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In PQR, if PQ = x, QR = x + 2, and PR = y, which of the ..

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by factor26 » Mon Nov 28, 2011 12:59 pm
In TRIANGLE PQR, if PQ = x, QR = x + 2, and PR = y, which of
the three angles of TRIANGLE PQR has the greatest degree
measure?
(1) y = x + 3
(2) x = 2

Og answer is a. i don't understand how this is as there are many values to be placed in for the value of x and y. i know the third side rule comes into play here but if the question yields answers that are not possible to use due to the third side rule, can we still use the statement?

1) y= x+3
x=1
y=4

pq = 1
qr = 3
pr = 4

cant use!

x=2
y=5

pq=2
qr=4
pr=5

can use!

thanks!
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by CappyAA » Mon Nov 28, 2011 1:31 pm
The question is not asking you to determine what are the possible sides. The question is asking you to determine if you can figure out which angle has the greatest degree of measure. In order to do this, you will need to figure out the length of the sides.

We know that PQ = x, QR = x+2, and PR = y.

From statement 1, we know that y = x+3. From this, we know that PQ = x, QR = x+2, and PR = x+3. Since x must be positive, this is sufficient. Remember, the question is not asking us what are valid lengths. It is also not asking us the specific angle. It is only asking us which angle is the biggest. No matter what, the angle across from the longest side (in this case PR, which is equal to y or x+3) will be the largest angle. SUFFICIENT

From statement 2, we know x = 2, but this tells us nothing about y. INSUFFICIENT

A
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by Anurag@Gurome » Mon Nov 28, 2011 9:18 pm
factor26 wrote:In TRIANGLE PQR, if PQ = x, QR = x + 2, and PR = y, which of
the three angles of TRIANGLE PQR has the greatest degree
measure?
(1) y = x + 3
(2) x = 2

Og answer is a. i don't understand how this is as there are many values to be placed in for the value of x and y. i know the third side rule comes into play here but if the question yields answers that are not possible to use due to the third side rule, can we still use the statement?

1) y= x+3
x=1
y=4

pq = 1
qr = 3
pr = 4

cant use!

x=2
y=5

pq=2
qr=4
pr=5

can use!

thanks!
The question asks which angle will be the largest. So, here we can use the fact that the longest side is always opposite to the largest interior angle. Since in this case we know that PR is the longest side, so the angle opposite to PR will be the largest; SUFFICIENT. So, the correct answer is A.
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by factor26 » Tue Nov 29, 2011 5:14 pm
oh wow ... i cant believe i didnt realize we get a y value in terms of x in statement 1 :( ... i think i was too focused on trying to disprove and totally missed the obvious!! thanks guys!!
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by mcdesty » Wed Jul 09, 2014 10:17 am
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