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Joined: 12 Aug 2015
Posts: 2537
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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1
[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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try to plug in any number less than -5 and check because that's the condition given in question.

x < -5 means x can be -6,-7,-8 ....
|x+3|>2
when x= -6 => |-6+3|>2 true
when x=-100 => |-100+3|>2 true
Intern  Joined: 13 Mar 2011
Posts: 21
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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Bunuel 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.

Yes. Basically we are given that x<-5 and then asked whether |x+3|>2 is true. We know that if x < -5, then |x+3|>2 must be true.

Chiragjordan 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

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

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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 61282
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 61282
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 61282
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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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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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 ????

Simplify 4<(7-x)/3 and you get x < -5. Any of the statement says it would be true.

(I) 5 < X i.e. X > 5 NOT true.

(II) |x+3|>2 - range for this is -5 < X < 5. True.

(III) -(x+5) i.e. -x-5 as x is less than -5 the values it would take will be -6, -7 and so on. in all these cases -(x+5) will be positive. True

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

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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.

In II. |x+3|>2
If we have two cases where x>-1 and x<-5, then how can it MUST BE TRUE? Not 100% clear on this.

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

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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.

Regarding the option II shouldn't the condition x>-1 be satisfied ?
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Joined: 02 Sep 2009
Posts: 61282
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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Animatzer 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.

Regarding the option II shouldn't the condition x>-1 be satisfied ?

Check here: if-4-7-x-3-which-of-the-following-must-be-true-99015.html#p853541
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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let's simpify from the beginning: 12<7-x
x<-5
let's test 1: doesn't work C,E out
let's test 2: |-6+3|>2 works fine
let's test 3: -(-6+5)= 1, hence, positive

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Posts: 10105
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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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 confused about statement II ????

Responding to a pm:
Quote:
In this question, I found that option two has two ranges. x > - or x < -5. So why this becomes sufficient? Don't we need only one clear answer to prove the sufficiency? If I have three ranges and one of them is good to prove the sufficiency, then also can we discard the other two?

You are given that x < -5. You obtain this because you are given that 4<(7-x)/3.
So x can take values such as -5.4, -6, -100, -54637 etc

Which of the following MUST BE TRUE?

II. |x+3|>2
Gives x < -5 OR x > -1
For every value that x can take, is this statement true? Yes. For every value that x can take it is "'less than 5" or "more than -1".
All our values are actually "less than -5". We need x to satisfy either "x < -5" or "x > -1".
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Posts: 61282
Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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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 confused about statement II ????

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-4-7-x-3-w ... 68681.html
_________________ Re: If 4<(7-x)/3, which of the following must be true?   [#permalink] 29 May 2017, 21:50

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