# Which one of the following is a pair of foods of which the organizer of the luncheon must select at least one?

Sean on October 4, 2018

PT 65, S2, Q13

Is there a shortcut for eliminating any answers, or is the only way to do this one by going through each one and placing them "out"?

Mehran on October 16, 2018

@smilde11 the trick here is understanding that the question is asking for the pair of foods of which the organizer must select at least one.

This means if you can show that both variables in a pair not being selected is impossible, you have found the correct answer.

Just based on this, your attention should gravitate to (D) and (E). Why? Because the non-existence of the variables in these answer choices invoke sufficient conditions of our rules allowing us to conclude something else.

The non-existence of the variables in (D) invoke the contrapositives of rules 3 and 4 (i.e. "not O ==> not G"; "not P ==> not W"), telling us that G and W are out (impossible since that makes four variables out).

The non-existence of W in (E) tells us that P is also absent (i.e. "not W ==> not P").

Notice (B) doesn't have this luxury because while "not O" tells us "not G", G is the other variable in (B) as opposed to something else we can conclude.

Hope that helps! Please let us know if you have any other questions.