## Q20

ManhattanPrepLSAT1
Atticus Finch

Posts: 2851
Joined: October 07th, 2009

### Q20

Rendona001
Vinny Gambini

Posts: 8
Joined: September 27th, 2016

### Re: Q20

Hi,

I got the correct answer (B) but this was by luck or by some crazy chain of ideas not sure but I am stumped!
Where do I start if P or W is out? Do I plug in the answer choices? When I go back to the conditionals or chart I know M --> ~P or ~T ; W--> ~P or ~S but none of these tell me when P or W is out.

Can someone please explain this question in detail? Thank you!

andrewgong01
Atticus Finch

Posts: 289
Joined: October 31st, 2016

### Re: Q20

For this question should it be done through inferences or should it be done through guess and check

I am not sure where the inference (in red) came from from the other answer key (the one on the student center) that said

In : L _ _ Out: P W M/T H/S

I am not sure how to make the inference that the remaining two outs must be M/T H/S [from the out]. I know that we know that H/SM M/PT or W/PS must always have at least one of them out but since we know P and W is out, how do we know where P came from since P shows up in two Out Rules (the M/PT and W/PS) rule. The W being out comes from the W/PS rule.

Thank you

ohthatpatrick
Atticus Finch

Posts: 4202
Joined: April 01st, 2011

### Re: Q20

Sometimes, conditional rules give us placeholders because they involve a minimum requirement somewhere.

Given the rule
P --> ~M
and contrapositive
M --> ~P

We can see that P and M couldn't both be in.

Can't both be IN = At least one is OUT

Since we have a minimum requirement of "at least one of P and M is OUT", we can put a
P/M+
placeholder in the OUT column.

When you have a rule that looks like
P --> ~M and ~R
M or R --> ~P

Then you have a minimum requirement of "at least one of MR and P is OUT", so we can put a
MR/P+
placeholder in the OUT column.

In this game, the 1st rule gives us a
H/SM placeholder in the OUT column.

2nd rule:
M/PT

3rd rule:
W/PS

So the OUT column has three placeholders
H/SM
M/PT
W/PS

The easiest way to satisfy those three would be to do
H M W

But another way to satisfy them, just to show you some options, would be
S M P

SM satisfies the first requirement
M satisfies the second
SP satisfies the third

For Q20, with P and W out, we want to see how many of our requirements have been satisfied.
W satisfies the third requirement (W/PS)
P on its own doesn't satisfy anything.

So in order to satisfy the first requirement (H/SM), we still need H or SM.
In order to satisfy the second requirement (M/PT), we still need M or T.

So our OUT column has
P
W
H/SM
M/PT

We only get four things out (because at least three must be IN), so the two letters in the answer choice must satisfy our two remaining requirements.

(A) H and L would still leave M/PT unsatisfied.
(B) This works
(C) H and S would still leave M/PT unsatisfied.
(D) L and M would still leave H/SM unsatisfied.
(E) S and T would still leave both H/SM and M/PT unsatisfied.

Hope this helps.

NeenaS624
Vinny Gambini

Posts: 2
Joined: October 26th, 2017

### Re: Q20

I think I must be totally misunderstanding this. Given the diagram with the contrapositives drawn in, it doesn't seem possible for a student to neither take physics nor writing. According to the diagram with contrapositives drawn in, if the student doesn't take physics then they must take writing, and if the student doesn't take writing then they must take physics. So how can they take neither course based on the rules?

I must be missing something really obvious here..

ohthatpatrick
Atticus Finch

Posts: 4202
Joined: April 01st, 2011

### Re: Q20

Well, return to the language of the game, rather than trying to decode this confusing looking diagram.

The obvious thing you're missing is kinda buried in the image, but these are all arrows on the diagram. Not double headed arrows, but single-direction arrows.

Their logic only flows in the direction of the arrowhead, never back into it.

So if W is taken, the P cannot be.

But there's no arrow going from "P cannot be taken" to "W must be taken". Conditional logic is not a two-way street. You only read it as, "IF left side, THEN right side".

The rule, as written in the game, says
"If you take writing, you can't take physics or stats".
so the contrapositive is
"If you're taking physics or stats, you can't take writing."

From those rules, we clearly can't take ALL of them. But we're certainly welcome to take NONE of them.

Pretend we are not taking writing, stats, or physics.

Now we read that last rule ..
"IF writing is taken ...."

Stop right there --- writing is NOT being taken. Therefore, this rule doesn't apply to our scenario and hence our scenario can't possibly be breaking it.

Any time the left side idea doesn't apply, the rule evaporates into thin air.

This sort of rule is incredibly common in In/Out games, and it fools people's eyes, because it looks like
Writing -> No Physics
Physics -> No Writing

People look at that and think that Writing and Physics must always be on opposite sides of the aisle, but they're not mutually exclusive. They can both be OUT.

When they are both OUT, neither of the left side ideas are triggered, so the rule is moot and harmless.

Hope this helps.

AndrewB184
Vinny Gambini

Posts: 6
Joined: January 27th, 2018

### Re: Q20

can someone explain in a visual way. the explanations above were just hard to follow.

ohthatpatrick
Atticus Finch

Posts: 4202
Joined: April 01st, 2011

### Re: Q20

The original explanation was the visual one, but we no longer have the capacity to host images in here, so it's not super easy to type visual explanations

If you weren't following the placeholder explanation, then just go for a plug-n-chug approach.

Every answer choice gives us a complete scenario for everybody who's in and out, since the question stem says that P and W are out and each answer choice provides two more people who would be out (there's a max of 4 in the out column).

So just write who's IN to the left of every answer choice, and add a P and a W to the right of every answer choice, and you basically have five scenarios. You can just measure them against the rules to see the four that break.

.......IN..................OUT
...M, S, T.....(A) H, L, P, W
...L, S, T.....(B) H, M, P, W
...M, L, T.....(C) H, S, P, W
...H, S, T.....(D) L, M, P, W
...H, L, M.....(E) S, T, P, W

Rule 1 kills (D) and (E).
Rule 2 kills (A) and (C).

Only (B) is left standing, so it's the correct answer.