If pq 4, is p 1 ?

Question

If pq > 4, is p > 1 ? (1) 2 < q < 6 (2) 0 < p < 2

Bunuel · Answer

(1) 2 < q < 6 --> if q=5 then pq=5p>4 --> p>\frac{4}{5} , so p may or may not be more than 1. Not sufficient. (2) 0 < p < 2 --> p could be any value from this range (so more, less or even equal to 1) and we would be able to find such q so that pq > 4 to hold true. Clearly insufficient. (1)+(2) Example from (1) is still valid: if q=5 then pq=5p>4 --> p>\frac{4}{5} , so p may or may not be more than 1. Not sufficient. Answer: E.

TehJay · Answer

pq > 4 means p > 4/q. Then p > 1 if q < 4. (1) q can be less than or greater than 4. Insufficient. (2) Clearly insufficient. Together: Any value of q in the range of (1) will give a value of p in the range of (2). If q = 3, p = 4/3 > 1. If q = 5, p = 4/5 < 1. Insufficient.

Bunuel · Answer

Bumping for review and further discussion.

EMPOWERgmatRichC · Answer

Hi hemanthp,

This question is a nice example of how, when TESTing VALUES, you can look for 'overlapping' TESTs that fit both Facts at the same time.

We're told that (P)(Q) > 4. We're asked if P is greater than 1. This is a YES/NO question.

Fact 1: 2 < Q < 6

IF....
Q = 5 and (P)(5) > 4....
IF....
P = 1, then the answer to the question is NO
P = 1.1, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: 0 < P < 2

Notice how the TESTs that we used in Fact 1 can ALSO be used in Fact 2!

IF....
P = 1, then the answer to the question is NO
P = 1.1, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know...
2 < Q < 6
0 < P < 2

But there's no more work required - we already have two TESTs that fit BOTH Facts:

IF....
Q = 5 and (P)(5) > 4....
IF....
P = 1, then the answer to the question is NO
P = 1.1, then the answer to the question is YES
Combined, INSUFFICIENT

Final Answer:

Show Spoiler

E

GMAT assassins aren't born, they're made,
Rich

stonecold · Answer

Here the best way to solve this question is to plug in Q=3 and p=1.9 and => Q=5.99 and P=0.9999 in the two statements and we can say that E is the answer.

Basshead · Answer

If pq > 4, is p > 1 ?

(1) 2 < q < 6

if q = 5 and p = 1; no
if q = 2 and p = 3; yes

Insufficient.

(2) 0 < p < 2

if p = 1.9 and q = 3; yes
if p = 0.9 and q = 5; no

Insufficient.

(1&2) The scenarios we used in statements 1 and 2 still apply. Insufficient.

Answer is E.

chetan2u · Answer

If pq > 4, is p > 1 ?
pq>4, so p>1 is what we are looking at.
For sure answer is YES if q<4, where q is positive.

(1) 2 < q < 6
Is q<4? No definite answer
Insuff

(2) 0 < p < 2
Clearly insufficient

Combined.
p=1 and q=5..,.,,NO
p=1.5 and q=5....YES

bumpbot · Answer

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If pq > 4, is p > 1 ?

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