers to substitute into the problem, we can use the actual answer-choices. This is called Plugging In. It is a very effective technique but not as common as Substitution.

Example

The digits of a three-digit number add up to 18. If the tenâ€™s digit is twice the hundredâ€™s digit and the hundredâ€™s digit is 1/3 the unitâ€™s digit, what is the number?

- 246
- 369
- 531
- 855
- 893

Solution

First, check to see which of the answer-choices has a sum of digits equal to 18.
For choice (A), 2 + 4 + 6 â‰ 18. Eliminate.
For choice (B), 3 + 6 + 9 = 18. This may be the answer.
For choice (C), 5 + 3 + 1 â‰ 18. Eliminate.
For choice (D), 8 + 5 + 5 = 18. This too may be the answer.
For choice (E), 8 + 9 + 3 â‰ 18. Eliminate.
Now, in choice (D), the tenâ€™s digit is
Hence, by process of elimination, the answer is (B).

__not__twice the hundredâ€™s digit, 5 â‰ 2 Ã— 8.**Note**that we did not need the fact that the hundredâ€™s digit is 1/3 the unitâ€™s digit.