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# GMAT Diagnostic Test Question 14

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GMAT Diagnostic Test Question 14 [#permalink]

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06 Jun 2009, 22:24
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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. $$|x - 2| < 3$$
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Last edited by bb on 28 Sep 2013, 21:27, edited 4 times in total.
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Re: GMAT Diagnostic Test Question 13 [#permalink]

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01 Jul 2009, 08:04
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Explanation:

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.

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Last edited by bb on 28 Sep 2013, 12:46, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 13 [#permalink]

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20 Jul 2009, 21:02
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]

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20 Jul 2009, 21:21
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]

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15 Sep 2009, 20:42
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]

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17 Sep 2009, 23:06
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:

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]

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18 Sep 2009, 04:26
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]

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18 Sep 2009, 05:53
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]

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24 Sep 2009, 00:15
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]

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25 Sep 2009, 23:39
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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]

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26 Sep 2009, 03:36
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]

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15 Oct 2009, 14:13
pls explain how |x-2|<3 is x(-1,5) ...really need help !
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Re: GMAT Diagnostic Test Question 13 [#permalink]

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15 Oct 2009, 14:28
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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 $$x \in (-1,5)$$.
pls explain how |x-2|<3 is x(-1,5) ...really need help !

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Re: GMAT Diagnostic Test Question 13 [#permalink]

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16 Oct 2009, 11:15
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 $$x \in (-1,5)$$.
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]

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18 Oct 2009, 09:33
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 $$x \in (-1,5)$$.
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]

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18 Oct 2009, 09:53
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]

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21 Nov 2009, 02:52
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]

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23 Nov 2009, 06:20
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]

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28 Nov 2009, 22:35
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]

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18 Dec 2009, 01:18
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, 01:18

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