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All but 4 of the counselors at a certain summer camp have a sailing ce

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All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

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New post 21 Jul 2018, 20:33
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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?
A) 7
B) 9
C) 11
D) 13
E) 15

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Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

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New post 21 Jul 2018, 21:16
gmatbusters 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?
A) 7
B) 9
C) 11
D) 13
E) 15



Total =22
All but 4 means neither =4
So people having one or both certification = 22-4=18

twice as many of the counselors have neither certification as have both certifications..... So both * 2 = neither.......both = 4/2=2
People having only sailing certification = 7-both =7-2=5

So people with first aid certification = 18-5=13

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All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

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New post 21 Jul 2018, 23:39
gmatbusters 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?
A) 7
B) 9
C) 11
D) 13
E) 15


Given data: 7 counselors have a sailing certification | P(Sailing C) = 7

Formula used: P(Total having C) = P(Sailing C) + P(First Aid C) - P(Both)

If there are x counselors at the summer camp, x - 4 have either certification.
For 22 counselors at the summer camp, only 18 have either of the 2 certifications.

Since twice as many counselors have neither certifications as have
both certifications, P(Both) = \(\frac{4}{2} = 2\) (as 4 have neither certification)

Substituting values, we get \(18 = 7 + F - 2\) -> \(18 = 5 + F\) -> \(F = 13\)

Therefore, the total number of counselors that have a first aid certification is 13(Option D)
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