absolute value

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colakumarfanta: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon May 03, 2010 2:55 am; Thanked: 1 times

absolute value

by colakumarfanta » Wed May 19, 2010 10:33 am

Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0

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Source: Beat The GMAT — Data Sufficiency | Wed May 19, 2010 10:33 am

indiantiger: Master | Next Rank: 500 Posts; Posts: 362; Joined: Fri Oct 02, 2009 4:18 am; Thanked: 26 times; Followed by:1 members

by indiantiger » Wed May 19, 2010 11:55 am

Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0
Lets take Statement 1 :

for this x + 2|y| = 0 to be valid
either x = 0 and y = 0 (one of the solutions) (this proves the question)
or
x= +/-2y or x=-6 and y = +/-3(one of the solutions) (this does not prove the question)
not sufficient

Lets take Statement 2 :
for this y + 2|x| = 0 to be valid
either x = 0 and y = 0 (one of the solutions) (this proves the question)
or
y=+/-2x or y = -6 and x = +/-3 (one of the solutions) (this does not prove the question)
not sufficient

rules out A,B,D
left with C or E
if we combine st1 and st2 we get one common solution that is x = 0 and y =0

hence (C)

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pm; Thanked: 50 times; Followed by:4 members

by akhpad » Thu May 20, 2010 12:13 am

colakumarfanta wrote: Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0

|x| + |y| = 0 only possible when both x = y = 0

Statement 1:
x + 2|y| = 0
x = - 2|y|

x is -ve and y can be either -ve or +ve

Not Sufficient

Statement 2:

Same as statement 1

Not Sufficient

Statement 1 and 2:
x = - 2|y| ----- a
y = -2 |x| or |y| = 2|x| -----b

from a and b
x = - 2|y| = -4|x|
x + 4|x| = 0 only possible when x = 0
x = 0 then y=0

Sufficient

Answer: C

What is OA?

One should post Q along with OA. It is a better practice.

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pm; Location: Irvine, CA; Thanked: 199 times; Followed by:85 members; GMAT Score:750

by tpr-becky » Thu May 20, 2010 9:34 am

recieve a PM for this one

becuase absolute values can only be positive - the question is really asking whether x and y are both equal to zero.

1) here it is possible for both x and y to be zero but not required (x could be -1/2 and y could be 1/4) so this is insufficient BCD

2) same applies to this one so it is also insufficient CE

if you try them together you find that you can replace y in the equation with, and as explained below you end up wiht
X +4/x/=0 which means that x must be zero, which also means that y must be zero

Answer is C.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Thu May 20, 2010 11:21 am

colakumarfanta wrote:Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 0

A slightly different approach (although similar in many respects to those already posted):

|x| and |y| are both non-negative; according, the only way to get a "Yes" answer is if both are 0. So, we can rephrase the question as:

Is x=y=0?

(1) we could pick x=y=0 to satisfy the statement, so we can get a "yes" answer.

However, we could also pick a negative value for x, in which case y could be negative or positive, so we can get a "no" answer.

Can get both a yes and a no: insufficient, eliminate A and D.

(2) exactly same logic as (1), swapping x and y. Insufficient: eliminate B.

Combined:

we can rewrite the statements as:

(1) |y| = -x/2

(2) |x| = -y/2

Ignoring the signs, we can see that y= .5x AND x = .5y. The only way this relationship can hold true is if x and y are both 0; that's a definite "yes" - together sufficient, choose (C).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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vanquish: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Thu Feb 04, 2010 8:07 pm

by vanquish » Tue May 25, 2010 7:29 pm

Hi all

Thank you for excellent ans above.

Can anyone help me with how to handle combining statements with Yes/No D.S questions. I always (everytime!) fail to select the correct ans on yes/no D.S, or takes me forever to figure out.

I normally try using testing values systematically e.g. -2, -1/2, 0 ,1/2, 2 to make sure it answers both statements and the question so as to decide C or E is the ans. It's too time consuming for actual GMAT sitting and error prone. Is this the right approach or is there a better way.

For instance, on the above example:
I tested 0 & -2, -1/2 and 0 on Statement 1 and 2 individally and narrowed down to C or E.
Then now i have to test -2, -1/2, 0 ,1/2, 2 on both statements and question to make sure i cover all possibilities. Is this the right approach. Is there any clever tips and quicker way of handling the assessment of combine statements for Y/N D.S questions.

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aslan: Master | Next Rank: 500 Posts; Posts: 153; Joined: Sat Jul 24, 2010 3:33 pm; Thanked: 5 times; Followed by:1 members

by aslan » Mon Nov 15, 2010 2:36 am

@vanquish:For DS just try to come up with a 'yes' first and then a 'no' first if both are coming then the statement is insufficient.Do not plugin values randomly from -1/2,0/12/1....Just think f those values first which will give you a 'yes' and 'no' statements.If you get a constant statement with pluggin then that stem holds true and is sufficient

P.S:this is for 'yes' no' DS only.

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bacchewar_prashant: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Tue Sep 28, 2010 11:34 pm; Thanked: 1 times

by bacchewar_prashant » Mon Nov 15, 2010 3:35 am

I was totally confused by the question. It totally sliped out of my that question is asking both x and y are zero or not.
Thanks for post nice question.

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Taran: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Fri Oct 01, 2010 7:34 am; Location: Pune, India; Thanked: 1 times; GMAT Score:680

by Taran » Thu Dec 16, 2010 10:36 pm

Hello all,

I was able to clearly see that ST1 and ST2 were not sufficient independently. However i made puppy face when i had to combine both to check the sufficiency. I was randomly about to pick E but suddenly realised something and went for C. Please help me as to how to combine the two statements and come up with an answer. Thanks....

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MM_Ed: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Sun Jun 19, 2011 3:19 pm; Thanked: 15 times

by MM_Ed » Tue Jul 05, 2011 6:38 pm

Absolute values are positive. The only way two positive numbers can equal 0 is if they are both 0. Neither statement alone is sufficient to establish this, so both are needed.

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 am; Location: pune; Thanked: 36 times; Followed by:3 members

by amit2k9 » Tue Jul 05, 2011 10:00 pm

possible only if x=y=0

a x=y=0 and x=-2 y=1|-1. not sufficient.

b x=y=0 and x=1|-1 y=2. not sufficient.

a+b only x=y=0 satisfies.

C it is.

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olegpoi: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Thu Aug 12, 2010 12:40 am; Thanked: 1 times; Followed by:1 members

by olegpoi » Tue Aug 30, 2011 11:55 am

IMO C

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feral2020: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Oct 20, 2010 11:16 am

by feral2020 » Thu Sep 01, 2011 2:16 pm

Should GMAT test takers assume that on any given question different variables may very well stand for the same number (e.g. a + b = 5 + 5)? Or is just for Data Suffiency questions?