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# M15 Q11

Author Message
Manager
Joined: 13 May 2010
Posts: 122

Kudos [?]: 24 [0], given: 4

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24 Jul 2012, 19:50
Is $$|x - y| \gt |x + y|$$ ?

$$x^2 - y^2 = 9$$
$$x - y = 2$$

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. S1 gives us information about $$(x - y)(x + y)$$ but does not tell how $$(x - y)$$ and $$(x + y)$$ compare to each other.

Statement (2) by itself is insufficient. S2 gives no information about $$(x + y)$$ .

Statements (1) and (2) combined are sufficient. From S1 and S2 it follows that $$2(x + y) = 9$$ from where $$(x + y) = 4.5$$ . Now we can state that $$|x - y| = 2 \lt |x + y| = 4.5$$ .

Kudos [?]: 24 [0], given: 4

MBA Section Director
Joined: 19 Mar 2012
Posts: 4736

Kudos [?]: 18073 [0], given: 1991

Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)

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24 Jul 2012, 20:27
teal wrote:
Is $$|x - y| \gt |x + y|$$ ?

$$x^2 - y^2 = 9$$
$$x - y = 2$$

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. S1 gives us information about $$(x - y)(x + y)$$ but does not tell how $$(x - y)$$ and $$(x + y)$$ compare to each other.

Statement (2) by itself is insufficient. S2 gives no information about $$(x + y)$$ .

Statements (1) and (2) combined are sufficient. From S1 and S2 it follows that $$2(x + y) = 9$$ from where $$(x + y) = 4.5$$ . Now we can state that $$|x - y| = 2 \lt |x + y| = 4.5$$ .

statement 1
$$x^2 - y^2 = 9$$
or, (x+y)(x-y)=9
Clearly not sufficient (different combinations of x+y and x-y are possible)

statement 2
x-y=2
not sufficient with no info on (x+y)

combining both together
x+y=9/2
x-y=2

so |x-y|<|x+y|
Sufficient
Hence C
_________________

Kudos [?]: 18073 [0], given: 1991

Manager
Joined: 13 May 2010
Posts: 122

Kudos [?]: 24 [0], given: 4

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24 Jul 2012, 23:02
can you please suggest some numbers to prove statement 2 insuff??

Kudos [?]: 24 [0], given: 4

MBA Section Director
Joined: 19 Mar 2012
Posts: 4736

Kudos [?]: 18073 [0], given: 1991

Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)

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24 Jul 2012, 23:08
consider x=2 and y=4
in this case |x+y| i.e 6>|x-y| i.e 2
Again consider x=2 and y=-4
in this case |x+y| ie 2 < |x-y| i.e 6
hope this helps.
_________________

Kudos [?]: 18073 [0], given: 1991

MBA Section Director
Joined: 19 Mar 2012
Posts: 4736

Kudos [?]: 18073 [0], given: 1991

Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)

### Show Tags

24 Jul 2012, 23:10
in general if you want to plug in numbers in questions like these, you need to consider positive, negative and fractional values of all the variables to eleminate/consider one option
Cheers
_________________

Kudos [?]: 18073 [0], given: 1991

Intern
Joined: 24 Feb 2010
Posts: 11

Kudos [?]: 9 [0], given: 0

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25 Jul 2012, 00:59
For statement 2, use these values to prove that the statement alone is insufficient.

x=2 and y=0
x=3 and y=1
x=-1 and y=-3

Always make a point to check for the inequality with 0 as a value.

Kind Regards,
Ravender

Kudos [?]: 9 [0], given: 0

MBA Section Director
Joined: 19 Mar 2012
Posts: 4736

Kudos [?]: 18073 [0], given: 1991

Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)

### Show Tags

25 Jul 2012, 01:07
palsays wrote:
For statement 2, use these values to prove that the statement alone is insufficient.

x=2 and y=0
x=3 and y=1
x=-1 and y=-3

Always make a point to check for the inequality with 0 as a value.

Kind Regards,
Ravender

@palsays
I dont think your values provide insufficiency
for x=2, y=0 |x+y|>|x-y|
for x=3, y=1 |x+y|>|x-y|
for x=-1, y=-3 |x+y|>|x-y|

You have to make one variable negative and one variable postive to show that |x+y|<|x-y|
Cheers
_________________

Kudos [?]: 18073 [0], given: 1991

Director
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1090 [0], given: 43

WE: Science (Education)

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25 Jul 2012, 01:10
teal wrote:
Is $$|x - y| \gt |x + y|$$ ?

$$x^2 - y^2 = 9$$
$$x - y = 2$$

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. S1 gives us information about $$(x - y)(x + y)$$ but does not tell how $$(x - y)$$ and $$(x + y)$$ compare to each other.

Statement (2) by itself is insufficient. S2 gives no information about $$(x + y)$$ .

Statements (1) and (2) combined are sufficient. From S1 and S2 it follows that $$2(x + y) = 9$$ from where $$(x + y) = 4.5$$ . Now we can state that $$|x - y| = 2 \lt |x + y| = 4.5$$ .

In fact, the given inequality can be rewritten as $$(x-y)^2>(x+y)^2$$ - we can square both sides, as they are both positive. Rearranging the terms, the question becomes $$xy<0$$ (is the product xy negative)?

Then, it is much easier to understand that neither (1), nor (2) alone is sufficient.
Taking both statements, one can explicitly find the values of x and y (although not necessary), and check whether their product is negative.
That's why the correct answer should be C.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1090 [0], given: 43

MBA Section Director
Joined: 19 Mar 2012
Posts: 4736

Kudos [?]: 18073 [0], given: 1991

Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)

### Show Tags

25 Jul 2012, 01:35
yeah true that. Precisely my point.
_________________

Kudos [?]: 18073 [0], given: 1991

Re: M15 Q11   [#permalink] 25 Jul 2012, 01:35
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# M15 Q11

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