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06 Mar 2023, 02:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
60% (01:15) correct
40%
(00:51)
wrong
based on 58
sessions
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Not Attempted Yet
The lengths of two sides of a triangle are 6 cm and 8 cm. What is the length of the third side of the triangle?
(1) The triangle is a right angle triangle.
(2) The length of the third side of the triangle is an integer.
(1) The triangle is a right angle triangle.
(2) The length of the third side of the triangle is an integer.
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:
Data Sufficiency Forum
Data Sufficiency Forum
06 Mar 2023, 16:34
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Since the sum of any two sides of a triangle needs to be greater than the third side, we have:
\(c + 6 > 8 \Rightarrow c > 2\)
\(c < 6 + 8 \Rightarrow c < 14\)
So, even before checking the statements, we know \(2 < c < 14\)
(I) The triangle is a right angle triangle.
Since it is a right triangle, we can apply Pythogoras. We have two possible hypothenuses: the unknown side of length \(c\) or the side of length \(8\).
First option: \(6^{2} + 8^{2} = c^{2} \Rightarrow c = 10\)
Second option: \(6^{2} + c^{2} = 8^{2} \Rightarrow c = 2\sqrt{7}\)
I is not enough
(II) The length of the third side of the triangle is an integer.
We know \(2 < c < 14\), so there are multiple options for integers in this interval.
II is not enough
(I + II)
With I, we have \(c = 10\) or \(c = 2\sqrt{7}\). With II, we know the length needs to be an integer, so the only possibility is \(c = 10\).
So the answer is \(C\)
\(c + 6 > 8 \Rightarrow c > 2\)
\(c < 6 + 8 \Rightarrow c < 14\)
So, even before checking the statements, we know \(2 < c < 14\)
(I) The triangle is a right angle triangle.
Since it is a right triangle, we can apply Pythogoras. We have two possible hypothenuses: the unknown side of length \(c\) or the side of length \(8\).
First option: \(6^{2} + 8^{2} = c^{2} \Rightarrow c = 10\)
Second option: \(6^{2} + c^{2} = 8^{2} \Rightarrow c = 2\sqrt{7}\)
I is not enough
(II) The length of the third side of the triangle is an integer.
We know \(2 < c < 14\), so there are multiple options for integers in this interval.
II is not enough
(I + II)
With I, we have \(c = 10\) or \(c = 2\sqrt{7}\). With II, we know the length needs to be an integer, so the only possibility is \(c = 10\).
So the answer is \(C\)
08 Mar 2023, 10:39
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Statement one should be enough. it says that the triangle is a right triangle, with two of its sides 6 and 8. This indicates that the triangle is special right triangle with sides (3:4:5) x 2 = 6:8:10. 10 is the 3rd side.
