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# If 4<(7-x)/3, which of the following must be true?

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If 4<(7-x)/3, which of the following must be true? [#permalink]

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12 Aug 2010, 15:05
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If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

[Reveal] Spoiler:
I am confused about statement II ????

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-4-7-x-3-w ... 68681.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 May 2017, 22:50, edited 3 times in total.
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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12 Aug 2010, 15:39
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mn2010 wrote:
If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

I am not confused about statement II ????

Good question, +1.

Note that we are asked to determine which MUST be true, not could be true.

$$4<\frac{7-x}{3}$$ --> $$12<7-x$$ --> $$x<-5$$. So we know that $$x<-5$$, it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range $$x<-5$$.

Basically the question asks: if $$x<-5$$ which of the following is true?

I. $$5<x$$ --> not true as $$x<-5$$.

II. $$|x+3|>2$$, this inequality holds true for 2 cases, (for 2 ranges): 1. when $$x+3>2$$, so when $$x>-1$$ or 2. when $$-x-3>2$$, so when $$x<-5$$. We are given that second range is true ($$x<-5$$), so this inequality holds true.

Or another way: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

III. $$-(x+5)>0$$ --> $$x<-5$$ --> true.

Hope it's clear.
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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12 Aug 2010, 15:50
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thanks Bunuel... Inequality still rattles me .... more practice I guess ....

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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14 Aug 2010, 08:50
thanks for the explanation bunuel.

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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20 Dec 2010, 05:29
Great question.
I thought we should eliminate II.

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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16 Jan 2011, 20:15
Bunuel wrote:
mn2010 wrote:
If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

I am not confused about statement II ????

Good question, +1.

Note that we are asked to determine which MUST be true, not could be true.

$$4<\frac{7-x}{3}$$ --> $$12<7-x$$ --> $$x<-5$$. So we know that $$x<-5$$, it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range $$x<-5$$.

Basically the question asks: if $$x<-5$$ which of the following is true?

I. $$5<x$$ --> not true as $$x<-5$$.

II. $$|x+3|>2$$, this inequality holds true for 2 cases, (for 2 ranges): 1. when $$x+3>2$$, so when $$x>-1$$ or 2. when $$-x-3>2$$, so when $$x<-5$$. We are given that second range is true ($$x<-5$$), so this inequality holds true.

Or another way: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

III. $$-(x+5)>0$$ --> $$x<-5$$ --> true.

Hope it's clear.

here for the |x+3| >2 we have 2cases- x> -1 or x <-5 (while second one satisfies the condn as asked but is not it we should be looking at all the possibilities and if all satisfies then only we can say that this option also holds as for as GMAT is concerned ) so I am not clear about the explanation for II to be true.
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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17 Jan 2011, 03:29
Expert's post
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yogesh1984 wrote:
Bunuel wrote:
mn2010 wrote:
If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

I am not confused about statement II ????

Good question, +1.

Note that we are asked to determine which MUST be true, not could be true.

$$4<\frac{7-x}{3}$$ --> $$12<7-x$$ --> $$x<-5$$. So we know that $$x<-5$$, it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range $$x<-5$$.

Basically the question asks: if $$x<-5$$ which of the following is true?

I. $$5<x$$ --> not true as $$x<-5$$.

II. $$|x+3|>2$$, this inequality holds true for 2 cases, (for 2 ranges): 1. when $$x+3>2$$, so when $$x>-1$$ or 2. when $$-x-3>2$$, so when $$x<-5$$. We are given that second range is true ($$x<-5$$), so this inequality holds true.

Or another way: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

III. $$-(x+5)>0$$ --> $$x<-5$$ --> true.

Hope it's clear.

here for the |x+3| >2 we have 2cases- x> -1 or x <-5 (while second one satisfies the condn as asked but is not it we should be looking at all the possibilities and if all satisfies then only we can say that this option also holds as for as GMAT is concerned ) so I am not clear about the explanation for II to be true.

Is $$|x+3|>2$$ true? --> this inequality is true if $$x>-1$$ OR $$x<-5$$. Now, it's given that $$x<-5$$, so it must hold true.

Or: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

Hope it's clear.
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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17 Jan 2011, 10:22
Quote:
Is $$|x+3|>2$$ true? --> this inequality is true if $$x>-1$$ OR $$x<-5$$. Now, it's given that $$x<-5$$, so it must hold true.

