Is p = q? (1) p + q = 2 (2) pq 0

Question

Is p = q?

(1) p + q = 2
(2) pq > 0

bhima22 · Answer

My answer is A

(1) p + q = 2

Becomes p=2-q. Therefore, P and Q cannot be equal.

(1) is sufficient.

(2) pq > 0

I'm picking numbers here.

p=q=2. Therefore, 2x2>0

p= 2, and q = 1. Therefore, 2x1>0.

(2) is not sufficient

Vetrick · Answer

Statement 1 : 
p+q = 2 
Let's take two test-cases 1+1 = 2 & 4 -2 = 2 . In one case p=q & in another p is not equal to Q 
Hence Statement 1 is insufficient.

Statement 2 : 
pq > 0 
This means either both P & Q are positive or both are negative. 
But with this info alone we can't conclude if p=q or not. 
Hence Statement 2 is also insufficient.

When we take both these together, we get 1. Both P & Q are positive 2. P+Q = 2. 
But this doesn't necessarily mean that P=Q=1 -> we can also have 3/2 + 1/2 = 2, in which case P is not equal to Q.

Therefore, answer is E.

nimaki · Answer

First, note that there is no specification on whether p and q are integers or not. That is how you arrive at both statements are sufficient.
 (1) p + q = 2 has many combinations. 4 + -2, 1.5 + 0.5, 1 + 1 ... etc so Statement 1 is NOT SUFFICIENT
 (2) pq > 0 is ambiguous because it only eliminates the possibility of one of the values being a negative number.

(BOTH)
As siscussed, if you know that we are looking for either an integer or a fraction, this option is also extremely wide.
Therefore, the ans is  E

iamjatinagrawal · Answer

We don't know if p and q are integers, hence the answer had to be  Option (E) .

Is p = q? (1) p + q = 2 (2) pq > 0

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