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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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Bunuel
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

Answer: B
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