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Re: All but 4 of the counselors [#permalink]
Okay, my doubt is question says "7 of the counselors have sailing certificate", it didn't say "7 of the counselors have sailing certificates only", then why do we have to assume that in 7 counselors, they don't have the other certificate?
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Re: All but 4 of the counselors [#permalink]
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7 of the counselors have sailing certificates only.....If this would have been the scenario we would not be subtracting the number of people having both the certificates from them.
n(A U B) = n(A) + n(B) - n(A ∩ B)
in the above formula "n(A)" is all the number of counselors having sailing certificate------.to make it "number of counselors having only sailing certificate" we are subtracting n(A ∩ B) from it.

hope it helps
I am not good at explaining.
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Re: All but 4 of the counselors [#permalink]
I understand now, I made a mistake while making Venn diagram.
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Re: All but 4 of the counselors [#permalink]
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phoenixio wrote:
All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid certification?

Show: ::
13


The first sentence of the problem means that 4 counselors have neither sailing certification nor first aid certification. Therefore, the second sentence means 2 counselors have both, and 7 have sailing certification.

We can use the formula for overlapping sets and substitute the known values to solve for x, the number of counselors with a first aid certification:

Total = Sailing + First Aid - Both + Neither

22 = 7 + x - 2 + 4

22 = 9 + x

13 = x
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All but 4 of the counselors [#permalink]
Sonalika42 wrote:
Given
total staff = 22
members having neither certificate = 4
members having sailing certificate = 7
members having both certificate = 2
let members having first aid certificate be = x

hence
22 = 7 + x - 2 + 4
from above we get x = 13
counselors have a first aid certification= 13


Doesn't it say members that have both certificates are 4?
'All but 4 have ....'

EDIT: Okay, sorry I misread the question. The answer is 13.
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All but 4 of the counselors [#permalink]
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