M15 Q11 : Retired Discussions [Locked]
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# M15 Q11

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Manager
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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 $$|x - y| = 2 \lt |x + y| = 4.5$$ .

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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
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24 Jul 2012, 23:02
can you please suggest some numbers to prove statement 2 insuff??
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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.
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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
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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
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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
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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.
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25 Jul 2012, 01:35
yeah true that. Precisely my point.
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Re: M15 Q11   [#permalink] 25 Jul 2012, 01:35
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# M15 Q11

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