How to solve this question?

Woopdeedoo
Posts: 6
Joined: Thu Nov 19, 2009 9:53 am

How to solve this question?

Postby Woopdeedoo » Wed Jan 13, 2010 2:37 am

Hey guys, i'm studying the logical games powerscore bible right now, and I'm stuck on a question. It's page 117.

"A university library budget committee must reduce exactly five of eight areas of expenditure --G, L, M, N, P, R, S, and W -- in accordance with the following conditions:
If both G and S are reduced, W is also reduced
If N is reduced, neither R nor S is reduced
If P is reduced, L is not reduced
Of the three areas L, M, and R, exactly two are reduced"


1. Is this the correct way to diagram/go about solving this problem?
GrSr --> Wr
Nr --> ¬Sr
Pr --> ¬Lr
2 of LMR

_ _ _ _ _ _ _ _
R R R R R ¬R ¬R ¬R

pos 1 - L R _ _ _ M _ _
pos 2 - L M _ _ _ R _ _
pos 3 - M R _ _ _ L _ _

2. I don't understand the answer, in the book it says
"2. Because three of the group of G, P, W, N/S must be reduced, this means that...
If G is not reduced, then P, W, and N/S must be reduced.
If P is not reduced, then G, W, and N/S must be reduced
If W is not reduced, then G, P, and N/S must be reduced."

I understand that 3 of of those letters must be reduced, but how do they know that 2 of GPW are always being reduced?

PoliticalJunkie
Posts: 228
Joined: Sun Sep 27, 2009 2:32 pm

Re: How to solve this question?

Postby PoliticalJunkie » Wed Jan 13, 2010 3:04 am

Almost there bud.

1. Rules look good, just remember to write down the contrapositive of all of them (you missed some big deductions not doing this)

The scenarios are

1. IN: LM_ _ _ OUT: PR _
2. IN: LRGSW OUT: PMN
3. IN: MR _ _ _ OUT: NL _

In 2, you have R already in the IN group. Take the contra of rule 2 and you get if R then NOT N meaning N is out and GSW are in the in group.

Before anything, you only have 3 open spots in each of the groups. The remaining variables are (1) GSWN and (3) GSWP.

Because there are 3 spots remaining you know 3 of GSW P/N must be reduced. You can then run through two options (1) run through more scenarios or (2) diagram out rules pertaining to the the above.

You know that 2 of GPW are reduced because of the N/S rule. Take scenarios 1: IN LMGSN OUT: PRW (violates rule 2)

Woopdeedoo
Posts: 6
Joined: Thu Nov 19, 2009 9:53 am

Re: How to solve this question?

Postby Woopdeedoo » Wed Jan 13, 2010 4:00 am

ahhh, ok that makes sense!! thanks buddy :)

was437
Posts: 18
Joined: Thu Oct 29, 2009 10:36 pm

Re: How to solve this question?

Postby was437 » Fri Jan 29, 2010 1:41 am

PoliticalJunkie wrote:Almost there bud.

1. Rules look good, just remember to write down the contrapositive of all of them (you missed some big deductions not doing this)

The scenarios are

1. IN: LM_ _ _ OUT: PR _
2. IN: LRGSW OUT: PMN
3. IN: MR _ _ _ OUT: NL _

In 2, you have R already in the IN group. Take the contra of rule 2 and you get if R then NOT N meaning N is out and GSW are in the in group.

Before anything, you only have 3 open spots in each of the groups. The remaining variables are (1) GSWN and (3) GSWP.

Because there are 3 spots remaining you know 3 of GSW P/N must be reduced. You can then run through two options (1) run through more scenarios or (2) diagram out rules pertaining to the the above.

You know that 2 of GPW are reduced because of the N/S rule. Take scenarios 1: IN LMGSN OUT: PRW (violates rule 2)


I've really got to stop doing LG when I'm not in a sober state! I have been sitting here trying to figure out how the hell you came up with 3 of GSW P/N must be reduced...or more specifically...how you know it was either P or N...and why...they are already solved...and how the next guy totally got it...no more smoke for me! lol.

Wouldn't W always have to be reduced?




Return to “LSAT Prep and Discussion Forum”

Who is online

Users browsing this forum: bearedman8, freefish, LarryFlint, tuesdayninja and 12 guests