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# All but 4 of the counselors on staff at a certain summer camp have sai

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
All but 4 of the counselors on staff at a certain summer camp have sai  [#permalink]

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27 Feb 2019, 23:15
00:00

Difficulty:

35% (medium)

Question Stats:

75% (02:18) correct 25% (02:05) wrong based on 59 sessions

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All but 4 of the counselors on staff at a certain summer camp have sailing certification, first aid certification, or both. Twice as many counselors have neither certification as have both certifications, and 7 counselors have sailing certification. If there are a total of 22 counselors on staff, then how many of the counselors have first aid certification?

A. 9
B. 13
C. 15
D. 22
E. 23

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Re: All but 4 of the counselors on staff at a certain summer camp have sai  [#permalink]

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28 Feb 2019, 03:53
Bunuel wrote:
All but 4 of the counselors on staff at a certain summer camp have sailing certification, first aid certification, or both. Twice as many counselors have neither certification as have both certifications, and 7 counselors have sailing certification. If there are a total of 22 counselors on staff, then how many of the counselors have first aid certification?

A. 9
B. 13
C. 15
D. 22
E. 23

given total counselors 22
neither is 4
One or both certification = 22-4=18

given ; Twice as many counselors have neither certification as have both certifications; 4/2=2
only sailing certification; 7-both =7-2=5

only first aid certification = 18-5=13
IMO B
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Re: All but 4 of the counselors on staff at a certain summer camp have sai  [#permalink]

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18 Mar 2019, 17:22
1
Quote:
then how many of the counselors have first aid certification?

Would this not include "only french" and "both"? 13 is the number of "only french". Should C not be the answer?
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Joined: 18 Jan 2019
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Re: All but 4 of the counselors on staff at a certain summer camp have sai  [#permalink]

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01 Apr 2019, 07:23
sumert wrote:
Quote:
then how many of the counselors have first aid certification?

Would this not include "only french" and "both"? 13 is the number of "only french". Should C not be the answer?

agreed, it should say "only first aid certification"
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Re: All but 4 of the counselors on staff at a certain summer camp have sai  [#permalink]

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03 Apr 2019, 18:02
Bunuel wrote:
All but 4 of the counselors on staff at a certain summer camp have sailing certification, first aid certification, or both. Twice as many counselors have neither certification as have both certifications, and 7 counselors have sailing certification. If there are a total of 22 counselors on staff, then how many of the counselors have first aid certification?

A. 9
B. 13
C. 15
D. 22
E. 23

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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Re: All but 4 of the counselors on staff at a certain summer camp have sai   [#permalink] 03 Apr 2019, 18:02
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