absolute value

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earth@work: Master | Next Rank: 500 Posts; Posts: 248; Joined: Mon Aug 11, 2008 9:51 am; Thanked: 13 times

by earth@work » Tue Nov 18, 2008 2:10 pm

If x = ± ıxı , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
(A) None (B) I only (C) III only (D) I and II (E) II and III

ıxı stands for absolute value of x
Ans:[spoiler](D)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Tue Nov 18, 2008 2:10 pm

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Tue Nov 18, 2008 2:51 pm

Ok I think all the three option could be true.

mod x could be -x or x.

mod x can also be equal to 0.

I can't see how third option is false???

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Nov 19, 2008 3:09 pm

This question would be a call for the experts on this forum like Stuart/Ron/Ian/Stacey or others.

I think interpretting this question is the biggest roadblock that I see. Is it x is equal to both +|x| and - |x| or x is equal to +|x| or -|x|. I would think its the former.

x = +- |x|

IMO its either just B) (meaning x=0 only) or all three like Mal's said. I also agree with Mal's on if x<0 is one of the correct choices then why not x>0?

I am sure we are missing something or the OA is wrong.

Earth@work whats the source and by any chance is there an explanation to this craziness

Last edited by cramya on Wed Nov 19, 2008 7:08 pm, edited 1 time in total.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: absolute value

by logitech » Wed Nov 19, 2008 3:34 pm

earth@work wrote:If x = ± ıxı , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
(A) None (B) I only (C) III only (D) I and II (E) II and III

ıxı stands for absolute value of x
Ans:[spoiler](D)[/spoiler]

x = ± ıxı so we have two equations:

1) x = ıxı

x - ıxı = 0

a) X> 0 ; x-x = 0 works

b) X<0 ; x-(-x) = 0 ---> 2x = 0 X=0 - this does not works since x is not less than 0

c) X =0 ; 0-0 = 0 - this works

2) x = - ıxı

x + ıxı = 0

a) X> 0 ; x+x = 0 and 2x = 0 ---> x = 0 this does not work since X is not greater than 0

b) X<0 ; x+(-x) = 0 ---> this works

c) X =0 ; 0-0 = 0 - this works

So IMO , all of them are okay but only 0 satisfies the both condition. Since the question stem uses "COULD" I would go with F) I, II and II but if it were asking MUST be true, I would choose B) I only

Oh did I mention that I hate typos ? So you guys know

LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

Re: absolute value

by lunarpower » Wed Nov 19, 2008 3:57 pm

earth@work wrote:If x = ± ıxı , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
(A) None (B) I only (C) III only (D) I and II (E) II and III

ıxı stands for absolute value of x
Ans:[spoiler](D)[/spoiler]

yeah, the writing of this question is a bit ridiculous.

the users above have this one pretty much covered, but here's a recap:

* preliminary observations:
if x > 0, then |x| is just x; therefore, x = |x|.
if x < 0, then |x|, which is positive, is the opposite of x; therefore, x = -|x|.
if x = 0, then everything is 0, and so x equals both |x| and -|x|.

* we're not sure whether "±" means "EITHER + or -" or "BOTH + and -". the answer to the problem will differ according to which of these meanings was intended.

* CASE 1: take "±" to mean "EITHER + or -".
in this case, every possible value of x will solve the equation, because, as noted in the preliminary observations, every possible value of x is equal to at least one of |x| and -|x|.
in this case the answer is "i, ii, and iii," which isn't one of the choices.
one of the previous posters called this "choice (f)". i like.

* CASE 2: take "±" to mean "BOTH + and -".
in this case, the only value of x that works is 0, as noted in the preliminary observations.
this is choice (b).

* since only one of the cases above appears in the answer choices, we may as well go with that one, so let's pick (b).

--

the official test will NEVER feature this sort of notational ambiguity, so rest easy. instead, concentrate on the takeaways ("preliminary observations") posted above regarding the absolute value, since those are what you'll actually be able to apply to other problems.

Last edited by lunarpower on Wed Nov 19, 2008 4:18 pm, edited 1 time in total.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Wed Nov 19, 2008 4:15 pm

I like the explanation of the user above.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Nov 19, 2008 7:12 pm

Thanks Guys! I had a typo of A) instead oF B)(corrected above) meaant to say 0 only if
x = +- |x| (x= +|x| and x = -|x|)

Ron, thank you for the takeaways and reiterating the absolute value concepts!

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earth@work: Master | Next Rank: 500 Posts; Posts: 248; Joined: Mon Aug 11, 2008 9:51 am; Thanked: 13 times

by earth@work » Thu Nov 20, 2008 11:23 am

cramya, this is from NOVA GMAT prep course.
i tried by plugging in nos. and i got the answer same as everyone here i.e B.
Ron & logitec thanks for the explanations... below is the explanation which the book gives for answer to be (D)..pls help me understand it in case u get what it's trying to explain :

Statement I could be true because ± 0 = −(+0)= −(0) = 0 . Statement II could be true because the
right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal. Since Statement III is the
opposite of Statement II, it must be false. But let’s show this explicitly: Suppose x were positive.
Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x
yields 1 = –1. This is contradiction. Hence, x cannot be positive. The answer is (D).

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rajataga: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Tue Dec 23, 2008 11:06 pm; Thanked: 2 times

by rajataga » Wed Dec 24, 2008 11:56 am

came across this while reading the forums.....

[email protected] had basically got the question only wrong the questions was

x = +-(x)

had nothing to do with absolute value.....lol

actually a very ambiguous question.....could be construed as EITHER be equal to + or - |X| or SHOULD be equal to + and - |X|

Last edited by rajataga on Wed Dec 24, 2008 12:10 pm, edited 4 times in total.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 24, 2008 11:58 am

[email protected] had basically got the question only wrong the questions was

x = +-(x)

had nothing to do with absolute value.....lol

That explains the craziness then

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