In an office, 40 percent of the workers have at least 5 years of servi

Question

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

(A) 48
(B) 64
(C) 80
(D) 144
(E) 160

chetan2u · Accepted Answer

If 90 % of the workers have fewer than 10 years of service then ten percent of the workers will have at least 10 years of service. This is given as 16..
So 10%=16, 100%=160
So total =160

Now at least 40% have 5 years of service so 40*160/100=64
But 16 have atleast 10 years, so atleast 5 but <10 =64-16=48

A

Bunuel , choice C may have typo and may be 80 for two reasons..
One it can be a trap answer
Second the choice in increasing order makes it >64

PKN · Answer

Given, 90 percent of the workers have fewer than 10 years of service. So, 10% of workers have more than 10 yrs of service.
Hence, 16 workers is equivalent to 10%
Total #workers=16*10=160

40 percent of the workers have at least 5 years of service, So 0.4*160=64 nos of workers have at least 5 years of service.

So the no of workers having at least 5 but fewer than 10 years of service=64-The no of workers having at least 10 years of service=64-16=48

Ans. (A)

Bunuel · Answer

Good catch Chetan. Edited. Thank you.

EgmatQuantExpert · Answer

Solution

Given:  
 • 40 percent of the workers have at least 5 years of service.
• 16 workers have at least 10 years of service.
• 90 percent of the workers have fewer than 10 years of service

To find:  
 • The number of the workers having at least 5 but fewer than 10 years of service

Approach and Working:   
 • Since 90% of the workers have fewer than 10 years of service, we can say 10% of the workers have at least 10 years of service
 o And, we also know that 16 workers have at least 10 years of service.
  So, 10% of the workers= 16 Workers
 Total workers= 160 Worker s

• Now, 40% of the workers have at least 5 years of service.
o  Hence, the number of workers having 5 years of service = 16*4= 64 workers.
o Out of 64, 16 have at least 10 years of service.
o Hence, 64-16= 48 workers have at least 5 but fewer than 10 years of service .

Hence, the correct answer is option A.

Answer: A

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In an office, 40 percent of the workers have at least 5 years of servi

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