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If 3x < 2y < 0, which of the following must be the greatest?

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If 3x < 2y < 0, which of the following must be the greatest?  [#permalink]

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New post 19 Mar 2015, 06:28
2
5
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A
B
C
D
E

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  25% (medium)

Question Stats:

74% (01:32) correct 26% (01:35) wrong based on 207 sessions

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Re: If 3x < 2y < 0, which of the following must be the greatest?  [#permalink]

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New post 19 Mar 2015, 07:43
Plugging in -1 for both x and y we get
A. 2y - 3x = 2
B. 3x - 2y = -1
C. -(3x - 2y) = 3
D. -(3x + 2y) = 15
E. 0

Answer: D
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Re: If 3x < 2y < 0, which of the following must be the greatest?  [#permalink]

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New post 23 Mar 2015, 04:44
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Re: If 3x < 2y < 0, which of the following must be the greatest?  [#permalink]

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New post 12 Aug 2019, 18:49
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Bunuel wrote:
If 3x < 2y < 0, which of the following must be the greatest?

A. 2y - 3x
B. 3x - 2y
C. -(3x - 2y)
D. -(3x + 2y)
E. 0


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We notice that -(3x - 2y) = -3x + 2y = 2y - 3x; i.e. the expression in answer choice A is equivalent to the expression in answer choice C. Therefore, neither A nor C can be the correct answer, and we eliminate both.

Next, notice that 3x - 2y is negative (since 3x < 2y); therefore, B cannot be the correct answer, either (because it is less than 0, which is answer choice E).

We need to decide between D and E. Notice that both 3x and 2y are strictly less than zero, and so is their sum. Since 3x + 2y is strictly less than zero, -(3x + 2y) is strictly greater than zero; which means D is the greatest.

Alternate Solution:

We can let x = -3 and y = -2 and check each answer choice.

Choice A: 2y - 3x = -4 - (-9) = 5

Choice B: 3x - 2y = -9 - (-4) = -5. Eliminate B.

Choice C: -(3x - 2y) = -(-5) = 5 (This is Choice B, with the sign reversed.) Because this is equal to Choice A, we can eliminate both A and C.

Choice D: -(3x + 2y) = -(-9 + (-4)) = -(-13) = 13. We compare this to Choice E and see that 13 is greater than 0. Choice D is the correct answer.

Answer: D
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Re: If 3x < 2y < 0, which of the following must be the greatest?   [#permalink] 12 Aug 2019, 18:49
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