What is the value of p+q?

Question

1. r - s = 5
2. rp + rq - sp - sq = 20

Source: Experts Global

BrentGMATPrepNow · Answer

Target question :    What is the value of p+q?

Statement 1 : r - s = 5  
No information about p or q
So, statement 1 is NOT SUFFICIENT

Statement 2 : rp + rq - sp - sq = 20  
We can  factor the left side in parts

Factor r from first 2 terms to get: r( p + q ) - sp - sq = 20
Factor -s from last 2 terms to get: r( p + q ) - s( p + q ) = 20
Since we have  p + q  in common in both parts, we can combine the terms
We get: (r - s)( p + q ) = 20
------------------------------------
ASIDE: This last step is no different from simplifying the expression 8 k  - 3 k  to get: (8 - 3) k 
To be more general: b( something ) - c( something ) to get: (b - c)( something )
-----------------------------------
Now that we know that (r - s)( p + q ) = 20, we can see that p+q can have many different values. 
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that r - s = 5
Statement 2 tells us that (r - s)( p + q ) = 20
Replace (r - s) with 5 to get: (5)( p + q ) = 20
So, IT MUST be the case that  (p + q) = 4 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

amanvermagmat · Answer

(1) r-s=5. Nothing about p and q. Insufficient.

(2) rp+rq-sp-sq = 20. Or r(p+q) - s(p+q) = 20 or 
(r-s)(p+q) = 20. Here we have factorised the left hand side. But still we cant say anything about (p+q) unless we know something about (r-s). (Because multiple cases are possible). Insufficient.

Combining the two statements: Substituting r-s=5, we get 5 (p+q) = 20 or p+q = 4. Sufficient.

Hence  C answer.

hasan4imam · Answer

rp+rq-sp-sq=20
or, r(p+q)-s(p+q)=20
or, (r-s)(p+q)=20
or, 5(p+q)=20
or, (p+q)= 4..ans

pushpitkc · Answer

Hi  hasan4imam

Though you have solved the problem perfectly.
This is a DS question, where the aim is to determine
if the statements are individually/combine to give us
an unique solution

The solution for an DS question is as follows : 
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

So, in this case the answer should be C
(since both the options combined are only enough to answer the question)

Hope that helps you!

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What is the value of p+q?

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What is the value of p+q?

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