Or: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

Hope it's clear.

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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17 Jan 2011, 18:52
Nice one, got it myself as D

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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19 Jun 2013, 04:52
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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21 Aug 2013, 08:41
For Option II What about x>-1, i'm not getting..

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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21 Aug 2013, 08:44
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manish333 wrote:
For Option II What about x>-1, i'm not getting..

Given that x<-5.

For any value of x less than -5 inequality |x+3|>2 will hold true.

Hope it's clear.
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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23 Aug 2013, 23:38
Good one! I got stumped with II, but now it makes more sense.
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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08 Jan 2014, 07:35
mn2010 wrote:
If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

I am confused about statement II ????

12 < 7-x => x < -5
I. 5 < x not possible.
II. |x+3| > 2 . now x < -5 or lets say x = -5.1 so |x+3| = |-2.1| = 2.1 > 2 So any case, it will always be more than 2. Definitely.
III. -(x+5) as x < -5 so x can be -5.1 so -(-.1) so +ve hence III is also possible.

hence D)
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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07 Mar 2015, 04:35
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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26 Aug 2015, 13:23
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I tried an alternate solution by plugging numbers

Given that $$x < -5$$, we could pick a number that satisfies this condition, lets say $$x = -7$$

I. $$5 < x$$, is $$5 < -7$$, Not true, Eliminate
II. $$|x + 3| > 2$$, plug in -7 in place of x, we get $$| -7 + 3 | > 2, |4| > 2$$, True
III. $$- (x + 5) > 0, - ( -7 + 5) = - (-2) = 2 > 0$$, True

Answer is D. II & III only
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Last edited by hideyoshi on 17 Feb 2016, 21:25, edited 1 time in total.

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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04 Sep 2015, 22:06
mn2010 wrote:
If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

[Reveal] Spoiler:
I am confused about statement II ????

According to II, x can be 2 or -10. But according to the given question x<-5. Hence II can not be true always.

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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05 Sep 2015, 04:03
vivek001 wrote:
mn2010 wrote:
If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

[Reveal] Spoiler:
I am confused about statement II ????

According to II, x can be 2 or -10. But according to the given question x<-5. Hence II can not be true always.

You did not understand the question. It's given that x < -5. Since x < -5 then |x + 3| > 2 is true (for any value of x less than -5, |x + 3| > 2 holds).
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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23 Sep 2015, 09:27
got this question correct, but selected wrong option as statement D is partially correct .

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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]

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02 Jan 2016, 15:15
Bunuel wrote:
mn2010 wrote:
If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

I am not confused about statement II ????

Good question, +1.

Note that we are asked to determine which MUST be true, not could be true.

$$4<\frac{7-x}{3}$$ --> $$12<7-x$$ --> $$x<-5$$. So we know that $$x<-5$$, it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range $$x<-5$$.

Basically the question asks: if $$x<-5$$ which of the following is true?

I. $$5<x$$ --> not true as $$x<-5$$.

II. $$|x+3|>2$$, this inequality holds true for 2 cases, (for 2 ranges): 1. when $$x+3>2$$, so when $$x>-1$$ or 2. when $$-x-3>2$$, so when $$x<-5$$. We are given that second range is true ($$x<-5$$), so this inequality holds true.

Or another way: ANY $$x$$ from the range $$x<-5$$ (-5.1, -6, -7, ...) will make $$|x+3|>2$$ true, so as $$x<-5$$, then $$|x+3|>2$$ is always true.

III. $$-(x+5)>0$$ --> $$x<-5$$ --> true.

Hope it's clear.

Hi Bunuel,
Statements I and III are perfectly clear. But let me ask you a question about statement II to clear all my doubts, if you don´t mind.

Question stem states that x < -5 and then asks "if this is true, then what else must be true?"

Statement II gives us 2 options. Case A: x > -1 OR Case B: x < -5. Since the question stem already stated that x < -5, then Case A cannot be true (since x cannot be less than -5 and bigger than -1 at the same time) and Case B must be true. Therefore, Statement II must be true.

Is this reasoning correct?

Thank you so much!
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Re: If 4<(7-x)/3, which of the following must be true?   [#permalink] 02 Jan 2016, 15:15

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