Q20 - Members of the VideoKing Frequent Viewers club

[ohthatpatrick]

Question Type:
Inference (if statements are true, which answer Must Be True)

Stimulus Breakdown:
Rule 1: Members of the club with 10+ rentals can get coupon only where they last rented a movie.
Rule 2: Members of the club with 10 or fewer rentals can only get coupon at Main St. location.
Facts: Pat has rented 10 or fewer videos and can receive the coupon at Walnut Lane location.

Answer Anticipation:
We need to figure out how these rules apply to Pat's situation. We know that Pat has rented fewer than ten videos, so we would think according to rule 2 that Pat can ONLY get the coupon at the Main Street location. But we don't even know if Pat is a member of club, so can we really apply those rules? Actually, COULD Pat even be a member of the club? If Pat were a member of the club and she had under 10 rentals, she'd only be able to get the coupon at the Main Street location. Since we know she CAN get the coupon at Walnut Lane, she must not be a member of the club!

Correct Answer:
D

Answer Choice Analysis:
(A) No, it might be that non-club members can receive it there. It might also be that club members with 10+ rentals, whose MOST RECENT rental was at Main St, can also get it there.

(B) We only know about Pat, and she's NOT a member of the club, so we have no way to prove this.

(C) We only know about Pat, and she's NOT a member of the club, so we have no way to prove this.

(D) This is what we figured out. Pat is NOT a member of the club. And we know he has a coupon, so we can prove that "at least one person NOT in the club can get the coupon".

(E) We couldn't possibly prove this weird connection exists. We don't really know WHAT rules, if any, govern Pat, given that she's NOT a club member and we were only given rules about club members.

Takeaway/Pattern: Inference (Must be true) likes to deal with conditional logic or otherwise math-y ideas. Here we were given two rules and then a set of particulars about Pat. Our job was to think about how the rules would apply to her situation. The only way Pat's situation could avoid breaking the rules was to realize "she must not be a club member".

#officialexplanation

[jennifer]

I understand that this is an inference question, and that the correct answer choice is D. However, I do not understand how we can infer that some people who are not members get a coupon? I am assuming that this person is Pat. How can we infer this, I am totally missing something. Please help. Thank you.

[americano1990]

Use your conditionals!! you will see how life savin' they can be!
Okay so we get two conditionals here

First:
Member & >10 movies--> Coupon @ latest location

Second:
Member & 10 or fewer movies --> Coupon @ Main Street

Now what do we know about Pat? We know that he got the coupon at Walnut Lane and that he rented 10 or fewer movies.
At this moment take a look at the first conditional. How can we play around with it? Ehhh.... Now, look at the second one and you will see that we can negate the right hand element of the conditional relationship since we know that Pat got his coupon from NON main street shop.

Okay so we get the following:
- (coupon @ Main street)--> - member OR - (10 or fewer)

We know that since Pat did get 10 or fewer rents, he must not be a member!! YAY!!! get it?

Thats why (D) is the answer: he got the coupon yet he aint no member! haha

Cool?

[shirando21]

Isn't B also true?

members of the club who have rented more than ten videos...

members of the Frequent viewers club who have not rented more than ten movies....

so there are members who have not rented more than ten videos, why not?

[joseph.m.kirby]

(B) is not provable because we don't know if there are any members who have rented less than 10 videos. Moreover, the correct answer (D) relates to an inference that Pat, who has rented less than 10 videos) is not a member.

americano1990 did a great job of diagramming the way to arrive at the inference for (D).

[shirando21]

ok, morgen's rule

[shodges]

Is (E) incorrect because it is a conditional that we cannot prove?

I originally chose it because I believed that Pat could not receive the coupon if he went there.

[sumukh09]

E is incorrect because it doesn't tell us whether Pat is actually a member or not and also it's the opposite of what we'd expect given the information in the stimulus. Assuming Pat was a member, then given that she hasn't rented more than 10 in the past month, we'd expect her to be able to receive the discount coupon.

[tzyc]

Use your conditionals!! you will see how life savin' they can be!
Okay so we get two conditionals here

First:
Member & >10 movies--> Coupon @ latest location

Second:
Member & 10 or fewer movies --> Coupon @ Main Street

Now what do we know about Pat? We know that he got the coupon at Walnut Lane and that he rented 10 or fewer movies.
At this moment take a look at the first conditional. How can we play around with it? Ehhh.... Now, look at the second one and you will see that we can negate the right hand element of the conditional relationship since we know that Pat got his coupon from NON main street shop.

Okay so we get the following:
- (coupon @ Main street)--> - member OR - (10 or fewer)

We know that since Pat did get 10 or fewer rents, he must not be a member!! YAY!!! get it?

Thats why (D) is the answer: he got the coupon yet he aint no member! haha

Cool?

We would not use the 1st conditional statement and negate the right side of it because we know he rented from the VK right?
Just want to double check...
Thanks!

[ohthatpatrick]

Right, the first conditional is troublesome because the trigger is
"Member and 10+ videos" ... that doesn't apply to Pat, so this takes us nowhere.

If we write the contrapositive of the first rule, the trigger is
"Not renting from the VK location last rented from" ... we have no idea whether that applies to Pat. We know Pat is renting from Walnut Lane, but we have no idea if that was the last location he rented from.

