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# If w < x < y < z, is the product of four numbers negative?

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Math Expert
Joined: 02 Sep 2009
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If w < x < y < z, is the product of four numbers negative?  [#permalink]

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10 Jun 2018, 04:06
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75% (01:10) correct 25% (01:16) wrong based on 10 sessions

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If w < x < y < z, is the product of four numbers negative?

(1) z > 0.
(2) wx < 0.

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Joined: 10 Jun 2018
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Re: If w < x < y < z, is the product of four numbers negative?  [#permalink]

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10 Jun 2018, 04:19
(1) does not tell us anything. z is greater than 0, and the other three numbers could be smaller than 0. In which case the product of three negatives and one positive would be a negative number. However, y for example could also be greater than 0, in which case the product of two negatives and two positives would be a positive.

(2) however, tell us a lot. The product of w and x is less than 0, and thus one of those numbers must be negative, the other positive. Neither can be 0 because then the product can not be less than 0. Since w < x, x must be the positive number and w must be the negative number. Since y and z are both greater than x, both must be positive as well. The product of one negative and three positives is negative. Always. Thus (2) is sufficient.

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Re: If w < x < y < z, is the product of four numbers negative? &nbs [#permalink] 10 Jun 2018, 04:19
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