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M15-11

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M15-11  [#permalink]

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New post 16 Sep 2014, 00:55
1
4
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A
B
C
D
E

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Re M15-11  [#permalink]

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New post 16 Sep 2014, 00:55
Official Solution:


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 \(|x - y| = 2 \lt |x + y| = 4.5\).


Answer: C
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Re: M15-11  [#permalink]

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New post 07 Dec 2014, 15:37
Why would 2) alone not be sufficient to answer the question.

From part 2 we can deduce that x= 2+y and then substitute that in the equation I 2 + y - y I = I 2 I and we substitute this is the other equation to get I 2 I > I 2+2y I. Now the least value for I 2+2y I is 0 so I2I >0 Yes sufficient. Am I missing something?
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Re: M15-11  [#permalink]

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New post 08 Dec 2014, 05:07
rsamant wrote:
Why would 2) alone not be sufficient to answer the question.

From part 2 we can deduce that x= 2+y and then substitute that in the equation I 2 + y - y I = I 2 I and we substitute this is the other equation to get I 2 I > I 2+2y I. Now the least value for I 2+2y I is 0 so I2I >0 Yes sufficient. Am I missing something?



(2) x - y = 2 --> the question becomes: is |2| > |2y + 2|? --> is |y + 1| < 1? If y = -1, the answer is YES but if y = 2 the answer is NO.
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Re: M15-11  [#permalink]

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New post 06 Jul 2015, 00:29
Bunuel wrote:
Official Solution:


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 \(|x - y| = 2 \lt |x + y| = 4.5\).


Answer: C


Hi bunuel,
Why can't (1) be sufficient. Here is my reasoning:

(x-y)(x+y)=9 can be rewritten as (5-4)(5+4) or even (4-5)(4+5).
Either ways, the answer to the main question will always yield a 'no'. Doesn't this mean statement 1 is sufficient?
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Re: M15-11  [#permalink]

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New post 06 Jul 2015, 01:01
1
samuraijack256 wrote:
Bunuel wrote:
Official Solution:


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 \(|x - y| = 2 \lt |x + y| = 4.5\).


Answer: C


Hi bunuel,
Why can't (1) be sufficient. Here is my reasoning:

(x-y)(x+y)=9 can be rewritten as (5-4)(5+4) or even (4-5)(4+5).
Either ways, the answer to the main question will always yield a 'no'. Doesn't this mean statement 1 is sufficient?


Why do you assume that x and y are integers? x^2 - y^2 = 9 has infinitely many solutions for x and y.

Even if you consider only integers, which is not right, you'll have more solutions:
x = ±5 and y = -4;
x = ±3 and y = 0;
x = ±5 and y = 4.
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Re: M15-11  [#permalink]

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New post 25 Jul 2016, 21:33
Bunuel wrote:
samuraijack256 wrote:
Bunuel wrote:
Official Solution:


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 \(|x - y| = 2 \lt |x + y| = 4.5\).


Answer: C


Hi bunuel,
Why can't (1) be sufficient. Here is my reasoning:

(x-y)(x+y)=9 can be rewritten as (5-4)(5+4) or even (4-5)(4+5).
Either ways, the answer to the main question will always yield a 'no'. Doesn't this mean statement 1 is sufficient?


Why do you assume that x and y are integers? x^2 - y^2 = 9 has infinitely many solutions for x and y.

Even if you consider only integers, which is not right, you'll have more solutions:
x = ±5 and y = -4;
x = ±3 and y = 0;
x = ±5 and y = 4.


Hi Bunuel,

Had a doubt here:

For this q - What if we have to simplify the question stem and open up the modulus sign?

1) Case 1: Both sides are positives - then we get
x-y> x+y... => y<0

2) Case 2: One is negative the other is positive:
X >0 in one case and X < 0 in the other

3) Case 3: Both sides are negative:
y>0

So now if we consider option c, X-y =2. X+y = 4.5... solving gives x = 3.25 and y = 1.25.

Now what case above to consider.

Is there a generic approach of solving these questions?
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Re: M15-11  [#permalink]

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New post 11 Jan 2017, 07:16
The answer has to be option C.

First statement - different combinations of x-y & x+y are possible. Hence NS
Second statement - x-y = 2. NS

Combine the two , x-y = 2, x+y = 4.5 ; hence sufficient.

Hence option C is correct.
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Re: M15-11  [#permalink]

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New post 11 Jan 2017, 13:27
Can anyone open the modulus and explain the solution algebraically?

spetznaz wrote:
The answer has to be option C.

First statement - different combinations of x-y & x+y are possible. Hence NS
Second statement - x-y = 2. NS

Combine the two , x-y = 2, x+y = 4.5 ; hence sufficient.

Hence option C is correct.
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Re: M15-11  [#permalink]

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New post 11 Mar 2017, 07:52
Bunuel wrote:
Is \(|x - y| \gt |x + y|\)?


(1) \(x^2 - y^2 = 9\)

(2) \(x - y = 2\)


if we square both sides of the prompt, doesent the question become whether xy<o or whether x and y both have opposite signs? would appreciate feedback.

Thank you.
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New post 11 Mar 2017, 08:04
OreoShake wrote:
Bunuel wrote:
Is \(|x - y| \gt |x + y|\)?


(1) \(x^2 - y^2 = 9\)

(2) \(x - y = 2\)


if we square both sides of the prompt, doesent the question become whether xy<o or whether x and y both have opposite signs? would appreciate feedback.

Thank you.

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Re: M15-11  [#permalink]

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New post 11 Mar 2017, 14:12
Can you please explain?

OreoShake wrote:
Bunuel wrote:
Is \(|x - y| \gt |x + y|\)?


(1) \(x^2 - y^2 = 9\)

(2) \(x - y = 2\)


if we square both sides of the prompt, doesent the question become whether xy<o or whether x and y both have opposite signs? would appreciate feedback.

Thank you.
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Re: M15-11  [#permalink]

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New post 12 Mar 2017, 03:47
cuhmoon wrote:
Can you please explain?

OreoShake wrote:
Bunuel wrote:
Is \(|x - y| \gt |x + y|\)?


(1) \(x^2 - y^2 = 9\)

(2) \(x - y = 2\)


if we square both sides of the prompt, doesent the question become whether xy<o or whether x and y both have opposite signs? would appreciate feedback.

Thank you.


\(|x - y| \gt |x + y|\)

\((|x - y|)^2 \gt (|x + y|)^2\)

\(x^2 - 2xy +y^2 > x^2+2xy+y^2\)

\(0>4xy\)

\(0>xy\)
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M15-11  [#permalink]

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New post 17 May 2018, 09:42
My approach for this question was X and Y has to be with opposite sign , in that case only
|x−y|>|x+y|?
Now we can find the sign of X and Y while when we use both statement.
Bunuel , can you please confirm my approach here
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New post 17 May 2018, 10:07
rahul2013 wrote:
My approach for this question was X and Y has to be with opposite sign , in that case only
|x−y|>|x+y|?
Now we can find the sign of X and Y while when we use both statement.
Bunuel , can you please confirm my approach here

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M15-11  [#permalink]

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New post 15 Jun 2018, 23:54
I understand the approach in the OE, but am a bit confused to why absolute values are necessary in the original problem?

EDIT: Never mind - I suppose with the ABS you can plug values to easily find out that (2) is insufficient. x=4 y=2 generates a "yes" because 2 is less than 6, but x=0 y=-2 generates a "no" because 2 is not less than 2.
M15-11 &nbs [#permalink] 15 Jun 2018, 23:54
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