workers

grandh01 wrote:In an office, 40 percent of the workers
have at least 5 years of service, and a
total of 16 workers have at least 10
years of service. If 90 percent of the
workers have fewer than 10 years of
service, how many of the workers
have at least 5 but fewer than 10 years
of service?
(A) 48
(B) 64
(C) 50
(D) 144
(E) 160

Since 90 percent of the workers have fewer than 10 years of service, that means
10 percent of them have at least 10 years, which is 16, as stated above.
So the total number of workers in this office is 160.
So we can tell that 64(0.4*160) workers have at least 5 years of service.
Among them, there's therefore 48 (64-16) of the workers that have at least 5 years
but less than 10 years of serving in this office.
So it's clearly A. Hope this helps.

Let the total number of workers be x.

0.40(x) = Workers who have atleast 5 years of service(5 or more years of service)

16 workers have atleast 10 years of service (10 or more years of service)

0.90(x) = workers that have fewer than 10 years of service

It then follows that 0.10(x) = 16 => x = 160

Workers who have atleast 5 but fewer than 10 years of service = 0.40(x) = 0.4(160) = 64

However, the 64 includes the 16 workers so the answer is 64 - 16 = 48

Choose A.