A group of 6 friends - Adam, Barbara, Sam, Cohen, Denise, and Kate hav

Question

A group of 6 friends - Adam, Barbara, Sam, Cohen, Denise, and Kate have been invited to a job interview at Company X. At least two people must accept their invites. Each of their decision to either go or not go is dependent on the following conditions:

Cohen goes if both Denise and Kate go. 
 Barbara goes if Adam does not go. 
 Kate does not go only if Sam goes. 
 At least one of Adam and Kate do not go.  
If Kate goes to the interview, what is the maximum number of friends who can go?

A) 2

B) 3

C) 4

D) 5

E) Cannot be determined

sayan640 · Answer

MartyMurray   KarishmaB  can you please help me on this one ?

luke96688 · Answer

I don't see how D can be right. I strongly think it is C. My configuration is that A and S cannot go assuming K goes and that means B will definitely go. D has no restrictions so assuming the max, D will go and if D and K who are assumed to be going, go, then C will also go. That leaves B C D and K going while A and S are not. answer is 4 and therefore C. If you disagree please let me know what I did wrong.

sayan640 · Answer

Waiting for experts' opinion in this regard.

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Chauhan1508 · Answer

I think so 5 is the answer because it’s asking maximum possibility. Since Kate and Barabara goes and Cohen Denise and Kate also needs to be there, we have no information regarding Denise so we can take that Denise did go too, so Cohen also did. As it was mentioned Kate does not go if only sam goes but we know that along with Kate Barbara goes so Kate can go even if sam is there so only one not going is adam

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darkmaster0099 · Answer

The answer is 5 (Option D)

Reasoning:
We need to find the maximum number of friends who CAN go.

We can safely deduce that since Kate goes, Adam will not go. 
Since Adam isn't going, Barbara can go too.
No conditions are stopping Denise from going. 
Since Denise and Kate both are going, Cohen goes too.

Now condition 3 which states, "Kate does not go only if Sam goes", is a tricky one. It doesn't state that Kate and Sam can't go together ever. The "only if" means that just ONLY Kate and Sam can't go. However, in this case, we've established that there are others who can go, Sam won't be the only one going. It's perfectly fine for Sam and Kate to go together as along as at least one other member is accompanying them. Bottom line - Sam can go.

So everyone except Adam CAN go.

Adiyogi123 · Answer

It clearly states Kate does not go if Sam goes. Then how can Kate go with Sam ? Shoudnt it be 4 people ?

sayan640 · Answer

Requesting  KarishmaB   MartyMurray  to help.

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KarishmaB · Answer

At least one of Adam and Kate do not go. If Kate goes, it means Adam does not go. Then Barbara goes. (Given: Barbara goes if Adam does not go. ) Given: Kate does not go only if Sam goes If Kate goes, it implies nothing about Sam. (In necessary conditions, B' does not lead to A') So Sam can still go. No restriction on Denise so she could go and hence Cohen also goes. So only Adam doesn't go. Everyone else goes. Answer (D) Conditional Statements are explained here: https://youtu.be/MmlwcTlHZz8

sayan640 · Answer

KarishmaB

Please check my reasoning and confirm whether I can think like this :-

"Kate does not go " only if "Sam goes" = true ( as given in the question)
That does not mean the following is also true i.e
Sam goes " only if "Kate does not go " ..
Sam goes " only if "Kate does not go "==> may or may not be true

Sam can go even if Kate also goes. ==> final conclusion ..hence no implication on Sam ' s going.

sayan640

Requesting KarishmaB MartyMurray to help.

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At least one of Adam and Kate do not go.

If Kate goes, it means Adam does not go. Then Barbara goes. (Given: Barbara goes if Adam does not go.)

Given:
Kate does not go only if Sam goes

If Kate goes, it implies nothing about Sam. (In necessary conditions, B' does not lead to A')
So Sam can still go.

No restriction on Denise so she could go and hence Cohen also goes.

So only Adam doesn't go. Everyone else goes.

Answer (D)

Conditional Statements are explained here: https://youtu.be/MmlwcTlHZz8

A group of 6 friends - Adam, Barbara, Sam, Cohen, Denise, and Kate hav

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A group of 6 friends - Adam, Barbara, Sam, Cohen, Denise, and Kate hav

Prep Toolkit

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