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

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139576 [0], given: 12794

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

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25 Dec 2017, 04:35
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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
[Reveal] Spoiler: OA

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Kudos [?]: 139576 [0], given: 12794

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Joined: 25 Feb 2013
Posts: 817

Kudos [?]: 381 [0], given: 42

Location: India
GPA: 3.82
In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang [#permalink]

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25 Dec 2017, 05:39
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

Kudos [?]: 381 [0], given: 42

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Joined: 24 Nov 2016
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Kudos [?]: 31 [0], given: 40

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

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25 Dec 2017, 14:57
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.

Kudos [?]: 31 [0], given: 40

Re: In triangle JKM, if JK = x, KM = y, and JM = z, which of the three ang   [#permalink] 25 Dec 2017, 14:57
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