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# If pq ≠ 0, is x an integer?

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Manager
Joined: 26 Aug 2004
Posts: 51
If pq ≠ 0, is x an integer?  [#permalink]

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Updated on: 23 Feb 2015, 12:58
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5% (low)

Question Stats:

82% (01:04) correct 18% (00:56) wrong based on 176 sessions

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If pq ≠ 0, is x an integer?

(1) x = 3p – 2q
(2) p = q

Originally posted by ice t on 29 Aug 2004, 15:03.
Last edited by Bunuel on 23 Feb 2015, 12:58, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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23 Feb 2015, 12:51
2
Hi All,

This question is ultimately about integers vs. non-integers and is perfect for TESTing VALUES.

We're told that PQ is not equal to 0, which means that neither P nor Q can be 0. We're asked if X is an integer. This is a YES/NO question.

Fact 1: X = 3P - 2Q

IF....
P=1
Q=1
X = 3-2 = 1
The answer to the question is YES.

IF....
P=1/2
Q=1/2
X = 3/2 - 2/2 = 1/2
The answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: P=Q

Both TESTs from above also fit this Fact.
Fact 2 is INSUFFICIENT.

Combined, we have the same two TESTs that fit both Facts.
We have a YES and a NO answer.
Combined, INSUFFICIENT

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Rich
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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29 Aug 2004, 22:26
1
1) x=3p-2q

2) p=q

(1) not sufficient. P and Q could be fractions, and the operation of x could result in some fraction as well.
(2) not sufficient. Same reason as above.

(1) and (2) put together doesn't tell us anything more than we already know.

So (E).
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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23 Feb 2015, 13:06
1
ice t wrote:
If pq ≠ 0, is x an integer?

(1) x = 3p – 2q
(2) p = q

The answer is straight E, without any algebra or number plugging.

If pq ≠ 0, is x an integer?

(1) x = 3p – 2q. So, we have that x is equal to some number (3p - 2q). We know nothing about p and q (other than neither of them is 0), hence we cannot determine whether it's an integer. Not sufficient.

(2) p = q. Clearly insufficient.

(1)+(2) x = 3p – 2q = 3p - 2p = p. And again we have that x is equal to some number p, which we know nothing about. Not sufficient.

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Re: If pq ≠ 0, is x an integer?  [#permalink]

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29 Aug 2004, 20:14
I'd go E almost instantly.

If p = q = .1, x is not integer
If p = q = 1, x is integer
Manager
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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30 Aug 2004, 05:42
I would choose E too.

p and q could be fractions like p = 1/2 and q = 5/7 or they both could be integers.

Regards,

Alex
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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30 Aug 2004, 06:37
actually this is from one of the paper tests and it gives the answer as A which makes no sense to me.

???
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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30 Aug 2004, 09:17
nope, E. Definately. The best we can get to is combining them together and seeing that x = p = q. But since we don't know what they are, just that their not zero, it's got to be E.
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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16 Sep 2016, 16:57
Correct answer is E. Here's why:

(1) x = 3p – 2q

We have no indication of the values that p and q can take on; for all we know, both could be decimals or fractions - either way, this statement is INSUFFICIENT

(2) p = q

We have the same issue as in (1). INSUFFICIENT
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Re: If pq ≠ 0, is x an integer?  [#permalink]

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10 Apr 2019, 09:19
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Re: If pq ≠ 0, is x an integer?   [#permalink] 10 Apr 2019, 09:19
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