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

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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02 Sep 2016, 05:52
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Question Stats:

55% (01:36) correct 45% (01:32) wrong based on 259 sessions

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

A. y = −5
B. y > −5
C. −y > 5
D. y ≤ −5
E. y ≥ −5

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Intern
Joined: 18 Jul 2016
Posts: 35
Re: If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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02 Sep 2016, 06:44
2
-y> x; -x<-5

--> y<-x; -x<-5

--> y<-x<-5

--> y<-5

--> -y>5 ---> IMO answer is C
Intern
Joined: 10 Nov 2014
Posts: 7
Re: If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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02 Sep 2016, 07:14
Provided info:

−y ≥ x, and −x < −5

y <= -x < -5

As '-x' is less than '-5' and Y is less than or equal to '-x'

we have y < -5 which is similar to -y > 5.

Point to remember : when dealing with inequalities and when multiplying with negative sign on both sides of the equation, we have to change the inequality.
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Joined: 04 May 2014
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Re: If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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12 Oct 2017, 00:56
-y>=x and -x<-5 or x>5
hence -y>=x>5 or -y>5
Target Test Prep Representative
Status: Head GMAT Instructor
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Re: If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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16 Oct 2017, 16:52
Bunuel wrote:
If −y ≥ x, and −x < −5, then which of the following must be true?

A. y = −5
B. y > −5
C. −y > 5
D. y ≤ −5
E. y ≥ −5

Dividing both sides of the first inequality by -1, we have y ≤ -x. Since -x < -5, y < -5. However, since we don’t have this inequality in the answer choices, we can multiply both sides of y < -5 by -1 and we have -y > 5.

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Re: If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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07 Jan 2018, 11:21
Bunuel wrote:
If −y ≥ x, and −x < −5, then which of the following must be true?

A. y = −5
B. y > −5
C. −y > 5
D. y ≤ −5
E. y ≥ −5

Bunuel I have a doubt, why can't the answer be D?

Given that: -x<-5 means after sign reversal: x>5
also -y >=x implies that -y >= 5
after sign reversal: y<= -5

Hence option D.
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: If −y ≥ x, and −x < −5, then which of the following must be true?  [#permalink]

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07 Jan 2018, 11:29
1
2
ImAnkitKaushik wrote:
Bunuel wrote:
If −y ≥ x, and −x < −5, then which of the following must be true?

A. y = −5
B. y > −5
C. −y > 5
D. y ≤ −5
E. y ≥ −5

Bunuel I have a doubt, why can't the answer be D?

Given that: -x<-5 means after sign reversal: x>5
also -y >=x implies that -y >= 5
after sign reversal: y<= -5

Hence option D.

Given: x > 5 and -y >= x. Notice that C and D differ only by = sign. Here y cannot be 5 because if it is, then we'd get 5 >= x and we know that x is strictly more than 5.
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Re: If −y ≥ x, and −x < −5, then which of the following must be true?   [#permalink] 07 Jan 2018, 11:29
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# If −y ≥ x, and −x < −5, then which of the following must be true?

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