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27 Oct 2021, 03:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
70% (00:46) correct
30%
(01:06)
wrong
based on 96
sessions
History
Date
Time
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Not Attempted Yet
In triangle ABC above, does \((AB)^2 + (BC)^2 = (AC)^2\) ?
(1) \(x + z = 100\)
(2) \(x = z\)
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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PyjamaScientist
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27 Oct 2021, 04:05
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Option (A) is the right answer.
Question is basically asking us, is \(y = 90^{\circ}\)?
Statement 1: \(x+z=100\)
This gives y = 80\(^{\circ}\).
Thus \(y\) \(\neq{}\) \(90\)\(^{\circ}\).
Sufficient.
Statement 2: \(x=z\)
This gives, \(2x + y = 180\)
\(y = 180 - 2x\)
\(Y\) can multiple values for different values of '\(x\)'.
Insufficient.
Question is basically asking us, is \(y = 90^{\circ}\)?
Statement 1: \(x+z=100\)
This gives y = 80\(^{\circ}\).
Thus \(y\) \(\neq{}\) \(90\)\(^{\circ}\).
Sufficient.
Statement 2: \(x=z\)
This gives, \(2x + y = 180\)
\(y = 180 - 2x\)
\(Y\) can multiple values for different values of '\(x\)'.
Insufficient.
27 Oct 2021, 05:04
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Bunuel
Solution:
For the above triangle to follow \((AB)^2 + (BC)^2 = (AC)^2\), it has to be a right angle triangle, right-angled at \(B\).
Or \(\angle B=y\) has to be \(90^o\)
Statement 1: \(x + z = 100\)
If \(x + z = 100\), then \(y=180-(x+z)=180-100=80\).
We get that \(y=80\) and thus we can be sure that \((AB)^2 + (BC)^2 = (AC)^2\) will not stand.
Statement 1 alone is sufficient to answer the question. We can eliminate options B, C and E.
Statement 2: \(x = z\)
If \(x = z\),
then\(y=180-(x+z)=180-2x\) or \(180-2z\).
Now we cannot be sure if \(180-2z\) or \(180-2x\) is equal to 90 or not. It is possible when \(x=z=45\) but that is unknown.
Thus, statement 2 alone is not sufficient.
Hence the right answer is Option A.
