# If the fourth sale is on printers, which one of the following must be true?

Yuer-Wang on November 24, 2019

Explanation plz

Can anyone explain why the 3rd sale must be speakers?

Irina on November 25, 2019

@Yuer-Wang,

Since this is a must be true question, all incorrect answer choices will either be false or could be true, and only the correct answer choice must be true in every scenario. Let's diagram the hypothetical in question. The game requires us to determine the order of sales for seven types of goods - H L M P R S T. If the fourth sale is on printers, which of the following must be true?

T/R __ __ P __ __ __
1. 2. 3. 4. 5. 6. 7

Per rule 2, P & S must be on sale during consecutive weeks, thus S must be on sale either during week 3 or week 5. Let's consider these two scenarios:

(1) If S are on sale during week 3

Since at least two weeks must separate S and H, H must be sold on week 6 or 7.

T/R __ S P __ __ __
/H /H

If H are sold on week 7, T must be sold on week 1:

T __ S P __ __ H

The remaining products - L M R are all free variables and could be in any order, thus we can automatically eliminate any answer choice that involves L, M or R - (A) (C). We can also eliminate (D) and (E) since in this scenario that complies with all the rules T is first and H is seventh. (B) is the only remaining answer choice.

Now let's consider the second scenario and see why (B) must be true:

(2) if S are on sale during week 5

T/R __ __ P S __ __

In this scenario, the only possible placement for H is week 2 in order to comply with the rule that requires at least two weeks separating H and S, but H cannot be #2 because we know that T or R must be #1 and L must be sold during an earlier week than H, and the earliest week during which L could be on sale is #2, thus H can never be #2, meaning it is impossible for S to be on sale during week 5.

T/R H __ P S __ __. < - invalid

Since the initial hypothetical - P sold during week 4 - presented us with two possible scenarios for S - and we have concluded that one of them must be false, we can conclude that the other one must be true - S must be sold during week 3 when P is sold during week 4.

Let me know if this makes sense and if you have any other questions.