Clarification on 0568 #45

Forum for the GRE subject test in mathematics.
newb
Posts: 6
Joined: Wed Oct 29, 2008 4:02 am

Clarification on 0568 #45

Postby newb » Tue Nov 04, 2008 12:41 am

Here is 45 on GRE 0568:

A circular region is divided by 5 radii into sectors as shown above. 21 points are chosen in the circular region, none of which is on any of the 5 radii. Which of the following statements must be true?

1. Some sector contains at least 5 of the points.
2. Some sector contains at most 3 of the points.
3. Some pair of adjacent sectors contains a total of at least 9 of the points.

A. 1. only
B. 3. only
C 1. and 2. only
D. 1. and 3. only
E. 1., 2., 3. only

The correct answer was D.

Can't all 21 points be found in one sector? Nothing in the question sounds like it's preventing this from happening... So 2. could be true, no?
What am I missing o_O ?

a huge thank you with a ! in advance :roll:

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

Postby Nameless » Tue Nov 04, 2008 12:50 am

Use the pigeonhole principle, since we have 21 points, and 5 regions so at least one region must contain 5 points. There is at least one of the other four regions must contain 4 points. So there at least two adjacent regions must contains 9 point. Therefore the answer is D

ngoc
Posts: 6
Joined: Mon Nov 03, 2008 5:54 am

Postby ngoc » Tue Nov 04, 2008 12:51 am

So if 21 points is in 1 sector (call that sector A), then the number points in sector A and its neighbor would be 21 > 9, so (3) is true.

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

Postby Nameless » Tue Nov 04, 2008 12:53 am

So if 21 points is in 1 sector

there is no "IF" here. :D what happens if "YOUR IF" is not true?

ngoc
Posts: 6
Joined: Mon Nov 03, 2008 5:54 am

Postby ngoc » Tue Nov 04, 2008 1:34 am

I'm just pointing to the newb guy that his counter example doesn't work. (Hence it's an IF, because it considers a particular case). Of course the logic argument relies on Pigeon hole.

newb
Posts: 6
Joined: Wed Oct 29, 2008 4:02 am

Postby newb » Fri Nov 07, 2008 1:33 am

Thanks very much for the help :)
I totally understand it now.
(Feeling really stupid at the moment.)




Return to “Mathematics GRE Forum: The GRE Subject Test in Mathematics”



Who is online

Users browsing this forum: jli220 and 5 guests