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In the figure above, what is the value of z?
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19 Jul 2016, 08:56
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
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Re: In the figure above, what is the value of z?
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Updated on: 13 Mar 2018, 11:31
Updated on: 13 Mar 2018, 11:31
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walker
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
Answer = C
Cheers,
Brent
RELATED VIDEOS
Originally posted by BrentGMATPrepNow on 19 Jul 2016, 11:46.
Last edited by BrentGMATPrepNow on 13 Mar 2018, 11:31, edited 1 time in total.
Last edited by BrentGMATPrepNow on 13 Mar 2018, 11:31, edited 1 time in total.
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Re: In the figure above, what is the value of z?
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23 Mar 2017, 16:36
23 Mar 2017, 16:36
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walker
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.
Answer: C
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