Substitution is a very useful technique for solving GMAT math problems. It often reduces hard problems to routine simpler ones. In the substitution method, we choose some numbers that have the properties given in the problem and plug them into the answer choices. The answer choice which satisfies all the conditions of the problem is the correct answer.
Example 1: By how much is the greatest of five consecutive even integers greater than the smallest among them?
Choose any 5 consecutive even integers, say 4, 6, 8, 10, 12. The largest in this group is 12 and the smallest is 4. Their difference is 12 – 4 = 8. Hence, the answer is (D).
Example 2: If n is an even integer, which one of the following is an odd integer?
- -2n - 4
- 2n2 - 3
It is given that n is even integer, so choose n as any even integer, say 2. Try substituting 2 in place of n in answer choices, the correct answer will be (D).
Plugging-in is similar to substitution. Instead of choosing some numbers, simply plug-in the answer choices in the problem to get the correct answer.
Example 3: If (a – b)(a + b) = 7 * 13, then which one of the following pairs could be the values of a and b, respectively?
- 7, 13
- 5, 15
- 3, 10
- –10, 3
- –3, –10