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M32-12

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M32-12 [#permalink]

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New post 17 Jul 2017, 06:28
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

42% (00:57) correct 58% (00:51) wrong based on 24 sessions

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Re M32-12 [#permalink]

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New post 17 Jul 2017, 06:28
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1
Official Solution:


Is \((x + y)^2 > x^2 + y^2\)?

First let's rephrase the question: is \(x^2 +2xy+ y^2 > x^2 + y^2\)?

First let's rephrase the question: is \(xy>0\)?

(1) \(|x| \leq 0\). The absolute value of a number cannot be negative, it can be 0 or positive. Thus, from this statement we can deduce that \(x=0\). Therefore, \(xy=0\). We have a NO answer to the question. Sufficient.

(2) \(\sqrt{y^2} \leq 0\). This is the same as \(|y| \leq 0\). So, we have the same as above: \(y=0\). Therefore, \(xy=0\). We have a NO answer to the question. Sufficient.


Answer: D
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Re: M32-12 [#permalink]

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New post 09 Aug 2017, 02:35
Wow what a question
this made me question my fundamentals for a moment this is really really a high-quality question
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Re: M32-12 [#permalink]

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New post 15 Aug 2017, 02:49
1
Bunuel wrote:
Official Solution:


Is \((x + y)^2 > x^2 + y^2\)?

First let's rephrase the question: is \(x^2 +2xy+ y^2 > x^2 + y^2\)?

First let's rephrase the question: is \(xy>0\)?

(1) \(|x| \leq 0\). The absolute value of a number cannot be negative, it can be 0 or positive. Thus, from this statement we can deduce that \(x=0\). Therefore, \(xy=0\). We have a NO answer to the question. Sufficient.

(2) \(\sqrt{y^2} \leq 0\). This is the same as \(|y| \leq 0\). So, we have the same as above: \(y=0\). Therefore, \(xy=0\). We have a NO answer to the question. Sufficient.


Answer: D


If I'd answered this question during the start of my prep I'd have got it wrong.

I think the key here is the square root operator \(\sqrt{any number}\) will only refer to the positive root (and not both positive & negative roots).

Had the second statement been \(y^2 \leq 1\), this would give both positive and negative roots (y is between -1 and 1).
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Re: M32-12 [#permalink]

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New post 11 Feb 2018, 06:45
Hi Bunuel,

This question confused me a little.

I was able to simplify the question to "xy>0?"

My issue was in translating the statements...

1) [x]<= 0

Converted [x] to x^2<=0
Since x squared cannot be less than 0...x^2 is 0, thus x is 0 and xy=0...meaning the answer to the question is no.

My question for this part is thus...whenever you see [x] or [y] etc... does that always translated into x^2, y^2 etc.?

2. For statement 2 why isn't √y^2 y? I thought this would be y<=0 making 2 insufficient.
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Re: M32-12 [#permalink]

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New post 11 Feb 2018, 08:00
1
ttaiwo wrote:
Hi Bunuel,

This question confused me a little.

I was able to simplify the question to "xy>0?"

My issue was in translating the statements...

1) [x]<= 0

Converted [x] to x^2<=0
Since x squared cannot be less than 0...x^2 is 0, thus x is 0 and xy=0...meaning the answer to the question is no.

My question for this part is thus...whenever you see [x] or [y] etc... does that always translated into x^2, y^2 etc.?

2. For statement 2 why isn't √y^2 y? I thought this would be y<=0 making 2 insufficient.


1. |x| is the absolute value of x. NOT [x]. || is modulus sign.

2. \(\sqrt{x^2}=|x|\) yes, but \(x^2=|x|\) IS WRONG.

3. For (2): since \(\sqrt{y^2}=|y|\), then \(\sqrt{y^2} \leq 0\) gives: \(|y| \leq 0\), which is the same info as in (1) but about y.


10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: M32-12 [#permalink]

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New post 11 Feb 2018, 09:42
Bunuel wrote:
ttaiwo wrote:
Hi Bunuel,

This question confused me a little.

I was able to simplify the question to "xy>0?"

My issue was in translating the statements...

1) [x]<= 0

Converted [x] to x^2<=0
Since x squared cannot be less than 0...x^2 is 0, thus x is 0 and xy=0...meaning the answer to the question is no.

My question for this part is thus...whenever you see [x] or [y] etc... does that always translated into x^2, y^2 etc.?

2. For statement 2 why isn't √y^2 y? I thought this would be y<=0 making 2 insufficient.


1. |x| is the absolute value of x. NOT [x]. || is modulus sign.

2. \(\sqrt{x^2}=|x|\) yes, but \(x^2=|x|\) IS WRONG.

3. For (2): since \(\sqrt{y^2}=|y|\), then \(\sqrt{y^2} \leq 0\) gives: \(|y| \leq 0\), which is the same info as in (1) but about y.


10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.


Thanks bro.
Re: M32-12   [#permalink] 11 Feb 2018, 09:42
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M32-12

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