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A software company named Hardsoft has three divisions, each staffed by

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A software company named Hardsoft has three divisions, each staffed by  [#permalink]

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New post 04 Nov 2019, 04:19
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Question Stats:

43% (02:39) correct 57% (02:52) wrong based on 22 sessions

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A software company named Hardsoft has three divisions, each staffed by at least 10 people. The ratio of men to women is 7:5 in Finance and Administration, 3:4 in Marketing and Sales and 8:7 in Research and Development. If there are 100 men working in Hardsoft and every Hardsoft employee works for one of the three divisions, then the difference between the maximum and minimum possible number of women working in Hardsoft is

(A) 39
(B) 40
(C) 41
(D) 42
(E) more than 42


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Re: A software company named Hardsoft has three divisions, each staffed by  [#permalink]

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New post 04 Nov 2019, 06:20
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Tricky one imo

Number of men in Finance and Administration=7a
Number of men in Finance and Administration=5a

Number of men in Marketing and Sales=3b
Number of men in Marketing and Sales=4b


Number of men in Research and Development=8c
Number of men in Research and Development=7c

Given- 7a+3b+8c=100, where a>0, b>1 and c>0

If we gotta maximize number of women, we have to maximize b

As, a>0 and c>0; hence b<29

There are no possible solution for b= 27 or 28

At b=26, a=2 and c=1

maximum number of women =5a+4b+7c = 121


To minimize the number of women we have to minimize 'b' and maximize 'a'.

7a+3b+8c=100
minimum possible value of b=2

7a+8c=94
a(max)=10 and c=3

Minimum possible number of women= 5a+4b+7c=50+8+21=79

Difference= 121-79=42




Bunuel wrote:
A software company named Hardsoft has three divisions, each staffed by at least 10 people. The ratio of men to women is 7:5 in Finance and Administration, 3:4 in Marketing and Sales and 8:7 in Research and Development. If there are 100 men working in Hardsoft and every Hardsoft employee works for one of the three divisions, then the difference between the maximum and minimum possible number of women working in Hardsoft is

(A) 39
(B) 40
(C) 41
(D) 42
(E) more than 42


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GMAT Club Bot
Re: A software company named Hardsoft has three divisions, each staffed by   [#permalink] 04 Nov 2019, 06:20
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