9. If X, Y and Z are positive integers, is X greater than Z – Y?
(1) X – Z – Y > 0.
2) z^2 = x^2+y^2
gud prob
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x – y – z > 0namitrajiv wrote:hI stop@800,
Can you kindly prove, hows b insufficient ,
x > z + y
y is positive
so if x is greater than z+y, it will certainly be greater than z-y as we are subtracting something [2y] positive.
so
B is sufficient
Example:
100 > 50
100 will always be greater than 50-x
where x is positive integer
Hope this helps!!!
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no actually I wanted to knw hw B is insufficient,
i.e z^2 = x^2+y^2 ,
it seems to me this is sufficient to prove that
x>z-y
e.g z= 13, y = 12, x =5
z= 13 , y = 12, x = 5
I cant find a case where the condition is insufficient
i.e z^2 = x^2+y^2 ,
it seems to me this is sufficient to prove that
x>z-y
e.g z= 13, y = 12, x =5
z= 13 , y = 12, x = 5
I cant find a case where the condition is insufficient
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stop@800 explained well above why the first statement is sufficient.
The second statement is also sufficient. If we know that x, y and z are positive, and that the Pythagorean relationship holds:
x^2 + y^2 = z^2
then we know that we can make a right angled triangle with sides x, y and z, where z is the hypotenuse. And in any triangle, the sum of two sides is always larger than the third side:
x + y > z
x > z - y
So the answer should be D.
The second statement is also sufficient. If we know that x, y and z are positive, and that the Pythagorean relationship holds:
x^2 + y^2 = z^2
then we know that we can make a right angled triangle with sides x, y and z, where z is the hypotenuse. And in any triangle, the sum of two sides is always larger than the third side:
x + y > z
x > z - y
So the answer should be D.
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Hi Ian,
in GMATLAND, ain't 0 a positive integer?
Also, the question stem does not say X Y Z are all different.
how can phythagoras be used then?
in GMATLAND, ain't 0 a positive integer?
Also, the question stem does not say X Y Z are all different.
how can phythagoras be used then?
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No, 0 is not a positive integer. It is an integer, but it isn't positive, and it isn't negative.cubicle_bound_misfit wrote:Hi Ian,
in GMATLAND, ain't 0 a positive integer?
Also, the question stem does not say X Y Z are all different.
how can phythagoras be used then?
If you have two lines of length x and y, and you connect them at right angles, the hypotenuse z will automatically satisfy
x^2 + y^2 = z^2
That's Pythagoras. It doesn't matter if x and y are different or equal. So you can make a triangle with sides x, y and z, and x+y must be greater than z.
(and while it's not especially important, in this question, x actually must be different from y if the second statement is true, because we know x, y and z are all integers -- if x were an integer and equal to y, then z would need to be equal to root(2)*x, which wouldn't be an integer).
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