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m08-q26

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Re: m08-q26q [#permalink] New post 31 Aug 2011, 02:38
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Brilliant question!! My initial thought was sqrt2 is a valid remainder. Haha. Surprising how assumptions can kill you!! Although I chose B (a good guess!)

I plugged in x is sqrt2, then argued with myself that Y can be four and the statement will hold true.

So, takeaway from this is REMAINDERS HAVE TO BE INTEGERS!

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Re: m08-q26 [#permalink] New post 03 Sep 2011, 08:13
Wow. Really created a flutter this one! And it was so simple all the while! Great explanations everybody.
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Re: m08-q26 [#permalink] New post 30 Aug 2012, 04:23
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pmal04 wrote:
If XY is divisible by 4, which of the following must be true?

(A) If X is even then Y is odd.
(B) If X = \sqrt{2} then Y is not a positive integer.
(C) If X is 0 then X + Y is not 0.
(D) X^Y is even.
(E) \frac{X}{Y} is not an integer.

[Reveal] Spoiler: OA
B

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The OE is not making sense to me. Why XY has to be an integer?
why can't it be 8*root2?


This question is also discussed here: if-xy-is-divisible-by-4-which-of-the-following-must-be-true-73389.html

Revised version of this question is below:

If x and y are positive integer and xy is divisible by 4, which of the following must be true?

A. If x is even then y is odd.
B. If x is odd then y is a multiple of 4.
C. If x+y is odd then \frac{y}{x} is not an integer.
D. If x+y is even then \frac{x}{y} is an integer.
E. x^y is even.

Notice that the question asks which of the following MUST be true not COULD be true.

A. If x is even then y is odd --> not necessarily true, consider: x=y=2=even;

B. If x is odd then y is a multiple of 4 --> always true: if x=odd then in order xy to be a multiple of 4 y mst be a multiple of 4;

C. If x+y is odd then \frac{y}{x} is not an integer --> not necessarily true, consider: x=1 and y=4;

D. If x+y is even then \frac{x}{y} is an integer --> not necessarily true, consider: x=2 and y=4;

E. x^y is even --> not necessarily true, consider: x=1 and y=4;

Answer: B.
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Re: m08-q26 [#permalink] New post 29 Aug 2013, 08:11
I kinda agree with the above post by rongali. Here are my 2 cents:-

"Y cannot be an integer" is easily proved wrong since y can be zero and therefore XY will be divisible by 4.

If Y cannot be a positive integer, then, considering that GMAT revolves around only real numbers, Y can be Zero, a negative Integer, a positive fraction or a negative fraction. If Y is zero, then XY is always divisible by 4. If Y is a negative integer, then XY will not be divisible by 4. If Y is a positive fraction, then XY could be or could not be divisible by 4, and likewise if Y is a negative Fraction, then XY could be or could not be divisible by 4.

But i think the catch of the question is that we cannot prove the parent statement wrong. So considering that XY IS DIVISIBLE by 4, we will have to ignore the possibilities mentioned above that do no lead to a proper divisibility by 4. Therefore, we are left with Y=0 OR Y=Negative Fraction, that produces XY divisible by 4 OR Y=Positive Fraction that produces proper divisibility. All in All, we realize that Y cannot be a positive integer because in that case XY will never be divisible by 4. Phewww, i'm exhausted.

Experts, please comment whether i'm thinking correctly.
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Re: m08-q26 [#permalink] New post 29 Aug 2013, 08:44
Expert's post
taransambi wrote:
I kinda agree with the above post by rongali. Here are my 2 cents:-

"Y cannot be an integer" is easily proved wrong since y can be zero and therefore XY will be divisible by 4.

If Y cannot be a positive integer, then, considering that GMAT revolves around only real numbers, Y can be Zero, a negative Integer, a positive fraction or a negative fraction. If Y is zero, then XY is always divisible by 4. If Y is a negative integer, then XY will not be divisible by 4. If Y is a positive fraction, then XY could be or could not be divisible by 4, and likewise if Y is a negative Fraction, then XY could be or could not be divisible by 4.

But i think the catch of the question is that we cannot prove the parent statement wrong. So considering that XY IS DIVISIBLE by 4, we will have to ignore the possibilities mentioned above that do no lead to a proper divisibility by 4. Therefore, we are left with Y=0 OR Y=Negative Fraction, that produces XY divisible by 4 OR Y=Positive Fraction that produces proper divisibility. All in All, we realize that Y cannot be a positive integer because in that case XY will never be divisible by 4. Phewww, i'm exhausted.

Experts, please comment whether i'm thinking correctly.


Notice that option B says that y is not a positive integer.

The old version of this question is discussed here: if-xy-is-divisible-by-4-which-of-the-following-must-be-true-73389.html

The revised version is here: m08-q26-78982-20.html#p1117292

Hope it helps.
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Re: m08-q26 [#permalink] New post 31 Aug 2013, 19:02
is it XY or X*Y ?

Because X = 1 (odd)

Y = 6 (not a multiple of 4 )

But XY = 16 ( multiple of 4 )


:/

So i guess it should be X*Y ..


please clarify .
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Re: m08-q26 [#permalink] New post 01 Sep 2013, 05:21
Expert's post
sathiyanarayanan wrote:
is it XY or X*Y ?

Because X = 1 (odd)

Y = 6 (not a multiple of 4 )

But XY = 16 ( multiple of 4 )


:/

So i guess it should be X*Y ..


please clarify .


Yes, it's x multiplied by y. If it were two-digit integer xy then it would be explicitly stated.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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Re: m08-q26 [#permalink] New post 14 Aug 2014, 04:40
nice question :)
Answer is B. the thing is, Y is not positive integer. because if X=\sqrt{2}, Y must be either zero or non integer. it can be 4\sqrt{2} which is not positive integer.
for short, assume B states if X=\sqrt{2}, Y is not integer (except 0)
Re: m08-q26   [#permalink] 14 Aug 2014, 04:40
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