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GMAT Diagnostic Test Question 14

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GMAT Diagnostic Test Question 14 [#permalink] New post 06 Jun 2009, 21:24
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GMAT Diagnostic Test Question 14
Field: modules
Difficulty: 600

If -1<x<5 then which of the following must be true?

A. |3-x| < -3
B. |x| < 4
C. |x|-2 > 2
D. |2 + x| > 3
E. |x - 2| < 3
[Reveal] Spoiler: OA

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Last edited by bb on 28 Sep 2013, 20:27, edited 4 times in total.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 01 Jul 2009, 07:04
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Explanation:
Official Answer: E

A. |3-x| < -3 --> absolute value is always non-negative, hence this options is wrong for any value of x;
B. |x| < 4 --> not necessarily true: consider x=4.5;
C. |x| - 2 > 2 --> |x|>4 --> not necessarily true: consider x=3;
D. |2 + x| > 3 --> not necessarily true: consider x=0;

So, we are left with option E only.

Just to check:
E. |x-2| < 3 --> -3<x-2<3 --> add 2 to each part: -1<x<5. So, this option is basically the same as the condition given in the stem.

Answer: E.
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Last edited by bb on 28 Sep 2013, 11:46, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 20 Jul 2009, 20:02
Can someone please explain in more detail why B is wrong? I'm plugging in different values and I can't find one between -1 and 5 that doesn't satisfy the inequality.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 20 Jul 2009, 20:21
Expert's post
topher wrote:
Can someone please explain in more detail why B is wrong? I'm plugging in different values and I can't find one between -1 and 5 that doesn't satisfy the inequality.


You should approach it the "opposite" way - instead try values outside of the (-1; 5) range and see if they work - for example (-4).
The question is asking you, which equation below represents the best a condition where -1 < x < 5, not which of the following equations will work with values of x.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 15 Sep 2009, 19:42
The question is

Which of the following inequalities satisfies the condition if the values of x are between -1 and 5?

Clearly states -1 < x < 5 and asking which of below will satisfy and I guess B will satisfy. Else have to refrain q clearly.

thxs
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 17 Sep 2009, 22:06
bb wrote:
Which of the following inequalities satisfies the condition if the values of x are between -1 and 5?

A. |3 – x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x – 2| < 3


dzyubam,
I tried to send you PM but it did not go for some reasons. The PM is still in my outbox.


B and E both satisfiy the conditions given in the question.

B. -1 < |x| < 5 --> |x| will always be greater than -1, so we are left with |x| < 5, from where x \in (-5,5). B is out too.

* (-5, 5) should be (-1, 5).
* Any value for x satisfies the condition in B.



E. |x – 2| < 3 --> x \in (-1,5). E is the correct answer.

* Any value for x satisfies the condition in E.



So B and E both are same. I guess the question needs to be modified..




Subject: GMAT Diagnostic Test Question 13

dzyubam wrote:
Explanation:
Rating:

Official Answer: E

A. |3 – x| < -3 --> no expression under modulus can be negative. A is out.

B. -1 < |x| < 5 --> |x| will always be greater than -1, so we are left with |x| < 5, from where x \in (-5,5). B is out too.

C. |x| - 2 > 2 --> it can be rewritten as |x| > 4, x can be any number outside the range (-4,4). C is out too.

D. |2 + x| > 3 --> x \in (-\infty, -5) \cup (1,\infty). D is out.

E. |x – 2| < 3 --> x \in (-1,5). E is the correct answer.

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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 18 Sep 2009, 03:26
Agree with GMATTiger, the question clearly states that x lies between -1 and 5. so we should just ignore the 'other' values i.e. -5<x<=-1 for B. B should also satisify the equation.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 18 Sep 2009, 04:53
well, I'm so new to gmat but
both b and e may seem like a correct answer,
in the actual test I will still prefer e because b probably should seem a trick to me,
the absolute value of any number can't be below zero,
so I think it's a false expression from the start, right?
or am I mixing things?
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 23 Sep 2009, 23:15
Sorry guys, I had limited access to Internet for 10 days. I agree the question is ambiguous. It has to be reworded somehow. Here are my two suggestions:

Which of the following inequalities satisfies the condition that the values of x are between -1 and 5?
Which of the following inequalities has solution for x in the range (-1,5)?

