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

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

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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 ce  [#permalink]

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New post 02 Dec 2018, 06:57
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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All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

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New post Updated on: 05 Dec 2018, 00:33
Bunuel 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. 14


solved using 2x2 matrix IMO D...
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Originally posted by Archit3110 on 04 Dec 2018, 00:20.
Last edited by Archit3110 on 05 Dec 2018, 00:33, edited 2 times in total.
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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 04 Dec 2018, 07:22
I would say D

------Fyes --- Fno --- Total
Syes--2--------5-------7
Sno---11-------4------15
Total--13------9------22
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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 04 Dec 2018, 07:29
stesmit why have you mentioned 4 under no first aid and no sailing certificate? Its given in question first line as both...


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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 04 Dec 2018, 07:36
All but 4 have a certificate. So 4 don't have any certificate. Correct me if I'm wrong..
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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 04 Dec 2018, 08:49
stesmit wrote:
All but 4 have a certificate. So 4 don't have any certificate. Correct me if I'm wrong..


I think it means that 4 "both" have certificate..

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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 04 Dec 2018, 11:41
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11
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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 04 Dec 2018, 11:43
Yamini27 wrote:
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11


Well even I have marked 11, let's wait for the official answer to get publish..

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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 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 ce  [#permalink]

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New post 05 Dec 2018, 08:09
Yamini27 wrote:
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11


f = only sailing
total no of people with sailing would be 11+2 (people with both certificate)
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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 05 Dec 2018, 08:11
pandeyashwin wrote:
Yamini27 wrote:
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11


f = only sailing
total no of people with sailing would be 11+2 (people with both certificate)

It's D 13 please check my solution 2x2 matrix

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Re: All but 4 of the counselors at a certain summer camp have a sailing ce   [#permalink] 05 Dec 2018, 08:11
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