Hi all,
As I've been going though my GMAT quantitative review second edition, I came across a question which just doesn't make sense logically, making me think it could be a mistake. It is question #150 (if anyone has the book); but if not, I'll try to describe it:
Essentially there is a pentagon PQRST, where PQ=3, QR= 2 RS = 4, and ST = 5. It then asks which of the lengths 5, 10, and 15 could be the value of PT?
They split up the pentagon into three separate triangles: PQT; QRT; and RST.
It then says that because RS=4 and ST=5, RT must be < RS+ST (4+5) and therefore RT<9. So, okay, this makes sense. If RT is LESS THAN 9, its highest value should be 8 (as its not "less than or equal to - just less than). But, then it goes on to analyze triangle QRT (again, QR=2, but QT is unknown, and RT<9). The solution states "then RT+2 < 9+2 = 11, which then implies QT<11.". However, I don't understand why they are assuming that RT can equal 9. The solution already confirmed that RT is LESS THAN 9. So if RT is less than nine, then again, it's highest value can be 8. As such, QT should really be less than 8 + 2 (i.e., RT+QR), implying that QT is < 10, not 11 as the book states.
Going by the books solution, if RT is < 9, and QT is <11, then QT could, according to QT<11, be 10. But, if RT<9, and its highest value can therefore be 8, and QR = 2, then 8+2 =10 which would be = to QT (i.e., again according to the books logic that QT <11). This defies the law of a triangle in that the length of one side must be less than the sum of the other two sides, not equal to it. So am I correct in saying that the book is wrong?
I know this is a confusing question so hopefully someone has the actually text to refer to.
Thanks in advanced for nay help.
As I've been going though my GMAT quantitative review second edition, I came across a question which just doesn't make sense logically, making me think it could be a mistake. It is question #150 (if anyone has the book); but if not, I'll try to describe it:
Essentially there is a pentagon PQRST, where PQ=3, QR= 2 RS = 4, and ST = 5. It then asks which of the lengths 5, 10, and 15 could be the value of PT?
They split up the pentagon into three separate triangles: PQT; QRT; and RST.
It then says that because RS=4 and ST=5, RT must be < RS+ST (4+5) and therefore RT<9. So, okay, this makes sense. If RT is LESS THAN 9, its highest value should be 8 (as its not "less than or equal to - just less than). But, then it goes on to analyze triangle QRT (again, QR=2, but QT is unknown, and RT<9). The solution states "then RT+2 < 9+2 = 11, which then implies QT<11.". However, I don't understand why they are assuming that RT can equal 9. The solution already confirmed that RT is LESS THAN 9. So if RT is less than nine, then again, it's highest value can be 8. As such, QT should really be less than 8 + 2 (i.e., RT+QR), implying that QT is < 10, not 11 as the book states.
Going by the books solution, if RT is < 9, and QT is <11, then QT could, according to QT<11, be 10. But, if RT<9, and its highest value can therefore be 8, and QR = 2, then 8+2 =10 which would be = to QT (i.e., again according to the books logic that QT <11). This defies the law of a triangle in that the length of one side must be less than the sum of the other two sides, not equal to it. So am I correct in saying that the book is wrong?
I know this is a confusing question so hopefully someone has the actually text to refer to.
Thanks in advanced for nay help.
