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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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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 ????


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

Originally posted by mn2010 on 12 Aug 2010, 15:05.
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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New post 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.

Answer: D.

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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New post Updated on: 17 Feb 2016, 21:25
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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

Originally posted by hideyoshi on 26 Aug 2015, 13:23.
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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New post 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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New post 05 Sep 2015, 04:03
2
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

I am confused about statement II ????



Correct answer is only III.
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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New post 17 Jan 2011, 03:29
1
2
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.

Answer: D.

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

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New post 10 Mar 2016, 10:59
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[quote="mn2010"]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

Hey Everyone I am facing majo issues with this one ..
the second statement specifies X>1 or X<-5
now x can be 100 too hence it will make the inequality insufficient...
I am rooting for B only

Someone i the thread mentioned X<-5 is given right... but what if X is 100 ..
i have every statement in this thread and still believe the answer is B ..

Can anyone tell me where am i doing wrong

P.S => DON'T tell me X<-5 IS GIVEN
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 01 Apr 2016, 02:26
1
leeto wrote:

Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true.
A simple check can prove it :

From II we have that Case A: x > -1 OR Case B: x < -5
From Case A let's take x = 0
4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working
Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .

Bunuel, please, could you confirm ?


This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add...
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 01 Apr 2016, 02:33
1
Bunuel wrote:
leeto wrote:

Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true.
A simple check can prove it :

From II we have that Case A: x > -1 OR Case B: x < -5
From Case A let's take x = 0
4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working
Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .

Bunuel, please, could you confirm ?


This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add...


The question uses the same logic as in the examples below:

If \(x=5\), then which of the following must be true about \(x\):
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x>-10

Answer is E (x>-10), because as x=5 then it's more than -10.

Or:
If \(-1<x<10\), then which of the following must be true about \(x\):
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x<120

Again answer is E, because ANY \(x\) from \(-1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120.

Or:
If \(-1<x<0\) or \(x>1\), then which of the following must be true about \(x\):
A. x>1
B. x>-1
C. |x|<1
D. |x|=1
E. |x|^2>1

As \(-1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>-1\). So B is always true.

\(x\) could be for example -1/2, -3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than -1. So we can say about \(x\) that it's more than -1.

On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be -1/2 and -1/2 is not more than 1.

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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New post 01 Apr 2016, 02:36
1
Bunuel wrote:
Bunuel wrote:
leeto wrote:

Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true.
A simple check can prove it :

From II we have that Case A: x > -1 OR Case B: x < -5
From Case A let's take x = 0
4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working
Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .

Bunuel, please, could you confirm ?


This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add...


The question uses the same logic as in the examples below:

If \(x=5\), then which of the following must be true about \(x\):
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x>-10

Answer is E (x>-10), because as x=5 then it's more than -10.

Or:
If \(-1<x<10\), then which of the following must be true about \(x\):
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x<120

Again answer is E, because ANY \(x\) from \(-1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120.

Or:
If \(-1<x<0\) or \(x>1\), then which of the following must be true about \(x\):
A. x>1
B. x>-1
C. |x|<1
D. |x|=1
E. |x|^2>1

As \(-1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>-1\). So B is always true.

\(x\) could be for example -1/2, -3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than -1. So we can say about \(x\) that it's more than -1.

On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be -1/2 and -1/2 is not more than 1.

Hope it's clear.


Similar questions to practice:
if-4x-12-x-9-which-of-the-following-must-be-true-101732.html
if-it-is-true-that-x-2-and-x-7-which-of-the-following-m-129093.html
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 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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New post 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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New post 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.

Answer: D.

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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New post 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.


Hmm... It was so obvious :( thanks for your patience & reply :)
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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

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New post 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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New post 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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New post 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] 08 Jan 2014, 07:35

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