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In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang

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In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang [#permalink]

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New post 25 Dec 2017, 05:35
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In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang [#permalink]

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New post 25 Dec 2017, 06:39
Bunuel wrote:
In triangle JKM, if JK = x, KM = y, and JM = z, which of the three angles has the least degree measure?


(1) \(x = y\sqrt{3}\)

(2) y = z/2


The angle opposite to the smallest side is the Smallest. So the question essentially asks which among positive numbers \(x\), \(y\) & \(z\) is smallest?

Statement 1: \(x = y\sqrt{3}=>x>y\). but we know nothing about \(z\). Insufficient

Statement 2: \(y=\frac{z}{2}=>z>y\). but we know nothing about \(x\). Insufficient

Combining 1 & 2: on substituting the value of \(y\) in statement 1 we have \(x=\sqrt{3}*\frac{z}{2}=>z>x\)

Hence we get \(z>x>y\). So angle opposite to side KM will be smallest. Sufficient

Option C
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Re: In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang [#permalink]

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New post 25 Dec 2017, 15:57
Bunuel wrote:
In triangle JKM, if JK = x, KM = y, and JM = z, which of the three angles has the least degree measure?


(1) \(x = y\sqrt{3}\)

(2) y = z/2


(1) \(x = y\sqrt{3}\). So, \(x>y\), no info on \(z\), insufficient.
(2) y = z/2. So, \(z>y\), no info on \(x\), insufficient.
(1) & (2). \(z=2y\) and \(x = y\sqrt{3}\), so \(y< y\sqrt{3} < 2y = y < x < z\); y is the smallest, sufficient.

(C) is the answer.
Re: In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang   [#permalink] 25 Dec 2017, 15:57
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In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang

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