Test each statement

A statement is sufficient when every case consistent with the question and that statement gives the same answer. Finding one possible answer is not enough if another is still possible. The information must also be consistent: impossible conditions do not establish an answer.

Test statement 1 alone. Start over and test statement 2 alone, without borrowing anything from statement 1. If neither works alone, test both together.

The five outcomes are: only statement 1 works; only statement 2 works; both are needed; either works alone; or even both together are insufficient.

For a yes/no question, a definite no is just as sufficient as a definite yes. The point is whether the answer is fixed.

The question asks for x, with x and y any real numbers. Statement 1 says x + y = 10. It allows x = 6 with y = 4, or x = 5 with y = 5. Different values of x are possible, so statement 1 alone is insufficient.

Statement 2 says y = 4. On its own it says nothing about x, so it is also insufficient.

Together, substitute y = 4 into x + y = 10. Then x = 10 − 4 = 6. Exactly one value of x works. Choose the outcome where both statements are needed, not either statement alone.

Again, x and y are real numbers and the question asks for x. Statement 1 says x + y = 12. Statement 2 says y = 5.

First test each statement on its own. If neither fixes x, combine them and ask whether two different answers are still possible. This lesson’s checkpoint asks only whether the combined information is sufficient; the practice uses all five outcomes.