Meanwhile, when we write the contrapositive of the second rule, the trigger is
"Not renting from Main Street location" ... we KNOW that applies to Pat, since he's renting from Walnut Lane.

So we know that Pat CAN'T be a "Member who has not rented 10 or more videos".

Since we know Pat "has not rented 10 or more videos", then we can infer that Pat must not be a Member.

To be honest, I approached this one w/o doing any diagramming.

Since the 2 rules hinged on "more than 10" vs. "not more than 10", I just focused my attention on the second rule since we were told that Pat was "not more than 10".

The second rule should have forced Pat to get the coupon from Main Street. But since Pat got his coupon from Walnut Lane, there had to be some way that the 2nd rule didn't apply to him. Oh! Maybe he's not a member.

Hope this helps.

[nflamel69]

For the poster who asked about B. It was my contender as well during my PT. However, if you read closely, we can only conclude that pat did not rent more than 10 videos in the LAST MONTH. While B is saying there are members who did not rent more than 10 videos. Even if we assume pat is a member, which we cannot, the answer would still be wrong since it doesn't address the time frame.

[redcobra21]

Thanks for the posts - those were really helpful.

I've got a question regarding the conditional logic. I think some of the posters were wrong in suggesting that we can infer that Pat must not be a member.

If we diagram the second conditional, we get:
Member of Club and NOT rent more than 10 videos --> Can Receive coupon only at Main Street

The contrapositive would be: CANNOT receive coupon only at Main Street --> NOT Member of Club or RENT more than 10 videos.

How can we infer that Pat "must not be a member" from this? We only know that Pat "can receive the special discount at Walnut Lane." However, this does not mean that Pat CANNOT receive coupon only at Main Street (which is what is needed to trigger the conditional). It does not say that Pat only receives the discount at Walnut Lane, so it might be possible that Pat can receive the discount Lane, but that he can ALSO receive it at Main Street.

I think the confusion stems in part from people interpreting the necessary clause of the second conditional as saying "must" as opposed to "can," which I think produces a different relationship.

Based on this, I don't really see how (D) is the correct answer.

What do you guys think? Am I missing something here? Thanks in advance for your help

A

[ericha3535]

Here is my two cent.

If not more than ten times and a member -> then must receive coupon at the main location.

Contrapositive is if not received at main location, then you are not either a member or got more than ten times.

Pat got it at walnut. Walnut is not main so the Contrapositive kicks in.

Also what did argument say? That he didn't get more than then times. What does this imply? That he is not a member then.

So a b c are all irrelevant because it's talking about a member.

E is wrong because it's talking about some hypo. Who knows what would happen...

Hth

[amil91]

Thanks for the posts - those were really helpful.

I've got a question regarding the conditional logic. I think some of the posters were wrong in suggesting that we can infer that Pat must not be a member.

If we diagram the second conditional, we get:
Member of Club and NOT rent more than 10 videos --> Can Receive coupon only at Main Street

The contrapositive would be: CANNOT receive coupon only at Main Street --> NOT Member of Club or RENT more than 10 videos.

How can we infer that Pat "must not be a member" from this? We only know that Pat "can receive the special discount at Walnut Lane." However, this does not mean that Pat CANNOT receive coupon only at Main Street (which is what is needed to trigger the conditional). It does not say that Pat only receives the discount at Walnut Lane, so it might be possible that Pat can receive the discount Lane, but that he can ALSO receive it at Main Street.

I think the confusion stems in part from people interpreting the necessary clause of the second conditional as saying "must" as opposed to "can," which I think produces a different relationship.

Based on this, I don't really see how (D) is the correct answer.

What do you guys think? Am I missing something here? Thanks in advance for your help

A

Yes it does. If she can receive the discount at Walnut Lane, then she cannot receive it only at the Main Street location. The text in the stimulus does explicitly say only at the Main Street location.

Great explanation americano, really helped clear this one up for me.

[dvr_75]

My whole issue with this is how do we know Walnut lane isn't the main street location? It could be - so I had my doubts about claiming for sure that Pat wasn't a member

[dvr_75]

Never mind....I read the question as 'main location' rather than 'main STREET location'. that changes everything

[e. chung]

When solving this one, I just thought 'oh, members... we're talking about people.' And then proceeded to do the formal logic without it as a condition (10+ --> coupon @ latest location).

Needless to say, I got the wrong answer.

Does anyone have a rule of thumb for avoiding this pitfall in the future?

I'll try to be more aware of what could possibly be a condition...

THANKS in advance!

[ganbayou]

Hi,
I was just wondering...can't we still use the first conditional statement because it will say either Pat is not a member or Pat did not rent more than 10? I mean, "Or" can include the meaning "both" right? SO I thought we can use the first conditional statement to arrive the answer as well...or "or" just mean A or B but not both?
Or is it because Walnut Lane location of VideoKing is not the place where Pat last rented a movie, so we cannot trigger contrapositive?

Thank you

[erikwoodward10]

I think the key here is not to get tied up in conditional logic. Don't mess too much with the diagrams here, but notice that the two statements address how members can get the coupon. Pat gets a coupon, but doesn't meet the either of the SCs that is required to get a coupon. So there must be some other way to get one. D is the only answer choice that addresses how someone can get a coupon without meeting one of our NCs. Don't bother negating or finding the contrapositive, just understand what the statements mean and move forward.