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01 Aug 2019, 05:44
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:05) correct
27%
(01:28)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(x+y>z?\)
(1) \(x^2+y^2>z^2\)
(2) x, y and z are sides of a triangle.
(1) \(x^2+y^2>z^2\)
(2) x, y and z are sides of a triangle.
01 Aug 2019, 06:46
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Is x+y>z? Yes /No
(1) x^2+y^2>z^2
(1)^2 +(2)^2 > (2)^2
.: x+y>z —> 1+2 >2 Yep!
However, (-1)^2 +(2)^2 > (2)^2
.: x+y >z —> -1+2>2 Nope!
(Not sufficient
(2) x, y and z are sides of a triangle.
Triangle inequality theorem
Adding any two side will always be greater than the third side (x+y) >z
Subtracting any two sides will always be smaller than the third side (x-y) <z
Since the sides are x,y,z we know that adding x+y >z Yep!
Sufficient
Smash that B!
Posted from my mobile device
(1) x^2+y^2>z^2
(1)^2 +(2)^2 > (2)^2
.: x+y>z —> 1+2 >2 Yep!
However, (-1)^2 +(2)^2 > (2)^2
.: x+y >z —> -1+2>2 Nope!
(Not sufficient
(2) x, y and z are sides of a triangle.
Triangle inequality theorem
Adding any two side will always be greater than the third side (x+y) >z
Subtracting any two sides will always be smaller than the third side (x-y) <z
Since the sides are x,y,z we know that adding x+y >z Yep!
Sufficient
Smash that B!
Posted from my mobile device
01 Aug 2019, 06:49
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Statement 1 is not sufficient because x and y can be negative. If x = -100, y = -100, and z = 1, then x^2 + y^2 > z^2 is true, but x+y is negative, so is definitely not larger than z. So using negative values for x and y, we can get a 'no' answer to the question, but using any positive values for x and y will give a 'yes' answer.
The sum of two sides of a triangle always exceeds the third side, so Statement 2 is sufficient, and the answer is B.
The sum of two sides of a triangle always exceeds the third side, so Statement 2 is sufficient, and the answer is B.
