Problem Solving

There are 3 different boards with four common members each and every two of them have 5 common members. If every board has equal number of members, then the total distinct members of all the three boards are:

a) 9
b) 11
c) 13
d) 17

This question can have multiple answers. For the purpose of exercising the concept involved, please just focus on the options provided.

PS: Its a modified question from Kaplan (might be some other publication as well)

IMO it should be 7 distinct members.

committee 1: ABCD E F
committee 2: ABCD E G
committee 3: ABCD F G

Total number of distinct members = 7 and each committee has equal number of members that is 6 members

pankajks2010 wrote:There are 3 different boards with four common members each and every two of them have 5 common members. If every board has equal number of members, then the total distinct members of all the three boards are:

a) 9
b) 11
c) 13
d) 17

This question can have multiple answers. For the purpose of exercising the concept involved, please just focus on the options provided.

PS: Its a modified question from Kaplan (might be some other publication as well)

I'm not sure why you'd modify a Kaplan question, only include 4 answer choices (instead of the 5 that appear on the actual GMAT) and leave it open to multiple correct answers, even though the question itself implies that there's only 1 possible answer.

As a result, the way you've modified it makes it an invalid (not to mention grammatically incorrect) question. For the sake of those studying for the GMAT, please only post GMAT-like questions in the problem solving forum.

Stuart Kovinsky wrote:I'm not sure why you'd modify a Kaplan question, only include 4 answer choices (instead of the 5 that appear on the actual GMAT) and leave it open to multiple correct answers, even though the question itself implies that there's only 1 possible answer.

As a result, the way you've modified it makes it an invalid (not to mention grammatically incorrect) question. For the sake of those studying for the GMAT, please only post GMAT-like questions in the problem solving forum.

Three points:
a) Well, as you would notice from my profile, that I have just started my GMAT prep, I didn't realize that putting up only 4 options would be so unlike GMAT. I appreciate your guidance to maintain an absolute focus on GMAT.
b) As far as modifying Kaplan's question is concerned, that was solely for the purpose of drawing attention to the underlying concept/formula with the forum members. I was just too excited to share that for the benefit of all. But, then, not by any means, I intended to take credit of Kaplan's hard-work or infringe Kaplan's copyright policy.
c) GMAT asks us to identify the best fit out of its options. Many a times it happens with CR or other topics that we deploy process of elimination. Similarly, although, this question can have multiple answers, I focussed on identifying the best fit among the options provided.

I would really appreciate if you could point out the grammatical errors in my write-up. That would help me in my preparation for GMAT and also in my communication, throughout my life.

While I admire your ambition, I'm a bit confused about your motives. Are you studying for the GMAT? If so, why not work on the questions that are actually out there rather than trying to create some of your own, especially since you're just getting started?

A big part of GMAT success is identifying recurring patterns. The main problem with many "home made" questions is that the question writer doesn't have enough experience with the exam to create questions that are similar to those on the actual GMAT. As a result, people who study those home made questions aren't preparing themselves for the actual exam and may be hurting, rather then helping, their scores.

Addressing one of the 3 points you made, every GMAT question has 1 answer that's categorically correct and 4 that are demonstrably wrong - even in verbal questions that may sound less certain. You will never find a GMAT question with more than 1 possible correct answer. The only mild exception to this rule is in sentence correction - there may be more than 1 answer that's grammatically correct, in which case it's your job to find the error-free choice that's stylistically superior to the others. However, while style may seem more ambiguous than grammar, the GMAT follows very consistent rules in deciding what "stylistically superior" means.

It's fine to reprint Kaplan questions here for discussion, as long as you credit Kaplan. We'd much rather you quote a question directly than change it, since those changes aren't reviewed by our curriculum committee and changed questions may be flawed.

The main wording issue with your question is the question itself, "then the total distinct members of all the three boards are". By using the word "are", the question implies that there's only one possible answer. Also, grammatically speaking, the question should be asking about the NUMBER of members. So, given that there's more than one possible answer, the question should read:

"..., then the number of distinct members serving on the three boards could be"

As far as solving the question, srcc25anu has the right approach. However, since each board could also have members who serve solely on that board, and since the boards must have an equal number of members, the correct answer is:

7 + 3n

in which n is any positive integer. In other words, the set of all possible answers is:

{7, 10, 13, 16, 19, ...}

of which only (C)13 appears among the choices.

Lets assume the three circles to be the three committees. The black shaded portion represents the common number of members in all the three committees. Similarly, the black & red region shows the common members in B&C. Similarly, the common members in other committees can be identified.

Now its provided that each committee has equal number of members. Lets assume that to be x. Every two committee has 5 members common in between them and 4 members are common in each of the committees.

Now, the number of distinct members = x+x+x-5-5-5+4; 3x-11
As 3x-11 has to be a positive integer, evaluating the options provided, its evident that the answer is C

PS: Please forgive me for the choice of colours and the size of circles not being uniform.

Stuart Kovinsky wrote:While I admire your ambition, I'm a bit confused about your motives. Are you studying for the GMAT?

The ambition and motive both are to beat the GMAT. I really appreciate your patience and respect the expert that you are. I admire your point to focus my preparation as per the structure & recurring pattern as identified by you experts. Thanks a lot!!

Can I request you to elaborate, how you derived the expression 7+3n (only if you think that the scope of this discussion can benefit my ambition with regard to GMAT)

pankajks2010 wrote:

Can I request you to elaborate, how you derived the expression 7+3n (only if you think that the scope of this discussion can benefit my ambition with regard to GMAT)

hi, i would like to answer your this query, although i'm not an expert, but i think i can handle this..!!

now consider the figure drawn by you, in this figure the black portion i.e. region bounded by all the three circles has a value of 4, and value of blue, red and yellow region=1 each.
let no. of members who are working exclusively in (say)board 1=n
now consider the following statement.!!

If every board has equal number of members

,
therefore no. of members working exclusively in board 2 as well as in board 3 will also be n.

hence total distinct members would be 7+3n..!!!

i hope it helps...!!!

Thanks Manpsingh!! It was helpful