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If 7 times the number of male workers in a certain factory equals 3

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manasiT22
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If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   Updated on: 09 Feb 2018, 14:41
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If 7 times the number of male workers in a certain factory equals 3 times the number of female workers, then which of the following can be the total number of workers in this factory?

A. 21
B. 37
C. 110
D. 128
E. 201

Source: examPAL
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C

Originally posted by manasiT22 on 05 Feb 2018, 12:45.
Last edited by manasiT22 on 09 Feb 2018, 14:41, edited 3 times in total.
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   05 Feb 2018, 13:08
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Consider x male , y female employee.
As per the statement 7x=3y
Implies y=7x/3
X+Y
x+7x/3+=10x/3
In the options 110 is a multiple of 10
So..
Option C
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   05 Feb 2018, 23:46
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dave13 wrote:
shivsuddala wrote:
Consider x male , y female employee.
As per the statement 7x=3y
Implies y=7x/3
X+Y
x+7x/3+=10x/3
In the options 110 is a multiple of 10
So..
Option C


how did you get 10x ? :?


Think it this way.
7M = 3F
Therefor M = (3/7) F
Now Total Workers in the factory are = M + F = (3/7)F + F = 10F/7
So whatever be the number of Workers; The number of female workers will always be an integer value.
Now lets check each option:
Option A = Total Workers is 21 implies 10F/7 = 21; giving an non-integer value for F
Option B = Total Workers is 37 implies 10F/7 = 37; again giving an non-integer value for F
Option C = Total Workers is 110 implies 10F/7 = 110; giving an integer value of F = 77 and that leaves number of males M = 33
7 times number of males = 7 x 33 = 231 = 3 times number of females = 3 x 77 = 231
Hence C is the only possible answer.
Option D = Total Workers is 128 implies 10F/7 = 128; again giving an non-integer value for F
Option E = Total Workers is 201 implies 10F/7 = 201; again giving an non-integer value for F
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   06 Feb 2018, 02:17
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Jiggy11 wrote:
If 7 times the number of male workers in a certain factory equals 3 times the number of female workers, then which of the following can be the total number of workers in this factory?

A. 21
B. 37
C. 110
D. 128
E. 201

Source: examPAL


7M = 3F

\(\frac{M}{F} = \frac{3}{7}\)

Since number of male workers and female workers must both be integers, M must be a multiple of 3 (say M = 3a) and F the same multiple of 7 (say F = 7a).

So the sum will be 3a+7a = 10a

Only option (C) is possible.
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   05 Feb 2018, 13:55
shivsuddala wrote:
Consider x male , y female employee.
As per the statement 7x=3y
Implies y=7x/3
X+Y
x+7x/3+=10x/3
In the options 110 is a multiple of 10
So..
Option C


how did you get 10x ? :?
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   25 May 2018, 21:58
shiv17 wrote:
Consider x male , y female employee.
As per the statement 7x=3y
Implies y=7x/3
X+Y
x+7x/3+=10x/3
In the options 110 is a multiple of 10
So..
Option C


Could you explain this in some other way too?
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Wisconsin92
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink] New post   25 May 2018, 22:01
If 7 times the number of male workers in a certain factory equals 3 times the number of female workers, then which of the following can be the total number of workers in this factory?

Work with it like this 7:3 is ratio of male to females.
Can be written as 7x:3x and hence total workers 7x+3x=10x
One factor is 10 and answer choice C is divisible by 10, hence correct.
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Re: If 7 times the number of male workers in a certain factory equals 3 [#permalink]
25 May 2018, 22:01
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