Answer Logic Questions on the SAT Math Test
The SAT occasionally tosses you a logic question, disguised as a simple math question. It gives you a set of statements or conditions, sometimes called the facts. These statements describe the relationship between or among people, items, or events.
You may, for example, be given statements about students at a school and then be asked which ones can be assigned to the same classes. You may be told facts about events that can happen on certain days of the week or about what different combinations of items are possible.
Before you start doodling to solve a logic problem, be sure you know all the people or items involved. Make a “program” of all the players by writing down the pool of people or events. For example, if the question talks about five teachers, Mahaffey, Negy, O’Leary, Plotnitz, and Quivera, use initials and jot down M, N, O, P, and Q on the test booklet.
Next, use a diagram to show the relationship between people or events. Here are a few of the most common diagrams.
- Calendar: Draw a simple calendar and fill in the events that happen on particular days.
- Ordering or sequencing: You may have a relationship problem in which some people are taller or heavier than others. Write a line of people, with A above B if A is taller than B, C at the bottom if she is the shortest, and so on.
- Grouping or membership: This problem asks you which items or people could belong to which group. For example, membership in a club may require four out of five characteristics. Often this type of question doesn’t require a graph, but it does require a lot of if … then statements, such as “If A is in the group, then B isn’t.”
Try your hand at this logic-based example.
Five spices — lemon pepper, marjoram, nutmeg, oregano, and paprika — are aligned next to one another between the left and right sides of a kitchen cabinet. Their arrangement must conform to the following conditions:
- The marjoram is immediately to the right of the paprika.
- The oregano is either all the way to the left or second from the left.
- The lemon pepper is farther left than the nutmeg.
- Which of the following could not be true?
- A. The paprika is second from the left.
- B. The marjoram is to the right of the lemon pepper.
- C. The nutmeg is exactly in the middle.
- D. The lemon pepper is exactly in the middle.
The answer is Choice (D). To help keep track of the information, write out initials for the roster of spices — L, M, N, O, and P — and make five simple dashes to represent the five positions of the spices:
___ ___ ___ ___ ___
The easiest condition to accommodate is the one that indicates that the oregano must be first or second from the left. Draw these two possibilities:
O ___ ___ ___ ___
___ O ___ ___ ___
The next thing to note is that the paprika and marjoram must always move together. So test out the answer choices, making sure to also fulfill the third condition. Choice (A) is fine, because you can write O, P, M, L, N and meet all conditions. Choice (B) also works, because you can write O, L, P, M, N. And for Choice (C), you can write either O, L, N, P, M or L, O, N, P, M.
Choice (D) is no good, though. If L is in the middle, you have to put P and M to its right, because they always travel together. But that doesn’t leave room to put N to the right of L, so you can’t fulfill the third condition. Choice (D) is the only option that doesn’t work, so that’s your answer.