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# How many people are employed at a certain manufacturing

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VP
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How many people are employed at a certain manufacturing [#permalink]  17 May 2004, 18:10
How many people are employed at a certain manufacturing plant with an annual payroll of \$2342000

(1) Three-fourths of the employees are clerical, at an average salary of \$16020

(2)With 8 percent more employees, the payroll would equal \$ 2548000

Is this data sufficient ? thank you
Senior Manager
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I think, the answer is C. Just a guess!
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Re: please give me an hand (Data sufficiency) [#permalink]  18 May 2004, 09:30
chunjuwu wrote:
How many people are employed at a certain manufacturing plant with an annual payroll of \$2342000

(1) Three-fourths of the employees are clerical, at an average salary of \$16020

(2)With 8 percent more employees, the payroll would equal \$ 2548000

Is this data sufficient ? thank you

I don't think it cannot be solved even by both combined.
Senior Manager
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Statement 1... tells about the clerks 'Three-fourths of the employees are clerical, at an average salary of \$16020 ' Therefore the remaining one forth ... but what is the NUMBER ... hence, insuffnt.

Statement 2 ....'With 8 percent more employees, the payroll would equal \$ 2548000' .. from this we can get the payroll of the total employees ....ie. 1.08x=2548000, through which we can calculate the payroll of all .....still we cannot get the whole number of employess.. Not sufficnt.

Combing both also does not give us the number. Hence the answer is E.
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Senior Manager
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Re: please give me an hand (Data sufficiency) [#permalink]  18 May 2004, 10:29
Let x be the number of employees.

Obviously, x should be a positive integer.

1. x is a multiple of 4. Insufficient.
2. x is a multiple of 25. Insufficient.

Combined 1 and 2: x is a multiple of 100.

(3x/4)16020 + (x/4)y = 2342000
or (3x)(4005)+ (xy/4) = 2342000.

3*200*4005 > 2342000.

There is only one solution, that is, x = 100.

Senior Manager
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Hi Hallelu

To be honest, I cannot understand your explaination .. with the multiple of 4 and multiple of 25...this goes way above my head. Would you be able to provide the source for the multiplication stuff ...its interesting (only if i can know your approach).

Thanks bro
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3/4 of 6 people = 4.25 people.
8% of 10 people = .8 people

I hope, you'll get it.
VP
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I think the answer is E.

set the total people = X and nonclerical employees have the average salary, Y
From A, we can only get:
0.75X * 16020 + 0.25X * Y = 234200

From B we can only get:
1.08X * each employees' salary = 254800

But, we don't know what percentage of the employees are clerical or nonclerical employees; therefore, we can solve the problem.

This answer is E. Does anybody have other thought?
Senior Manager
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Hi Hallelujah

You have mentioned the mnumbers "6 people" and "10 people" ....

3/4 of 6 people = 4.25 people.
8% of 10 people = .8 people

I understand the number being a WHOLE number as ... thanks for that...

Now, coming back to your previous post. You have mentioned that "x is a multiple of 100" ... well, it can be 200, 300, 400 ....

But in your last statement, you took it to be 100, why not the other multiples of 100?. I hope I brought the error in your reasoning. Hence the EXACT number cannot be determined with the information given. Making it E as the answer.

Regards
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Senior Manager
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If the number of employees is more than or equal to 200, the total salary of 3/4 employees is greater than \$2342000. Hence, except for 100, all ther positive multiples of 100 are ruled out.
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The answer(C) that Hella has given is correct and his solution perfect.
Not sure if such difficult DS can be a part of actual GMAT.

Great work Hella.

cheers
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beautiful solution halle!
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lets do it together....

Senior Manager
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Hi Halle

HATS OFF HALLE

I agree and the explaination is clear. Thanks for the insight. Pardon me, if i had been stubborn in proving my point.

Regards
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VP
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Way to go, Halle

you are right,

thank you.
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Re: please give me an hand (Data sufficiency) [#permalink]  31 May 2004, 19:19
hallelujah1234 wrote:
Let x be the number of employees.

Obviously, x should be a positive integer.

1. x is a multiple of 4. Insufficient.
2. x is a multiple of 25. Insufficient.

Combined 1 and 2: x is a multiple of 100.

(3x/4)16020 + (x/4)y = 2342000
or (3x)(4005)+ (xy/4) = 2342000.

3*200*4005 > 2342000.

There is only one solution, that is, x = 100.

Don't mean to beat on a dead horse here, but I missed this one.
Where does the 200 in '3*200*4005>234200 come in?
Also, how do you make the leap to this equation in general? Thanks in advance.
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Ooooooo my gosh .. i am confused in here again. I am abck to straching my head. Can Halle or others be kind enough to explain step-by-step. Please. One request, please explain step-by-step .. I get confused with sudden insertion of 3/4 of 6, or 8% of 10 etc...

Thanks for the patience guys.

Regards
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Senior Manager
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hallelujah1234 wrote:
If the number of employees is more than or equal to 200, the total salary of 3/4 employees is greater than \$2342000. Hence, except for 100, all ther positive multiples of 100 are ruled out.

The above explains why not 200, or any positive multiple of 100 except 100.
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I am new to this forum but not new to math,got some awards in my school days. I see lot of posts here asking to explain in a very detailed way.I have a piece of advice.

Best way to find solutions to a math problem is to analyze it yourself.Even if you dont get the answer, dont give up,try again from all possible angles,start from basics,try again,timing is not the issue when you are in learning mode.Only then, you look for the real answer.Then you will understand what people are talking about.I felt members were asking too spoon-feedy questions (not this thread though).Either they are looking at the forum questions without clearing the basic concepts or they are straightway jumping to the answers.
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