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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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5% (low)

Question Stats:

90% (00:54) correct 10% (01:12) wrong based on 1343 sessions

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

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

Attachment:

OG2017_DS237.png [ 167.88 KiB | Viewed 16570 times ]

Attachment:

DS04594_f001.jpg [ 4.75 KiB | Viewed 8583 times ]

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

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Updated on: 13 Mar 2018, 11:31
5
Top Contributor
2
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

Cheers,
Brent

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Originally posted by GMATPrepNow on 19 Jul 2016, 11:46.
Last edited by GMATPrepNow on 13 Mar 2018, 11:31, edited 1 time in total.
##### General Discussion
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Re: In the figure above, what is the value of z?  [#permalink]

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19 Jul 2016, 09:14
1
walker wrote:

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

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

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

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23 Mar 2017, 16:36
3
walker wrote:

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

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

We need to determine the value of z in the following diagram:

Note that z is equal to the length of the rectangle and the base of the triangle. If we let the base of the triangle = b, z = b + y.

Statement One Alone:

x = y = 1

Although we know that x = 1, we do not know the value of b or the base of the triangle. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

w = 2

Knowing only the value of w does not allow us to determine z. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we know that x = y = 1 and w = 2, and we can determine b using the Pythagorean theorem.

x^2 + b^2 = w^2

1^2 + b^2 = 2^2

1 + b^2 = 4

b^2 = 3

b = √3

Thus, z = y + b = 1 + √3.

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

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03 Apr 2019, 20:11
x=y=1 implies its a square but we still need one ore side of the trianglee or an angle to find the other side with first statement so insufficient.
Statement 2 is clearly insufficient alone.

But both the statements combined are sufficient as we have 2 sides known.
Re: In the figure above, what is the value of z?   [#permalink] 03 Apr 2019, 20:11
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