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# If pqr < 0 < pqs, is q < 0

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If pqr < 0 < pqs, is q < 0  [#permalink]

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03 Aug 2019, 09:57
2
00:00

Difficulty:

75% (hard)

Question Stats:

32% (02:01) correct 68% (01:53) wrong based on 19 sessions

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If pqr < 0 < pqs, is q < 0?

1)pr > 0
2)pr > ps

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Re: If pqr < 0 < pqs, is q < 0  [#permalink]

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03 Aug 2019, 11:19
Notice none of the letters can be zero, so each is either positive or negative.

From the stem we know that pqr < 0, so we know (pr)(q) < 0, and pr and q must have opposite signs. If, from Statement 1, pr is positive, then q must be negative, and Statement 1 is sufficient.

If we multiply the inequality in Statement 2 by q on both sides, then if q is positive, we'll leave the inequality alone, and if q is negative, we'll reverse the inequality. So if q were positive, pqr > pqs would need to be true. But the stem tells us that is not true -- the stem tells us that pqr < pqs. So q cannot be positive, and since q is not zero, q must be negative and Statement 2 is sufficient.
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Re: If pqr < 0 < pqs, is q < 0   [#permalink] 03 Aug 2019, 11:19
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