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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 ten’s digit is twice the hundred’s digit and the hundred’s digit is 1/3 the unit’s digit, what is the number?

A. 246
B. 369
C. 531
D. 855
E. 893

 

First, check to see which of the answer-choices has a sum of digits equal to 18.

 

For choice (A), 2 + 4 + 6 ≠ 18. Eliminate.

 

For choice (B), 3 + 6 + 9 = 18. This may be the answer.

 

For choice (C), 5 + 3 + 1 ≠ 18. Eliminate.

 

For choice (D), 8 + 5 + 5 = 18. This too may be the answer.

 

For choice (E), 8 + 9 + 3 ≠ 18. Eliminate.

 

Now, in choice (D), the ten’s digit is not twice the hundred’s digit, 5 ≠ 2  8. Eliminate.

 

Hence, by process of elimination, the answer is (B).

 

Note that we did not need the fact that the hundred’s digit is 1/3 the unit’s digit.
 





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