How many more first-time jobless claims were filed in week P than in

Question

How many more first-time jobless claims were filed in week P than in week T ?

(1) For weeks P, Q, R, and S, the average (arithmetic mean) number of first-time jobless claims filed was 388,250.

(2) For weeks Q, R, S, and T, the average (arithmetic mean) number of first-time jobless claims filed was 383,000.

DavidTutorexamPAL · Answer

We'll write our data as equations so we understand what we need to do.
This is a Precise approach.

(1) so (P+Q+R+S)/4 = 388,250.
As we're asked to find P - T, this is not enough.
Insufficient.

(2) so (Q+R+S+T)/4 = 383,000.
Similarly to the above, we cannot isolate P - T from this equation alone.
Insufficient.

Combined:
Subtracting the two equations gives us (P - T)/4 = 5,250 --> P - T = 21,000
Sufficient.

(C) is our answer.

Lanolin13 · Answer

I don't understand how either of these or combined is sufficient. We only know the average of two groups of four weeks, but cannot isolate the individual weeks inside the average sets, can we?

For instance, P = 1,000; Q = 388,250; R = 388,250; and S = 775,500; the average is still 388,250. Or it could be P = 2,000; Q = 388,250; R = 388,250; and S = 774,550; with the average of 388,250. Or each could be the same 388,250 resulting in the average of 388,250. Here we have 3 different possibilities of, from what I can see, an almost infinite set of possibilities for what P could be. Then the same for T. So how can we definitively say we have enough information to tell what P - T equals?

Perhaps my logic is off here, if anyone can offer any suggestions I would love to resolve it.

Bunuel · Answer

Individually, you are correct: neither statement lets us isolate P or T, because Q, R, and S can vary. But together we do not need to know Q, R, or S individually, because the same sum Q + R + S appears in both equations.

From statement (1):

P + Q + R + S = 4 * 388,250 = 1,553,000

From statement (2):

Q + R + S + T = 4 * 383,000 = 1,532,000

Subtracting the second equation from the first eliminates Q, R, and S:

P + Q + R + S - (Q + R + S + T) = P - T = 21,000

So even though P and T cannot be found separately, the difference P - T is fixed. Therefore, the two statements together are sufficient.

Lanolin13 · Answer

Thank you! I get it now. I also had the unfortunate error of misreading the second set Q, R, S, T as being a completely different set with no overlap something akin to reading it as T, U, V, W. I really appreciate the detailed and prompt explanation. I also need to double check my reading of the problem going forward

How many more first-time jobless claims were filed in week P than in

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