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

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Apr 20, 2017 11:49 pm
ziyuenlau wrote:If pq > 4, is p > 1 ?

(1) 2 < q < 6
(2) 0 < p < 2

OA=E
Hi ziyuenlau,

These types of questions can be checked with a few extreme testing values.

We have pq > 4

Statement 1: 2 < q < 6

Case 1: Say q = 5/2

pq > 4 => p*(5/2) > 4 => p > 8/5 or p > 1; the answer is YES.

Case 2: Say q = 5

pq > 4 => p*(5) > 4 => p > 4/5; p may or may not be greater than 1; the answer is YES/No. No unique answer.

Statement 2: 0 < p < 2

Clearly insufficient. p may or may not be greater than 1.

Statement 1 & 2: 2 < q < 6 & 0 < p < 2

Cases discussed in statement 1 apply here too. Thus, there is no unique answer. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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by hazelnut01 » Fri Apr 21, 2017 12:14 am
Jay@ManhattanReview wrote:
ziyuenlau wrote:If pq > 4, is p > 1 ?

(1) 2 < q < 6
(2) 0 < p < 2

OA=E
Hi ziyuenlau,

These types of questions can be checked with a few extreme testing values.

We have pq > 4

Statement 1: 2 < q < 6

Case 1: Say q = 5/2

pq > 4 => p*(5/2) > 4 => p > 8/5 or p > 1; the answer is YES.

Case 2: Say q = 5

pq > 4 => p*(5) > 4 => p > 4/5; p may or may not be greater than 1; the answer is YES/No. No unique answer.

Statement 2: 0 < p < 2

Clearly insufficient. p may or may not be greater than 1.

Statement 1 & 2: 2 < q < 6 & 0 < p < 2

Cases discussed in statement 1 apply here too. Thus, there is no unique answer. Insufficient.
Dear Jay@ManhattanReview, I could not understand statement (2). No info about q. How could we test the value?
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by Jay@ManhattanReview » Fri Apr 21, 2017 12:21 am
ziyuenlau wrote:
Jay@ManhattanReview wrote:
ziyuenlau wrote:If pq > 4, is p > 1 ?

(1) 2 < q < 6
(2) 0 < p < 2

OA=E
Hi ziyuenlau,

These types of questions can be checked with a few extreme testing values.

We have pq > 4

Statement 1: 2 < q < 6

Case 1: Say q = 5/2

pq > 4 => p*(5/2) > 4 => p > 8/5 or p > 1; the answer is YES.

Case 2: Say q = 5

pq > 4 => p*(5) > 4 => p > 4/5; p may or may not be greater than 1; the answer is YES/No. No unique answer.

Statement 2: 0 < p < 2

Clearly insufficient. p may or may not be greater than 1.

Statement 1 & 2: 2 < q < 6 & 0 < p < 2

Cases discussed in statement 1 apply here too. Thus, there is no unique answer. Insufficient.
Dear Jay@ManhattanReview, I could not understand statement (2). No info about q. How could we test the value?
Hi ziyuenlau,

As far as statement 2 goes, we have information some about p (given that 0 < p < 2) and we need to test whether p > 1, so there is no need to bother about q.

As per 0 < p < 2, we can deduce that if 0 < p =< 1, the answer is NO; however, if 1 < p < 2, the answer is Yes. Insufficient.

Hope this is clear!

-Jay
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