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If u < v < 0 < w, then which of the following must be positive? (A) w
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13 Jan 2023, 07:44
13 Jan 2023, 07:44
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Question Stats:
75% (01:24) correct
25% (01:10) wrong based on 16 sessions
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If \(u < v < 0 < w\), then which of the following must be positive?
(A) w − uv
(B) u − wv
(C) u(w − v)
(D) v(u − w)
(E) w(u − v)
(A) w − uv
(B) u − wv
(C) u(w − v)
(D) v(u − w)
(E) w(u − v)
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Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If u < v < 0 < w, then which of the following must be positive? (A) w
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21 Jan 2023, 10:50
21 Jan 2023, 10:50
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Re: If u < v < 0 < w, then which of the following must be positive? (A) w
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05 Feb 2023, 10:36
05 Feb 2023, 10:36
2
Expert Reply
OE
A product is positive either if both terms are positive or if both terms are negative. Looking at choice (A), you see that the product uv is positive; however, that product is subtracted from another positive quantity, w. The result may or may not be positive. In choice (B), a negative quantity (wv) is subtracted from another negative quantity, u. The result is once again indeterminate: If wv is more negative than u, then the result of the subtraction operation would be positive, but otherwise it would be negative. The other three answer choices are all products. In choice (C), w − v, which is positive (because w is greater than v), is multiplied by the negative quantity, u. The result will be negative. Choice (E) is also the product of one positive and one negative quantity. By contrast, in choice (D), two negative terms are multiplied together, as v < 0 and u < w, so u – w < 0. Thus, choice (D) yields a result that will be positive.
A product is positive either if both terms are positive or if both terms are negative. Looking at choice (A), you see that the product uv is positive; however, that product is subtracted from another positive quantity, w. The result may or may not be positive. In choice (B), a negative quantity (wv) is subtracted from another negative quantity, u. The result is once again indeterminate: If wv is more negative than u, then the result of the subtraction operation would be positive, but otherwise it would be negative. The other three answer choices are all products. In choice (C), w − v, which is positive (because w is greater than v), is multiplied by the negative quantity, u. The result will be negative. Choice (E) is also the product of one positive and one negative quantity. By contrast, in choice (D), two negative terms are multiplied together, as v < 0 and u < w, so u – w < 0. Thus, choice (D) yields a result that will be positive.