What do you all think? Is either of the rewordings any better than the original?
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 25 Sep 2009, 22:39
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dzyubam wrote:
Sorry guys, I had limited access to Internet for 10 days. I agree the question is ambiguous. It has to be reworded somehow. Here are my two suggestions:

Which of the following inequalities satisfies the condition that the values of x are between -1 and 5?
Which of the following inequalities has solution for x in the range (-1,5)?

What do you all think? Is either of the rewordings any better than the original?


I would go for the following:


Quote:
Which of the following inequalities must be true if the values of x are between -1 and 5?

A. |3 – x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x – 2| < 3

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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 26 Sep 2009, 02:36
I've updated the PDF and the online version per GMAT TIGER's suggestion. +1.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 15 Oct 2009, 13:13
pls explain how |x-2|<3 is x(-1,5) ...really need help !
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 15 Oct 2009, 13:28
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In order to solve the modulus inequality you have to consider two possible values of x: a positive one and a negative one. First, you just strip the modulus signs and solve the inequality:
x-2<3
x<5
This is the range of x for positive values of x. Now you need to solve a different inequality for negative x:
-x+2<3
x>-1
What we did here is flip the signs of the expression inside the modulus and solve the new inequality. This is range of x for negative x. Combining both x<5 and x>-1 you get the solution x \in (-1,5).
harjaskooner wrote:
pls explain how |x-2|<3 is x(-1,5) ...really need help !

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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 16 Oct 2009, 10:15
dzyubam wrote:
In order to solve the modulus inequality you have to consider two possible values of x: a positive one and a negative one. First, you just strip the modulus signs and solve the inequality:
x-2<3
x<5
This is the range of x for positive values of x. Now you need to solve a different inequality for negative x:
-x+2<3
x>-1
What we did here is flip the signs of the expression inside the modulus and solve the new inequality. This is range of x for negative x. Combining both x<5 and x>-1 you get the solution x \in (-1,5).
harjaskooner wrote:
pls explain how |x-2|<3 is x(-1,5) ...really need help !


thanks ! now i understand it !
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 18 Oct 2009, 08:33
harjaskooner wrote:
dzyubam wrote:
In order to solve the modulus inequality you have to consider two possible values of x: a positive one and a negative one. First, you just strip the modulus signs and solve the inequality:
x-2<3
x<5
This is the range of x for positive values of x. Now you need to solve a different inequality for negative x:
-x+2<3
x>-1
What we did here is flip the signs of the expression inside the modulus and solve the new inequality. This is range of x for negative x. Combining both x<5 and x>-1 you get the solution x \in (-1,5).
harjaskooner wrote:
pls explain how |x-2|<3 is x(-1,5) ...really need help !


thanks ! now i understand it !


Guys, my understanding from the GMAT is that between means a closed set i.e. and based on your question does not include the values -1 nor 5 but rather 0, 1, 2, 3 & 4 - of course I am assuming x is an integer. This suggest to me that questions of this sort will not appear in the real test as we seem to have two correct answers to the same question, namely B and D
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 18 Oct 2009, 08:53
LUGO wrote:
Guys, my understanding from the GMAT is that between means a closed set i.e. and based on your question does not include the values -1 nor 5 but rather 0, 1, 2, 3 & 4 - of course I am assuming x is an integer. This suggest to me that questions of this sort will not appear in the real test as we seem to have two correct answers to the same question, namely B and D


The highlighted part is not correct. X could be a fraction or -ve as well.

-1 < x < 5 means values excluding -1 and 5.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 21 Nov 2009, 01:52
I am still having trouble understanding the stem correctly... when I did the problem, i still got both B and E to be true...
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 23 Nov 2009, 05:20
I agree we have to rephrase the question. What it was intended to mean is something like this:

Which of the following inequalities has its solution in the range (-1,5)?

If you guys have a better suggestion, please share. I will update the question when we agree on rephrasing.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 28 Nov 2009, 21:35
why dont we change the answer choice b itself??

because in the given range B will always hold true...
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 18 Dec 2009, 00:18
Which of the following inequalities represents the same range as of X between -1 and 5?
Re: GMAT Diagnostic Test Question 13   [#permalink] 18 Dec 2009, 00:18
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