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

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GMATBusters
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All but 4 of the counselors at a certain summer camp have a sailing [#permalink] 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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D
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   21 Jul 2018, 21:16
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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

D
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   21 Jul 2018, 23:39
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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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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   02 Dec 2018, 06:53
Could anyone explain "All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both." this statement means? I cannot solve out its structure...
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   02 Dec 2018, 06:57
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Hi faltan

All but 4 of the counselors at a certain summer camp have a sailing certification: means that except 4 counselors, all remaining counselors have a sailing certifications.

faltan wrote:
Could anyone explain "All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both." this statement means? I cannot solve out its structure...
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   05 Dec 2018, 08:07
Given , neither certificate = 4

"twice as many of the counselors have neither certification as have both certifications". This means people with both the certificate is half of neither = 2.

No of people with sailing = 7
Let the no of people with only sailing = x

22 = 7 +x + 4 - 2
x = 11

Total sailing = 11 + 2 = 13
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   19 Dec 2020, 17:38
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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

Solution:

We can use the formula:

Total = Sailing + First Aid - Both + Neither

We are given that Total = 22, Sailing = 7 and Neither = 4. Since we are also given that Neither is twice Both, then Both = 2. Therefore, we have:

22 = 7 + First Aid - 2 + 4

22 = 9 + First Aid

13 = First Aid

Answer: D
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   06 Sep 2022, 02:26
Drawing a table might help.

From the question, the following table can be drawn:
Attachment:
1.png
1.png [ 2.43 KiB | Viewed 6905 times ]


"If twice as many of the counselors have neither certification as have both certifications" --> 4 = 2*(no. of ppl with both S&F) --> no. of ppl with both S&F = 2
Attachment:
2.png
2.png [ 2.51 KiB | Viewed 6909 times ]


Now you can work out no. of ppl with S but no F = 7-2=5
Attachment:
3.png
3.png [ 2.66 KiB | Viewed 6906 times ]


Next, work out total no. of ppl with no F = 5+4=9
Attachment:
4.png
4.png [ 2.8 KiB | Viewed 6883 times ]


So total no. of ppl with F = 22-9 = 13
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink] New post   17 Apr 2024, 06:34
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Re: All but 4 of the counselors at a certain summer camp have a sailing [#permalink]
17 Apr 2024, 06:34
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