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Re: If 4<(7-x)/3, which of the following must be true? [#permalink]
12 Aug 2010, 14:39

10

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

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.

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

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. _________________

Re: If 4<(7-x)/3, which of the following must be true? [#permalink]
17 Jan 2011, 02:29

Expert's post

1

This post was BOOKMARKED

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.

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.

Re: If 4<(7-x)/3, which of the following must be true? [#permalink]
07 Mar 2015, 03:35

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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