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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x > 2y and y < −5, which of the following must be true?

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Math Expert V
Joined: 02 Sep 2009
Posts: 64068
If x > 2y and y < −5, which of the following must be true?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 60% (02:17) correct 40% (02:11) wrong based on 192 sessions

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If x > 2y and y < −5, which of the following must be true?

A. x/y > 2

B. x > y

C. x/2 < y

D. x/y < 2

E. 2y + x < 0

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GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2061
Re: If x > 2y and y < −5, which of the following must be true?  [#permalink]

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2
3
We know y is negative here, so when we divide by y on both sides of the inequality below, we need to reverse the inequality:

x > 2y
x/y < 2

which is D.

B is not right -- notice that If y is negative, then 2y < y. When we know x > 2y, we can't be sure if x > y; we could have:

2y < x < y
2y < y < x

It's maybe easier to see just picking numbers: if, say, y = -10, then when we know x > 2y, we know x > -20. But x could be -15, which is less than y, or x could be 100, which is greater than y.
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Current Student P
Joined: 18 Aug 2016
Posts: 588
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 If x > 2y and y < −5, which of the following must be true?  [#permalink]

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Bunuel wrote:
If x > 2y and y < −5, which of the following must be true?

A. x/y > 2

B. x > y

C. x/2 < y

D. x/y < 2

E. 2y + x < 0

Second attempt

if x> 2y then for every value of y (y<-5)
x/y<2
D
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Luckisnoexcuse

Originally posted by Luckisnoexcuse on 08 Jul 2017, 05:18.
Last edited by Luckisnoexcuse on 08 Jul 2017, 06:53, edited 1 time in total.
Senior Manager  S
Joined: 21 Mar 2016
Posts: 492
Re: If x > 2y and y < −5, which of the following must be true?  [#permalink]

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divide the first equation by y..
the equation becomes x/y <2..

ans D
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10533
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Re: If x > 2y and y < −5, which of the following must be true?  [#permalink]

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3
Bunuel wrote:
If x > 2y and y < −5, which of the following must be true?

A. x/y > 2

B. x > y

C. x/2 < y

D. x/y < 2

E. 2y + x < 0

We can let y = -6 and x = -6, we see B is false. Since x/y = 1, A is also false. Since x/2 = -3, C is also false. This leaves us with choices D and E, which are each true when x = y = -6. However, if y = -6 and x = 18, we see that x/y = -3 and 2y + x = 6, which only makes D true. Thus, the correct answer is D.

Alternate Solution:

We observe that answer choices A and D are x/y > 2 and x/y < 2. The only way both of these statements can be false is if x/y = 2 or in other words, x = 2y; but that is impossible since x > 2y. Thus, either A or D must be correct; so we can eliminate all the other answer choices and just focus on comparing x/y and 2.

Note that from the second inequality y < -5, we know that y is a negative number. If we divide each side of the inequality x > 2y by the negative number y, we obtain x/y < 2.

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Intern  B
Joined: 25 May 2018
Posts: 21
Re: If x > 2y and y < −5, which of the following must be true?  [#permalink]

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Can someone explain why option E is wrong?
Non-Human User Joined: 09 Sep 2013
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Re: If x > 2y and y < −5, which of the following must be true?  [#permalink]

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_________________ Re: If x > 2y and y < −5, which of the following must be true?   [#permalink] 02 Apr 2020, 06:00

# If x > 2y and y < −5, which of the following must be true?   