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

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Jan 09, 2020 10:58 pm
AAPL wrote:Princeton Review

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

1) r = 180 - (p + q)
2) p = 60

OA C
Let's take each statement one by one.

1) r = 180 - (p + q)

This does not help. Insufficient

2) p = 60

This does not help. Insufficient

(1) and (2) together

Even after combing the two statements, we can't be sure that p = q = 60.

Case 1: We have p = 60. Say r = 90 and q = 30, then p ≠ q.
Case 1: We have p = 60. Say r = 60 and q = 60, then p = q = 60.

Insufficient

The correct answer: E

Hope this helps!

-Jay
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Re: For the triangle shown above, does p=q=60?

by deloitte247 » Fri Jan 17, 2020 9:21 am
The sum of the interior angle of a triangle = 180 degrees
Therefore, p+q+r = 180
Statement 1: r = 180 - (p + q)
p+q+r = 180
Different sum of 3 integers can equal to 180 and p=q=60 in some variation and for some other variation, it is not. e.g 60+60+60=180, 60+30+90=180, 20+50+110=180.
Based on this, statement 1 is thus NOT SUFFICIENT.

Statement 2: p=60
If p=60, the value of q and r will decide if p=q=60 but since the value of p, q and r are unknown, statement 2 is NOT SUFFICIENT.

Combining both statements together:
p=60 and r =180 - (p+q)
Therefore, r=180 - (60 + q)
r = 180 - 60 + q
r-q = 120
The value of q and r will determine if p=q=60 but the value of q and r are unknown. Therefore, the combination of both statements ARE NOT SUFFICIENT.

Answer = option E
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