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If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the

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If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   30 Aug 2016, 05:23
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If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?

I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
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E
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Harish Yannam
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Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   30 Aug 2016, 06:57
ANSWER: E Statement Ⅰ must be true, because if all three variables are positive integers and x2=z2 plus the square of another positive integer, then x has to be greater than z;, plug in numbers to verify. Ⅲ must be true because the square of a positive integer is always a positive integer, and y2+z2 is equal to the square of a positive integer (i.e.=x2). Ⅱ does not have to be true because if you square both sides of x=y+z, you get x2=y2+2yz+z2, which does not agree with the original statement
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Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   30 Aug 2016, 12:26
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Bunuel wrote:
If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?

I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer

A. I only
B. II only
C. III only
D. I and II only
E. I and III only



D since negative numbers are not considered.
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If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   Updated on: 31 Aug 2016, 03:19
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x^2=y^2+Z^2 ; eg:- 5^2=4^2+3^2 ; 25=16+9 (x,y and z are all positive)

Ans D

Originally posted by Turkish on 30 Aug 2016, 16:52.
Last edited by Turkish on 31 Aug 2016, 03:19, edited 1 time in total.
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If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   Updated on: 01 Sep 2016, 16:32
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x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.

I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers

Answer (E).

Edited: option E is the correct answer.

Originally posted by Donnie84 on 30 Aug 2016, 17:46.
Last edited by Donnie84 on 01 Sep 2016, 16:32, edited 1 time in total.
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Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   31 Aug 2016, 10:45
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Donnie84 wrote:
x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.

I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers

Answer (D).


I think you meant option E. Please recheck.
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Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   01 Sep 2016, 16:32
abhimahna wrote:
Donnie84 wrote:
x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.

I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers

Answer (D).


I think you meant option E. Please recheck.


Oh yes, E is what I meant.
+1 to you.
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Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink] If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the   25 Feb 2024, 23:53
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Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]
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