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Three interviewers, A, B, and C are interviewing 40

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Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 14 Aug 2011, 11:40
3
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A
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Difficulty:

  85% (hard)

Question Stats:

48% (02:02) correct 52% (02:03) wrong based on 451 sessions

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Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?

(A) 0
(B) 2
(C) 6
(D) 8
(E) 12
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 11:52
2
DeeptiM wrote:
Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
(A) 0
(B) 2
(C) 6
(D) 8
(E) 12



Answer is A = 0

If A admitted 15 are overlapping with B admission of 17 But C doesnot overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 11:58
timeishere wrote:
DeeptiM wrote:
Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
(A) 0
(B) 2
(C) 6
(D) 8
(E) 12



Answer is A = 0

If A admitted 15 are overlapping with B admission of 17 But C doesnot overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.


well might be a silly ques but how do you know they are overlapping??
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 12:04
1
i thought it was straight 12.
applicant interview by A + applicant interview by B + applicant interview by C - total.
15+17+20-40=52-40=12

Did i miss something?
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 12:07
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jamifahad wrote:
i thought it was straight 12.
applicant interview by A + applicant interview by B + applicant interview by C - total.
15+17+20-40=52-40=12

Did i miss something?


Isnt the ques saying that applicant has to get admission from all the three to get admission.
"Only with three interviewers' admission can an applicant be admitted."
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 12:11
Ah Got it!

Thanks timeshare.
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 12:14
DeeptiM wrote:
timeishere wrote:
DeeptiM wrote:
Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
(A) 0
(B) 2
(C) 6
(D) 8
(E) 12



Answer is A = 0

If A admitted 15 are overlapping with B admission of 17 But C doesnot overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.


well might be a silly ques but how do you know they are overlapping??


Because the ques is asking for least number of admissions.
So take the worst case.

In case, the ques had asked for maximum admission, then take all 3 overlapping. Then the answer would be 15.
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 18:29
A - 15

B - 17

C - 20

as the question is asking for least possible applicants/admissions, there could be zero admissions.

there might be overlaps between A,B; B,C ; C,A. that doesn't necessarily mean there will be overlaps between all A,B and C.

Answer is A.
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Re: PS - Word Problem!!  [#permalink]

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New post 14 Aug 2011, 21:19
can someone confirm that this question doesn't lend itself to using the overlapping sets equation

A+B+C -AB - AC - CB - 2ABC = total

when I first read the question it seemed like it could, but then looking over it again, how many people A admitted, and how many people B admitted , etc has no bearing on the total number of people. In fact, they could all admit 0, so A+B+C = 0 and then that above formula can't work.

seems like it was just an effort to mislead us to thinking this was a overlapping set problem
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 14 Dec 2014, 19:20
Can anyone please post the graphical explanation as a solution for this problem ?
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 15 Dec 2014, 00:09
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pairakesh10 wrote:
Can anyone please post the graphical explanation as a solution for this problem ?


There isn't much you need to do here for a graphical representation. Think of having a rectangle with 40 elements in it.
Now draw a circle in it with 15 elements. Draw another circle which doesn't overlap this circle at all and has 20 elements in it. You have accounted for 35 elements and still have 5 elements leftover in the rectangle. Now the third circle with 17 elements can be drawn in any way inside the rectangle. There will be no elements lying in all three circles since the first two circles have no overlap. Hence it is not necessary that even one person gets admitted.
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 10 May 2016, 10:32
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'A' is the answer.

Question asks the LEAST number of applicants admitted. And, an applicant only be admitted when all three interviewers gave admission.

Interviewer C admitted- 20
Interviewer B admitted- 17
Interviewer A admitted- 15

Suppose 'B' admitted 17 candidates other than 'C' admitted. And then 'A' admitted remaining '3' (40-20-17=3) and any '12' from either 'C' or 'B'. In this case not even a single candidate is selected by all three, making the answer to be 'A'
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 18 Jun 2016, 01:35
Bunuel I got it right , but don't know if my method and understanding is right on this

total = a+b+c -{sum of two}+ all three +neither

40 = 52 - {x} +y
so to minimise Y , we need to maximise X , which can be 12 hence Y = 0

please correct me if I am missing anything
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 03 Sep 2016, 11:06
Lets say II represents sum of exactly two group overlap and III represents three overlap.
Now (A+B+C)-Total =Surplus=(15+17+20) - 40=12. Which can accommodate in II or III.
Also, (A+B+C)-Total =Surplus=II+2*III. So, if all 12 accommodates in II then III=0 (least value).
Ans- A.
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 19 Apr 2018, 16:58
DeeptiM wrote:
Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?

(A) 0
(B) 2
(C) 6
(D) 8
(E) 12


We can assume all 15 applicants admitted by A are also 15 of the 17 applicants admitted by B. Thus, so far, 17 applicants are admitted by at least one of the two interviewers A and B. However, since 17 + 20 = 37 < 40, it’s possible that none of these 17 applicants who are admitted by A and/or B are admitted by C, so the least number of applicants admitted by all three interviewers is 0.

Answer: A
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Re: Three interviewers, A, B, and C are interviewing 40  [#permalink]

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New post 15 Sep 2018, 07:16
we have 15+17<40
so, we can choose 15 person get admittion from interview A and 17 persons get admission from interviewe B and both these group dose not have overlapping member ( we have 40 which is more than 37)

A is correct
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Re: Three interviewers, A, B, and C are interviewing 40 &nbs [#permalink] 15 Sep 2018, 07:16
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