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If x, y, and z are the lengths of the three sides of a triangle, is y

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GMATBusters
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If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink] New post   10 Nov 2018, 09:47
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If x, y, and z are the lengths of the three sides of a triangle, is y > 4?

(1) z = x + 4
(2) x = 3 and z = 7
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D
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If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink] New post   10 Nov 2018, 10:01
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gmatbusters wrote:
If x, y, and z are the lengths of the three sides of a triangle, is y > 4?

(1) z = x + 4
(2) x = 3 and z = 7


Here we use the property of triangle that sum of any 2 sides has to be greater than the third side.

Statement 1 Three sides of triangle are x, y, x+4
Since sum of any 2 sides has to be greater than third side,
\(x+y>x+4\)
y>4. Hence, Statement 1 is SUFFICIENT

Statement 2 Sides of triangle are 3, y, 7
\(3+y>7\)
y>4. Hence Statement 2 is SUFFICIENT

Hence Answer is D
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jinghao
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Re: If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink] New post   17 Jan 2019, 07:45
Condition of triangle;
|x-z|<y<x+z

(1)z=x+4
|x-z|=|x-(x+4)|=4
4<y

(2)x=3, y=7
|x-z|=|3-7|=4
4<y

Answer: D

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BrentGMATPrepNow
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If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink] New post   Updated on: 06 Mar 2023, 00:26
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GMATBusters wrote:
If x, y, and z are the lengths of the three sides of a triangle, is y > 4?

(1) z = x + 4
(2) x = 3 and z = 7


IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

Given: x, y, and z are the lengths of the three sides of a triangle

Target question: Is y > 4?

Statement 1: z = x + 4
This means that x and x+4 are the lengths of two sides of the triangle.
When we apply the rule above, we can see that: (x + 4) - x < length of third side (aka y) < (x + 4) + x
Simplify: 4 < y < 2x + 4
At this point we can see that the answer to the target question is YES, y IS greater than 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 3 and z = 7
When we apply the rule above, we can see that:7 - 3 < length of third side (aka y) < 7 + 3
Simplify: 4 < y < 10
The answer to the target question is YES, y IS greater than 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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Originally posted by BrentGMATPrepNow on 12 Feb 2020, 14:12.
Last edited by Bunuel on 06 Mar 2023, 00:26, edited 2 times in total.
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Re: If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink] New post   12 Mar 2021, 01:45
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Given: x, y and z are lengths of triangle.
Is y > 4?
In a triangle |z - x| < y < z + x.

Statement 1:
z = x + 4
=> z - x = 4
=> |z - x| = 4 < y
Therefore, y > 4.
Statement 1 is Sufficient.

Statement 2:
x = 3 and z = 7
=> z - x = 7 - 3 = 4
=> |z - x| = 4 < y
Therefore, y > 4.
Statement 2 is also Sufficient.

So, correct answer is option D.
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Re: If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink] New post   13 Apr 2023, 09:28
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Re: If x, y, and z are the lengths of the three sides of a triangle, is y [#permalink]
13 Apr 2023, 09:28
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