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

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Math Expert
Joined: 02 Sep 2009
Posts: 56357
In an office, 40 percent of the workers have at least 5 years of servi  [#permalink]

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16 Aug 2018, 08:39
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52% (02:33) correct 48% (01:55) wrong based on 33 sessions

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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) 80
(D) 144
(E) 160

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Posts: 7763
Re: In an office, 40 percent of the workers have at least 5 years of servi  [#permalink]

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16 Aug 2018, 09:30
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Bunuel 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

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
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Re: In an office, 40 percent of the workers have at least 5 years of servi  [#permalink]

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16 Aug 2018, 09:33
Bunuel 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

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)
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Re: In an office, 40 percent of the workers have at least 5 years of servi  [#permalink]

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16 Aug 2018, 10:16
chetan2u wrote:
Bunuel 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

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

Good catch Chetan. Edited. Thank you.
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Joined: 04 Jan 2015
Posts: 2944
Re: In an office, 40 percent of the workers have at least 5 years of servi  [#permalink]

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17 Aug 2018, 01:47

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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Re: In an office, 40 percent of the workers have at least 5 years of servi   [#permalink] 17 Aug 2018, 01:47
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