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# If p & q are non zero integers, is -1 < p/q < 1 ?

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If p & q are non zero integers, is -1 < p/q < 1 ?  [#permalink]

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08 Aug 2019, 21:07
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Difficulty:

55% (hard)

Question Stats:

50% (01:38) correct 50% (01:22) wrong based on 34 sessions

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If p & q are non zero integers, is -1 $$<\frac{p}{q}$$ < 1 ?

1) $$q > p$$
2) $$pq > 0$$

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Re: If p & q are non zero integers, is -1 < p/q < 1 ?  [#permalink]

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08 Aug 2019, 22:09
1. P/q<1 but we have no info if p/q>-1. So insufficient

2. pq>0 but no way to find equation for p/q. Insufficient

Combining 1&2 gives no information either.

Hence E

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Re: If p & q are non zero integers, is -1 < p/q < 1 ?  [#permalink]

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09 Aug 2019, 01:18
In questions like these, you need to learn to pick the hidden clues given in the question, for you to be able to derive value from them.

For example, in this question, q has to be non-zero because of the fact that it comes in the denominator. As we know, division by zero is not tested on the GMAT.
p being a non-zero integer tells us that the value of $$\frac{p}{q}$$ cannot be ZERO. Also, in this question, we are trying to find if $$\frac{p}{q}$$ is a proper fraction, since these are the values that lie in between -1 and 1.

The analysis approach is the safer approach in this question. However, trying values also works just fine since we have constraints on p and q.

From statement I, q>p.
If q = 3 and p = 2, $$\frac{p}{q}$$ is a proper fraction. If q = -2 and p = -3, $$\frac{p}{q}$$ is not a proper fraction.
Statement I alone is insufficient to say if $$\frac{p}{q}$$ is always a proper fraction.

From statement II, pq>0. This means that p and q are of the same signs. In that case, we see that we can take the same values and prove that the statement is insufficient to answer the question.

Combining both statements I and II, the same set of values of p and q are sufficient to prove that the combination of values also is insufficient to answer the question uniquely.

The correct answer option is E.
Hope this helps!
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Re: If p & q are non zero integers, is -1 < p/q < 1 ?   [#permalink] 09 Aug 2019, 01:18