Is p + q > 1/p + 1/q ?
(1) p < q < 1
(2) pq < 1
OA:E
Target question: Is p + q > 1/p + 1/q ?
This is a good candidate for
rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Let's rewrite 1/p + 1/q
Find a common denominator of pq to get: q/pq + p/pq
Add to get: (p + q)/pq
REPHRASED target question: Is p + q > (p + q)/pq?
Notice that (p + q) appears on both sides of the inequality.
Also notice that if pq = 1, the two quantities, (p+q) and (p + q)/pq, will be equal.
Also notice that if p+q is positive AND pq is between 0 and 1, then (p+q) < (p + q)/pq
Also notice that if p+q is negative AND pq is between 0 and 1, then (p+q) > (p + q)/pq
These observations will help up TEST VALUES
Statement 1: p < q < 1
There are several values of p and q that satisfy statement 1. Here are two:
Case a: p = 1/4 and q = 1/2. In which case, p + q = 1/4 + 1/2 =
3/4, AND (p + q)/pq = (3/4)/(1/8) =
6. In other words,
(p+q) < (p + q)/pq
Case b: p = -1/2 and q = -1/4. In which case, p + q = (-1/2) + (-1/4) =
-3/4, AND (p + q)/pq = (-3/4)/(1/8) =
-6. In other words,
(p+q) > (p + q)/pq
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: pq < 1
There are several values of p and q that satisfy statement 2. Here are two:
Case a: p = 1/4 and q = 1/2. In which case, p + q = 1/4 + 1/2 =
3/4, AND (p + q)/pq = (3/4)/(1/8) =
6. In other words,
(p+q) < (p + q)/pq
Case b: p = -1/2 and q = -1/4. In which case, p + q = (-1/2) + (-1/4) =
-3/4, AND (p + q)/pq = (-3/4)/(1/8) =
-6. In other words,
(p+q) > (p + q)/pq
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Notice that I used the SAME values for p and q in my earlier work. So, the same values satisfy BOTH statements. That is....
There are several values of p and q that satisfy BOTH statements. Here are two:
Case a: p = 1/4 and q = 1/2. In which case, p + q = 1/4 + 1/2 =
3/4, AND (p + q)/pq = (3/4)/(1/8) =
6. In other words,
(p+q) < (p + q)/pq
Case b: p = -1/2 and q = -1/4. In which case, p + q = (-1/2) + (-1/4) =
-3/4, AND (p + q)/pq = (-3/4)/(1/8) =
-6. In other words,
(p+q) > (p + q)/pq
Since we cannot answer the
REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
