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# In the figure above, what is the value of z?

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In the figure above, what is the value of z? [#permalink]

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19 Jul 2016, 08:56
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In the figure above, what is the value of z?

1) x = y = 1
2) w = 2

[Reveal] Spoiler:
Attachment:

OG2017_DS237.png [ 167.88 KiB | Viewed 672 times ]
[Reveal] Spoiler: OA

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In the figure above, what is the value of z? [#permalink]

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19 Jul 2016, 09:14
walker wrote:

In the figure above, what is the value of z?

1) x = y = 1
2) w = 2

[Reveal] Spoiler:
Attachment:
OG2017_DS237.png

Stat 1: X = Y = 1 , from the figure we can understand that all sides are equal and it is square. Z = 1 + A .. we are not sure of A ( A is the bottom line in right angled triangle)...Insufficient.

Stat 2: W = 2... We are not sure the about atleast the other side of the right angled triangle to know the value of A...Insufficient.

Stats 1 + 2 = $$1^2$$ + $$A^2$$ = $$2^2$$ ... we can get the value of A... both sufficient to get the value of Z.

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Re: In the figure above, what is the value of z? [#permalink]

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19 Jul 2016, 11:46
Top Contributor
walker wrote:

In the figure above, what is the value of z?

1) x = y = 1
2) w = 2

IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video at the bottom of the page.

Target question: What is the value of z?

Statement 1: x = y = 1
This statement locks a few lengths into place. However, if we MENTALLY grab the bottom right vertex, we can pull it right to left, without affecting the fact that x = y = 1.
This means that we can alter the length of bottom side, which means we can alter the value of z
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: w = 2
This statement locks the hypotenuse into place. However, if we MENTALLY grab the left-most side (with length x), we can move that side right and left, without affecting the fact that w = 2
This means that we can alter the length of bottom side, which means we can alter the value of z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Knowing that x = 1 and w = 2 means we can use the Pythagorean Theorem to find the length of the bottom side of the right triangle.
Once we know the length of the bottom side of the right triangle, we can add it to 1 to get the length of bottom side, which means we can definitely determine the value of z
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

[Reveal] Spoiler:
C

Cheers,
Brent

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Re: In the figure above, what is the value of z? [#permalink]

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23 Aug 2016, 05:10
C

I got mislead by reading 2 as sq.root of 2, and ended up with A ..
(thinking that B is just another way of writing A).

C is good.
Re: In the figure above, what is the value of z?   [#permalink] 23 Aug 2016, 05:10
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