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If x is an integer and |2x + 3| 12 then which of the following must [#permalink]
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Bunuel wrote:
If x is an integer and \(|2x+3|≤12\), then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4


\(|2x+3|≤12\)

\(|x+3/2|≤6\)

So x is a point that is a distance of 6 or less from -1.5
So x would be less than 4.5 or more than -7.5

\(-7.5 \leq x \leq 4.5\)

<------------------------ (-7.5) ================== (4.5) ---------------------->

x can take any value in the "===" region. For each value in this region, x is definitely greater than -8.

Answer (C)

Originally posted by KarishmaB on 19 Oct 2018, 01:42.
Last edited by KarishmaB on 17 Oct 2022, 03:42, edited 1 time in total.
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If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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Hi [url=https://gmatclub.com:443/forum/memberlist.php?mode=viewprofile&un=VeritasKarishma]VeritasKarishmaAnother way!
Attachments

IMG_20181021_115527.jpg
IMG_20181021_115527.jpg [ 1.45 MiB | Viewed 6067 times ]


Originally posted by HAPPYatHARVARD on 20 Oct 2018, 06:53.
Last edited by HAPPYatHARVARD on 21 Oct 2018, 09:08, edited 2 times in total.
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
Quote:
A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4.25 which is greater than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

Answer: Option C


Quick clarification question - with regard to answer D, x is an integer—so 4.25 being greater than 4 is not the reason why the choice is wrong. It's because x could be 4, which is not included by x < 4. Is that correct?
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
Expert Reply
fogarasm wrote:
Quote:
A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4.25 which is greater than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

Answer: Option C


Quick clarification question - with regard to answer D, x is an integer—so 4.25 being greater than 4 is not the reason why the choice is wrong. It's because x could be 4, which is not included by x < 4. Is that correct?


fogarasm Thank you for pointing out the mistake in the mistake. I missed the information in quick solving the question. :)
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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Graphical approach shall be as per attached sketch
Attachment:
WhatsApp Image 2018-10-21 at 10.32.28.jpeg
WhatsApp Image 2018-10-21 at 10.32.28.jpeg [ 60.94 KiB | Viewed 6060 times ]
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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HAPPYatHARVARD wrote:
Hi [url=https://gmatclub.com:443/forum/memberlist.php?mode=viewprofile&un=VeritasKarishma]VeritasKarishmaAnother way!


Yes, this method uses the definition of absolute values. The method I have shown is based on the concept of looking at absolute value in terms of distance.
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
GMATinsight wrote:
Bunuel wrote:
If x is an integer and \(|2x+3|≤12\), then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4


\(|2x+3|≤12\)

i.e. \(-12 ≤ 2x+3 ≤ 12\)

i.e. \(-12-3 ≤ 2x ≤ 12-3\)

i.e. \(-15 ≤ 2x ≤ 9\)

i.e. \(-7.5 ≤ x ≤ 4.5\)

Out of all options we see

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

Answer: Option C


I got the same range but won't x > -8 include values above 4.5 ?
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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shobhiitgupta wrote:
GMATinsight wrote:
Bunuel wrote:
If x is an integer and \(|2x+3|≤12\), then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4


\(|2x+3|≤12\)

i.e. \(-12 ≤ 2x+3 ≤ 12\)

i.e. \(-12-3 ≤ 2x ≤ 12-3\)

i.e. \(-15 ≤ 2x ≤ 9\)

i.e. \(-7.5 ≤ x ≤ 4.5\)

Out of all options we see

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

Answer: Option C


I got the same range but won't x > -8 include values above 4.5 ?



The logic is,

When it's known that \(-7.5 ≤ x ≤ 4.5\) then for all possible values of x we can say that each value will certainly be greater than -8

on the other hand you can prove all other options incorrect as per the following explanation (already mentioned in previous solutions)

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

I hope this helps!!!
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
VeritasKarishma wrote:
Bunuel wrote:
If x is an integer and \(|2x+3|≤12\), then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4


\(|2x+3|≤12\)

\(|x+3/2|≤6\)

So x is a point that is a distance of 6 or less from -1.5
So x would be less than 4.5 or more than -7.5

\(-7.5 \leq x \leq 4.5\)

<------------------------ (-7.5) ================== (4.5) ---------------------->

x can take any value in the "===" region. For each value in this region, x is definitely greater than -8.

Answer (C)

For more, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... edore-did/



But this satisfies option D too.. X<4, if its <4.5, it could be less that 4 too right?
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Re: If x is an integer and |2x + 3| 12 then which of the following must [#permalink]
If x is an integer and \(|2x+3|≤12\), then which of the following must be true?

-12 <= 2x+3 <= 12
-7.5 <= x <= 4.5

A. x < -9
B. x < -8
C. x > -8: MUST BE TRUE
D. x < 4
E. x > 4

IMO C

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Re: If x is an integer and |2x + 3| 12 then which of the following must [#permalink]
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