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# X and Y are the lengths of two non-hypotenuse sides of a right triangl

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X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 04:52
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75% (hard)

Question Stats:

51% (01:58) correct 49% (01:22) wrong based on 85 sessions

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X and Y are the lengths of two non-hypotenuse sides of a right triangle, is the third side of the triangle an integer?

(1) X is a prime number.
(2) Y is an odd integer.

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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 05:06
If X=3 and Y = 3

Third Side = $$\sqrt{x*x + y*y}$$ = $$\sqrt{9+9}$$ = $$\sqrt{18}$$ = 4.24 ( Not an Interger.

Ans should be E.
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 07:35
0ld wrote:
If X=3 and Y = 3

Third Side = $$\sqrt{x*x + y*y}$$ = $$\sqrt{9+9}$$ = $$\sqrt{18}$$ = 4.24 ( Not an Interger.

Ans should be E.

You are getting a definite answer as NO. hence it shouldn't be E. It should be C.

Take any such combination of X and Y such that both the statements are met, you will always get a non integral value of the hypotenuse.
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 07:40
abhimahna wrote:
0ld wrote:
If X=3 and Y = 3

Third Side = $$\sqrt{x*x + y*y}$$ = $$\sqrt{9+9}$$ = $$\sqrt{18}$$ = 4.24 ( Not an Interger.

Ans should be E.

You are getting a definite answer as NO. hence it shouldn't be E. It should be C.

Take any such combination of X and Y such that both the statements are met, you will always get a non integral value of the hypotenuse.

Ahh. Thank you. Nice problem.
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 07:47
rohit8865 wrote:
X and Y are the lengths of two non-hypotenuse sides of a right triangle, is the third side of the triangle an integer?

(1) X is a prime number.
(2) Y is an odd integer.

Similar question to practice: x-and-y-are-the-lengths-of-two-non-hypotenuse-sides-of-a-right-triangl-220780.html
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 08:16
but if x = 2 (since 2 is also a prime number), then the hypotenuse is an integer, so in my opinion the answer should be E.

What am I missing?
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 09:12
glatzekatze wrote:
but if x = 2 (since 2 is also a prime number), then the hypotenuse is an integer, so in my opinion the answer should be E.

What am I missing?

Yes, X could be equal to 2. But what is the value of y you are considering?.

Take any value of y and then find out the hypotenuse. You yourself will get to know why C is the answer.
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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12 Sep 2016, 09:16
abhimahna wrote:
glatzekatze wrote:
but if x = 2 (since 2 is also a prime number), then the hypotenuse is an integer, so in my opinion the answer should be E.

What am I missing?

Yes, X could be equal to 2. But what is the value of y you are considering?.

Take any value of y and then find out the hypotenuse. You yourself will get to know why C is the answer.

oh I'm so stupid, I somehow thought that we are looking for the Area, not the hypotenuse :D I think I might need some more sleep before tackling math!
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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14 Sep 2016, 22:31
Statement 1
X is prime so third side may or may not be integer
Statement 2
Y is a odd no is again not a sufficient condition to answer the question

Now when we combine both of the above mentioned condition we have
X ={ 2,3,5,7....
Y= { 1,3,5,7,....
Clearly of third side to be an integer it has to satisfy.
√(X^2+Y^2)
And by Euclid's formula for this to happen either of x or y has to be even.
On our set we have only one even term 2 which cannot be paired with any other no to yield an integer as third line
So combine both condition we have reached the conclusion that third side is not an integer.

https://en.m.wikipedia.org/wiki/Pythagorean_triple

So IMO C is the correct answer.
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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29 Oct 2018, 20:35
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl   [#permalink] 29 Oct 2018, 20:35
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