Data Sufficiency

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 avg number of first-time jobless claims filed was 388,250
2) for weeks Q, R, S, and T, the avg number of first-time jobless claims filed was 383,000

Answ: C

Please explain. Thanks!!!

Yes, C is the soln.

(i) =>
P+Q+R+S = (388,250 * 4)

(ii) =>
Q+R+S+T= (383,000 * 4)

Now, we have to find P-T which is equal to:
[P+Q+R+S] - [Q+R+S+T]
= (388,250 - 383,000) *4

Hence both the choices combined yield the required value

we need to find the value of P-T

St 1 tells us P+Q+R+S = 388250*4
P = 388250*4-Q-R-S
But since it doesnt tell us anything about T its INSUFF

St 2 tells us Q+R+S+T = 383000*4
T=383000*4-Q-R-S
but since it doesnt tell us anything about P its INSUFF

Combining them we get
P = 388250*4-Q-R-S
T=383000*4-Q-R-S

Subtract the two statements we get P-T = (388250*4)-(383000*4)
Hence the answer is C

If we are trying to find the difference in the number of jobless claims between the 2 weeks why do we multiply 4? I thought P+Q+R+S/4 gave us $388,250 so whats the point in multiplying 4

(388,250 - 383,000) *4 to yield the required value?

vladmire wrote:If we are trying to find the difference in the number of jobless claims between the 2 weeks why do we multiply 4? I thought P+Q+R+S/4 gave us $388,250 so whats the point in multiplying 4

(388,250 - 383,000) *4 to yield the required value?

First thing to note is this is DS, so we don't need to actually calcuate. As soon as you see you have enough info, you're done.

On this particular question, as long as you know the average formula, you should reach (C) very quickly by combining the two equations you get.

If we actually wanted to solve, we need to multiply by 4 precisely because of the equation you provided.

(P+Q+R+S)/4 = 388250
(Q+R+S+T)/4 = 383000

Rearranging to make it easier to get the relationship (P-T) that we want:

P+Q+R+S = 4(388250)
T+Q+R+S = 4(383000)

Subtracting the second equation from the first:

P-T = 4(388250) - 4(383000)
P-T = 4(388250 - 383000)
P-T = 4(5250)
P-T = 21000

We could have just multiplied both big numbers by 4 before doing the subtraction, but it's much easier to do the arithmetic with smaller numbers.