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11 May 2020, 05:45
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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:
85%
(hard)
Question Stats:
45% (02:28) correct
55%
(02:12)
wrong
based on 166
sessions
History
Date
Time
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Not Attempted Yet
A triangle has sides of length 12, 15 and k units. What is the length of the longest side?
(1) The perimeter of the triangle is a multiple of 9.
(2) One of the interior angles of the triangle is equal to the sum of the other two interior angles.
Are You Up For the Challenge: 700 Level Questions
(1) The perimeter of the triangle is a multiple of 9.
(2) One of the interior angles of the triangle is equal to the sum of the other two interior angles.
Are You Up For the Challenge: 700 Level Questions
11 May 2020, 06:06
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Bunuel
Rule :- The third side or k here has to be less than the sum of other sides and more than the difference of other two sides.
so \(15-12<k<15+12.......3<k<27\)
(1) The perimeter of the triangle is a multiple of 9.
So k+12+15 or k+27 is a multiple of 9. Thus k is a multiple of 9.
Hence k could be 9 or 18
Insuff
(2) One of the interior angles of the triangle is equal to the sum of the other two interior angles.
So let the angles be a, b and c, so a+b+c=180 and a+b=c...c+c=180...c=90
Thus, we have a right angled triangle.
Now the hypotenuse could be k, so \(k=\sqrt{12^2+15^2}=\sqrt{369}=3\sqrt{41}\)
or the hypotenuse could be 15, so \(k=\sqrt{15^2-12^2}=\sqrt{81}=9\)
Insuff
Combined
k=9
C
General Discussion
ArunSharma12
Joined: 25 Oct 2015
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11 May 2020, 06:27
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Bunuel
Given:
3 < K< 27
statement 1:
27 + k = 9*x
k: [9,18]
not sufficient
statement 2:
c = a + b
a + b + c =180
triangle is right angled.
case 1: when 15 is largest side
\(k^2 + 144 = 225\)
\(k^2 = 81 0\)
K = 9
case 2: when k is largest side
\(225 + 144 = k^2\)
\(369 = k^2\)
K is not an integer.
not sufficient
combining both statements,
K = 9.
Ans: C
