pushpitkc wrote:

What is the value of p+q?

1. r - s = 5

2. rp + rq - sp - sq = 20

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 partsFactor 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

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ASIDE: This last step is no different from simplifying the expression 8

k - 3

k to get: (8 - 3)

kTo 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) = 4Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

_________________

Brent Hanneson – Founder of gmatprepnow.com