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M27-02

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M27-02  [#permalink]

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New post 16 Sep 2014, 00:26
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (01:41) correct 59% (02:09) wrong based on 206 sessions

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Re M27-02  [#permalink]

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New post 16 Sep 2014, 00:26
2
3
Official Solution:


(1) \(4y^2+3x^2=x^4+y^4\)

Rearrange: \(3x^2-x^4=y^4-4y^2\);

\(x^2(3-x^2)=y^2(y^2-4)\).

Notice that LHS is even for any value of \(x\): if \(x\) is odd then \(3-x^2=odd-odd=even\) and if \(x\) is even, then the product is naturally even. So, \(y^2(y^2-4y)\) is also even, but in order for it to be even \(y\) must be even, since if \(y\) is odd, then \(y^2(y^2-4y)=odd*(odd-even)=odd*odd=odd\). Sufficient.

(2) \(y=4-x^2\)

If \(x=odd\) then \(y=even-odd=odd\) but if \(x=even\) then \(y=even-even=even\). Not sufficient.


Answer: A
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Re: M27-02  [#permalink]

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New post 06 Feb 2016, 02:05
wow this was cool. pluging in 1, 0, 2 helps
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Re: M27-02  [#permalink]

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New post 10 Aug 2016, 21:58
3
Bunuel wrote:
Official Solution:


(1) \(4y^2+3x^2=x^4+y^4\)

Rearrange: \(3x^2-x^4=y^4-4y^2\);

\(x^2(3-x^2)=y^2(y^2-4)\).

Notice that LHS is even for any value of \(x\): if \(x\) is odd then \(3-x^2=odd-odd=even\) and if \(x\) is even, then the product is naturally even. So, \(y^2(y^2-4y)\) is also even, but in order for it to be even \(y\) must be even, since if \(y\) is odd, then \(y^2(y^2-4y)=odd*(odd-even)=odd*odd=odd\). Sufficient.

(2) \(y=4-x^2\)

If \(x=odd\) then \(y=even-odd=odd\) but if \(x=even\) then \(y=even-even=even\). Not sufficient.


Answer: A


I did it without regrouping.

1) 4y^2 - is alway even; 3x^2 could be even or odd, depending on X;
x^4 will be even or odd, depending on X, but it will be the same as above; y^4 is unknown?
e + e = e => e = e + something, then this something is even
e + o = o => o = o + something, then this something is even

2) Not sufficient
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Re: M27-02  [#permalink]

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New post 04 Jun 2017, 00:56
Hello Sir,

I assumed s1 in this way, kindly let me know if my assumption is correct.

After re-grouping to X on one side and Y on the other,

I found that no matter if X is odd or even, the solution of X^2(3-X^2) is always even. Therefore inorder to achieve this even number, Y must always be even since Odd does not satisfy the X^2(3-X^2).

Thank you Sir.
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Re: M27-02  [#permalink]

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New post 10 Sep 2018, 12:39
Why am I not able to see the answer choices for Quant questions?
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Re: M27-02  [#permalink]

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New post 10 Sep 2018, 20:36
1
katkepin wrote:
Why am I not able to see the answer choices for Quant questions?


This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.
Ultimate GMAT Quantitative Megathread

Hope this helps.
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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: M27-02  [#permalink]

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New post 11 Sep 2018, 11:54
this was very helpful! thank you
Bunuel wrote:
Hope this helps.
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Re: M27-02 &nbs [#permalink] 11 Sep 2018, 11:54
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