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For the triangle shown above, does p = q = 60?

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For the triangle shown above, does p = q = 60?  [#permalink]

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New post Updated on: 06 Feb 2019, 21:36
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (01:38) correct 42% (01:20) wrong based on 31 sessions

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For the triangle shown above, does p = q = 60 ?

(1) r = 180 – (p + r)

(2) p = 60

Official explanation:
First, take a moment to rephrase the question. If p = q = 60, the triangle is equilateral. So, the question is equivalent to asking "Is the triangle equilateral?” Statement (1) is, by itself, insufficient to answer the question, although it does provide the very useful information that r = q. If you’re comfortable working with triangles, you may have immediately read “180 minus the sum of p and r” as being equal to q. If not, you can prove this by doing some algebraic manipulation. Add (p + r) to both sides to yield r + p + r = 180, but since 180 also equals p + q + r, you can combine the equations to get r + p + r = p + q + r. Subtract a p and a q from each side, and you’re left with r = q. Nonetheless, this is still insufficient to answer the question. If r and q are both 60, the answer is “yes”; if they’re both 45—remember, you can’t trust the diagrams in Data Sufficiency—the answer is “no.” We’re down to BCE.

Statement (2), by itself, is also insufficient to answer the question; the only thing it tells us about q and r is their sum, which equals 120. Eliminate (B). When we combine the statements, though, we can determine whether the triangle is equilateral. If r and q are equal and their sum is 120, then they, like p, equal 60. If all three angles equal 60, the triangle is equilateral, and
the correct answer is (C).

Originally posted by energetics on 06 Feb 2019, 13:58.
Last edited by Bunuel on 06 Feb 2019, 21:36, edited 2 times in total.
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Re: For the triangle shown above, does p = q = 60?  [#permalink]

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New post 06 Feb 2019, 14:05
P+q+r=180 (sum of angles of a triangle)
St. 1
P+r+r=180
==>r=q
However we do not know if r=q=60,since they can be anything
Imsufficient

St.2
P=60
We do not know anything about q and r
Insufficient

Combining,
We get r=q=60
Hence both statements are required
Ans:C

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Re: For the triangle shown above, does p = q = 60?   [#permalink] 06 Feb 2019, 14:05
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For the triangle shown above, does p = q = 60?

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