Is P + Q R + S ?

Question

Is P + Q > R + S ?

(1) P > R + S
(2) Q > R + S

whiplash2411 · Answer

Are you sure the answer is E?

I was thinking C.

Statement 1 is insufficient, because Q could be a negative number. Similarly Statement 2 is insufficient. But together we get P+Q>2(R+S) and hence it should be greater than R+S. Not sure why it's E

paam0101 · Answer

This question is as is from Kaplan 800. Even I chose C as the answer. I couldn't understand Kaplan reasoning for why it is E.

Bunuel · Answer

P+Q>2(R+S)  does not mean that  P+Q>R+S .

For example:
If  P+Q=6>4=2(R+S) , then yes, as:  P+Q=6>2=R+S ;
If  P+Q=-6>-8=2(R+S) , then no, as:  P+Q=-6<-4=R+S .

So, answer is E.

whiplash2411 · Answer

Ah, tricky. Thanks Bunuel.

utfan2424 · Answer

Answer is E, as Bunuel indicated.

Consider if Q and P both equal -4 and R+X = -5.

Temurkhon · Answer

P+Q>R+S? Yes/No

St.1 P>R+S. No information about Q. INSUFF

St.2.Q>R+S. No information about P. INSUFF

St.1+St.2. can do algebraically

P>R+S
+
Q>R+S
----------
P+Q>2(R+S)

two options: if P+Q positive, then > R+S, if negative <R+S. INSUFF

E

Neeraj5 · Answer

Consider the below cases to understand the problem better

Case 1:
let P=-2 and Q=-3 and R+S=-5.
here P>R+S and Q>R+S
but P+Q > R+S does not hold true.

Case 2:
let P=-1 and Q=-1 and R+S=-5.
here P>R+S and Q>R+S
but P+Q > R+S holds true.

Due to this ambiguity the  answer is E

Is P + Q > R + S ?

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