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Problem Solving - Beatthegmat practice question

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by kuiper » Tue Nov 09, 2010 11:15 pm
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

OA given: D

I was thinking if x and y are assumed to be -0.1 then D can't be true. And that means answer should be E in all cases.

Am I missing something?
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by beat_gmat_09 » Tue Nov 09, 2010 11:20 pm
kuiper 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

OA given: D

I was thinking if x and y are assumed to be -0.1 then D can't be true. And that means answer should be E in all cases.

Am I missing something?
x and y both are negative. Pick x =-2, y=-1
a. 2(-1)-3(-2) = -2+6=4
b. 3(-2)-2(-1)= -6+2 = -4
c. -(3(-2)-2(-1)) = -(-6+2)=-(-4)=4
d. -(3(-2)+2(-1))=-(-6-2)=-(-8) = 8
e. 0

8 is greatest, hence D
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by beat_gmat_09 » Tue Nov 09, 2010 11:22 pm
If x and y both are -0.1 then
D. -(3*(-0.1) + 2*(-0.1)) = -(-0.3-0.2) = -(-0.5) = +0.5 > 0
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by kuiper » Tue Nov 09, 2010 11:25 pm
Thanks.

I don't know why I was missing it so far.
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by Scott@TargetTestPrep » Mon Aug 12, 2019 5:38 pm
kuiper 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

OA given: D
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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