Which one of the following could be the order in which the programs are shown, from earliest to latest?

Irina on November 12, 2019

@Meredith,

This is a long game with 7 questions, so the target time is probably more in the 12+ minute range rather than 8:45. Remember, 8:45 is the average target time per game, meaning some games should only take you 5-6 minutes and more challenging games could take 10-11 or even 12-13 minutes. It sounds like you considered all the possible scenarios for G but it is not necessary for this game and might account for some of the extra time.

There are multiple ways to set up this game, one approach is to use the start time as your base:

__ __ __ __ __ __
1 1:30 2 2:30 3 3:30

The game involves five programs total: 1 hour long G - and 4 half-hour programs - R S T W. Since G is an hour-long, we know that we must have GG sequence somewhere in this timeline.

The following rules apply:
(1) G starts on the hour rather than half-hour.
This rule tells us that the only 3 slots we could put the first G in are 1 pm, 2 pm or 3 pm. It cannot be the second or the fourth program shown.

__ __ __ __ __ __
1 1:30 2 2:30 3 3:30
/G /G /G

(2) T starts on the half-hour rather than the hour.
This rule tells us that T must go in either 1:30, 2:30 or 3:30 slot

__ __ __ __ __ __
1 1:30 2 2:30 3 3:30
/G /T /G /T /G /T

(3) R is shown earlier than S
This rule tells us that R cannot go in 3:30 slot and S cannot go in 1 pm slot

__ __ __ __ __ __
1 1:30 2 2:30 3 3:30
/G /T /G /T /G /T
~S ~R

(4) if W is shown earlier than T, it is shown immediately before T.
If W > T, WT. This rule tells us that if W is shown before T, then it is shown on the hour and immediately before T, in this scenario, we could determine the pairs for every hour (not in exact order):
WT GG RS

Let's look at the questions:

Question 1 requires us to apply the rules to determine the possible order. Our last inference for rule (4) allows us to eliminate answer choices (E) (SR), (D) (WT), and (A) (RS must be together). We can also eliminate (C) because this order would require G to start on half-hour - RTWGGS. Thus, we are left with (B) as the only order that complies with all the rules.


Question 2 asks us if W is the first program then how many orders are there in which the remaining programs could be shown?

Let's think about this, if W is #1, then rule 4 is in effect and we know all the pairs per our inference above - WT GG RS. Since W is #1, T must be #2, but pairs GG and RS could switch places, resulting in two possible orders:

(1) W T G G R S
(2) W T R S G G

The correct answer choice is (B).

Question 3 asks if R is the second program, then each of the following could be true except:
Let's diagram this scenario. If R is the second program, it could either start at 1:30 pm or 2 pm:

On a real test you always want to start with a setup that has fewer hypothetical scenarios, so let's try the scenario where R starts at 2 Pm first. If it starts at 2 pm, then GG must be the first program. We know that if W > T, then RS and WT must be together, but if W is shown later than T, then T must be shown at 2:30 because of rule (2) - T must start at half-hour, resulting in two scenarios:

G G R S W T
1 1:30 2 2:30 3 3:30

G G R T W/S W/S
1 1:30 2 2:30 3 3:30

This setup allows us to eliminate answer choices (A), (B), (C), and (E), leaving (D) as the correct answer. We do not even need to test the setup when R starts at 1:30 pm.

Question 4 asks us if S is the third program, then which of the following must be true?

Let's diagram this scenario. If S is the third program, then G and R could be the first two programs as in our scenario above - the logic game questions often build on each other, so make use of your previous diagrams, or the only other option could be R & T because R must always be earlier than S per rule (3) and W cannot be #1 and #2 in this scenario or it would have to go together with T, and the earliest S could be shown is #4 not #3. If T/R are #1 and #2, and S is #3 starting at 2 pm, we can infer that G must start at 3 pm per rule (1) and the only remaining program W must start at 2:30 pm.

Let's diagram both possible scenarios. We can copy/ paste the first scenario from question 3:

(1) G G R S W T
1 1:30 2 2:30 3 3:30

(2) T/R T/R S W G G
1 1:30 2 2:30 3 3:30

Now, let's look at the answer choices:
(A) is true for scenario 1 but not scenario 2
(B) is true for scenario 2 but not 1
(C) is true for scenario 2 but not 1
(D) is true for scenario 1 but not 2
(E) is true for both and is, therefore, the correct answer.

Question 5 asks us if G is the third program, which of the following could be true?

So if G is #3, we know that it starts at 2 pm and is preceded by two half-hour programs. Now we know that T must start on half-hour so T could either start at 1:30 or 3:30. If T is at 3:30, then rule (4) applies and we can determine all the pairs:

R S G G W T
1 1:30 2 2:30 3 3:30

If T is at 1:30, then if W > T , then again we can determine the order of all the programs:


W T G G R S
1 1:30 2 2:30 3 3:30

If T > W, then R must be #1 because R> S so neither W nor S could be #1. S/W could be the last two programs in either order.

R T G G S/W S/W
1 1:30 2 2:30 3 3:30

Thus, we can conclude that the only option that could be true is (C) - S is #4 in the last scenario.


Question 6 asks which of the following cannot be true.
This is a challenging question, and one way to approach it is to look at the prior diagrams:

SG - refer to the diagram above for question 5, this could be true, eliminate (A)
GS - refer to diagram for question 5, could be true, eliminate (C)
RT - refer to diagram for question 5, eliminate (D)
TW - refer to diagram for question 3, eliminate (E)

We are left only with the answer choice (B), let's see why it cannot be true.
If W is shown immediately before R - WR, where could we put this pair?
W cannot go first or at 1:30 pm because it would require T to follow immediately after per rule (4)
W cannot go at 3 pm because R must be shown before S per rule (3).
We cannot go at 2 pm because it is impossible to comply with the rules as either T must be before W and S must be after R leaving no space for GG.

T W R S
1 1:30 2 2:30 3 3:30

There is no scenario where WR combination could be possible, thus we can conclude that it cannot be true.

Question 7 is a substitution question. These questions are one of the most challenges ones, so if you are running short on time, it is best to skip these on a real test. The question asks us which of the following if substituted for the condition that G starts on the hour would have the same effect on determining the order in which the programs are shown.

Instead of trying to figure out all the possible inferences from the original rule which is what the students tend to do, let's think how could we paraphrase this rule. As part of the initial setup, we determined that G could only start at 1, 2 or 3 pm meaning it must either be first, last or third, it could not be second or fourth - it is the same inference (C) makes and is, therefore, this is the correct answer choice.

Let me know if you have any other questions.

Nishant-Varma on September 14, 2021

Thank you so much, Irina!