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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]  12 Aug 2010, 14:05
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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

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

Last edited by mn2010 on 12 Aug 2010, 14:44, edited 1 time in total.
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Re: Quant Review 2nd Edition DS#156, Inequality [#permalink]  12 Aug 2010, 14:39
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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: Quant Review 2nd Edition DS#156, Inequality [#permalink]  12 Aug 2010, 14:50
thanks Bunuel... Inequality still rattles me .... more practice I guess ....
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Re: Quant Review 2nd Edition DS#156, Inequality [#permalink]  14 Aug 2010, 07:50
thanks for the explanation bunuel.
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Re: Quant Review 2nd Edition DS#156, Inequality [#permalink]  20 Dec 2010, 04:29
Great question.
I thought we should eliminate II.
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Quant Rev #156: Inequalities [#permalink]  16 Jan 2011, 14:13
If $$4 < \frac {7-x}{3}$$, 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
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Re: Quant Rev #156: Inequalities [#permalink]  16 Jan 2011, 14:25
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Merging similar topics.
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Re: Quant Review 2nd Edition DS#156, Inequality [#permalink]  16 Jan 2011, 19:15
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: Quant Review 2nd Edition DS#156, Inequality [#permalink]  17 Jan 2011, 02:29
Expert's post
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: Quant Review 2nd Edition DS#156, Inequality [#permalink]  17 Jan 2011, 09:22
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: Quant Review 2nd Edition DS#156, Inequality [#permalink]  17 Jan 2011, 17:52
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]  19 Jun 2013, 03:52
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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]  21 Aug 2013, 07:41
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]  21 Aug 2013, 07:44
Expert's post
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]  23 Aug 2013, 22:38
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]  08 Jan 2014, 06:35
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]  07 Mar 2015, 03:35
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Re: If 4<(7-x)/3, which of the following must be true?   [#permalink] 07 Mar 2015, 03:35
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