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Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#permalink]
07 Feb 2012, 11:35

1

This post received KUDOS

Expert's post

In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?

Important properties of a triangle. The shortest side is always opposite the smallest angle. The longest side is always opposite the largest angle.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient. (2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#permalink]
03 Jul 2013, 12:37

I've got a question. What if x=0.5 ? In that case, sum of PQ and QR would be 3 whereas PR would be 3.5 Wouldn't this invalidate (a) making (c) the right answer ? Or am I overreaching by questioning the validity of the triangle when it is stated that PQR is a triangle ?

Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#permalink]
03 Jul 2013, 12:46

1

This post received KUDOS

Expert's post

gmatnoob23 wrote:

I've got a question. What if x=0.5 ? In that case, sum of PQ and QR would be 3 whereas PR would be 3.5 Wouldn't this invalidate (a) making (c) the right answer ? Or am I overreaching by questioning the validity of the triangle when it is stated that PQR is a triangle ?

The length of any side of a triangle must be larger than the positive difference of the other two sides:

Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#permalink]
18 Nov 2013, 20:22

Buneul I believe that statement (2) should be interpreted as follows: firstly, if x=2 then PQ=x=2; also, QR= x+2=4. Now the possible values of the third side lie between (4-2=)2 and (4+2=)6 that is the third side PR can take the values 3,4 or 5. For (PQ,PR,QR)=(2,3,4) largest angle is P. Next for (2,4,4) angle P=Q=greatest. Lastly, for (2,5,4) largest angle is Q. As, we are getting three different answers this statement is clearly insufficient.

Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#permalink]
19 Nov 2013, 01:08

Expert's post

madn800 wrote:

Buneul I believe that statement (2) should be interpreted as follows: firstly, if x=2 then PQ=x=2; also, QR= x+2=4. Now the possible values of the third side lie between (4-2=)2 and (4+2=)6 that is the third side PR can take the values 3,4 or 5. For (PQ,PR,QR)=(2,3,4) largest angle is P. Next for (2,4,4) angle P=Q=greatest. Lastly, for (2,5,4) largest angle is Q. As, we are getting three different answers this statement is clearly insufficient.

From my post above: (2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

Most of your reasoning is correct. What you did wrong is that you assumed that the length of PR must be an integer. _________________