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# What is the total number of executives at Company P

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Joined: 08 Jan 2016
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What is the total number of executives at Company P  [#permalink]

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23 May 2016, 01:56
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4
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Difficulty:

5% (low)

Question Stats:

83% (01:01) correct 17% (01:02) wrong based on 209 sessions

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What is the total number of executives at Company P?

(1) The number of male executives is $$\frac{3}{5}$$ the number of female executives.
(2) There are 4 more female executives than male executives.
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Joined: 02 Sep 2009
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Re: What is the total number of executives at Company P  [#permalink]

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23 May 2016, 02:05
1
What is the total number of executives at Company P?

(1) The number of male executives is $$\frac{3}{5}$$ the number of female executives --> m = 3/5*f. Not sufficient.

(2) There are $$4$$ more female executives than male executives --> m = f - 4. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for m and f and get the total number of executives (m+f). Sufficient.

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Re: What is the total number of executives at Company P  [#permalink]

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21 Apr 2018, 06:25
Bunuel wrote:
What is the total number of executives at Company P?

(1) The number of male executives is $$\frac{3}{5}$$ the number of female executives --> m = 3/5*f. Not sufficient.

(2) There are $$4$$ more female executives than male executives --> m = f - 4. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for m and f and get the total number of executives (m+f). Sufficient.

Bunuel but we still dont know the nimber of females, so what that there are 4 more females than man ?? .... but still number of females is not mentioned...also number of males is not mentioned either... how can C be correct answer ?
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What is the total number of executives at Company P  [#permalink]

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21 Apr 2018, 06:29
1
dave13 wrote:
Bunuel wrote:
What is the total number of executives at Company P?

(1) The number of male executives is $$\frac{3}{5}$$ the number of female executives --> m = 3/5*f. Not sufficient.

(2) There are $$4$$ more female executives than male executives --> m = f - 4. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for m and f and get the total number of executives (m+f). Sufficient.

Bunuel but we still dont know the nimber of females, so what that there are 4 more females than man ?? .... but still number of females is not mentioned...also number of males is not mentioned either... how can C be correct answer ?

The solution you quote explains this: We have two distinct linear equations with two unknowns.

We have m = 3/5*f and m = f - 4. You should be able to solve this system of equations and get the values of m and f. I'll let you practice and do it yourself.
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Re: What is the total number of executives at Company P  [#permalink]

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21 Apr 2018, 06:57
Bunuel wrote:
dave13 wrote:
Bunuel wrote:
What is the total number of executives at Company P?

(1) The number of male executives is $$\frac{3}{5}$$ the number of female executives --> m = 3/5*f. Not sufficient.

(2) There are $$4$$ more female executives than male executives --> m = f - 4. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for m and f and get the total number of executives (m+f). Sufficient.

Bunuel but we still dont know the nimber of females, so what that there are 4 more females than man ?? .... but still number of females is not mentioned...also number of males is not mentioned either... how can C be correct answer ?

The solution you quote explains this: We have two distinct linear equations with two unknowns.

We have m = 3/5*f and m = f - 4. You should be able to solve this system of equations and get the values of m and f. I'll let you practice and do it yourself.

ok so we have to system equations

$$m = \frac{3}{5}*f$$ ----> $$f =\frac{5}{3}*m$$

$$m = f - 4$$

$$m = \frac{5}{3}*m - 4$$ rearrange

$$4 = \frac{5}{3}*m - m$$ multiply by 3 both sides

$$12 = 5m - 3m$$

$$12 = 2m$$

$$m = 6$$

Bunuel have i solved it correctly ?
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Re: What is the total number of executives at Company P  [#permalink]

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21 Apr 2018, 07:28
1
dave13 wrote:
ok so we have to system equations

$$m = \frac{3}{5}*f$$ ----> $$f =\frac{5}{3}*m$$

$$m = f - 4$$

$$m = \frac{5}{3}*m - 4$$ rearrange

$$4 = \frac{5}{3}*m - m$$ multiply by 3 both sides

$$12 = 5m - 3m$$

$$12 = 2m$$

$$m = 6$$

Bunuel have i solved it correctly ?

Yep dave13 absolutely correct solution.

However, since this is a DS question we are okay to mark the answer once we ascertain that we have two different liner equations... Saving important time on the test.

I think Bunuel was making this point.

Best,
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Joined: 31 May 2017
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Re: What is the total number of executives at Company P  [#permalink]

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21 Apr 2018, 08:26
What is the total number of executives at Company P?

(1) The number of male executives is 3/5 the number of female executives.
This does not give the number of executives in the company. Not sufficient.

(2) There are 4 more female executives than male executives.
This says the difference in number of employees between Male and Female executives. But does not give the exact number of executives - Not sufficient.

Now (1) + (2) = Number of male executives is 3/5 of female , in other words number of male employees is 60% of total number of female employees, i.e. Number of female employees is 40% more than male and that value is 4 from second statement.

if 40% is 4, 100% is 10. Number of female employees is 10 with this we get number of male employees is 6. Total number of employees in company is 16.

Options (1) and (2) together is sufficient.

Ans: C
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Re: What is the total number of executives at Company P &nbs [#permalink] 21 Apr 2018, 08:26
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