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# Department X of a factory has 100 workers. What is the average (arithm

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Department X of a factory has 100 workers. What is the average (arithm  [#permalink]

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16 Oct 2018, 23:15
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Difficulty:

25% (medium)

Question Stats:

76% (01:12) correct 24% (01:21) wrong based on 47 sessions

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Department X of a factory has 100 workers. What is the average (arithmetic mean) annual wage of the workers at the factory?

(1) The average annual wage of the workers in Department X is $15,000. (2) The average annual wage of the workers at the factory other than those in Department X is$20,000.

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Joined: 15 Feb 2018
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Department X of a factory has 100 workers. What is the average (arithm  [#permalink]

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22 Oct 2018, 20:39
Department X
Factory

When information about one area is given and it is asking about another, automatically think of weighted averages.

$$w_dx_d$$+$$w_fx_f$$/n
Where w is weight, x is average, d is department, f is factory, n is total number of workers

1) Gives $$x_d$$, but not the others. Insufficient
2) Gives $$x_f$$, but not the others. Insufficient.

Together, insufficient.
E

Also the difficulty of knowing whether to include department workers in the factory total. Probably should.

In this example, doing it without inclusion for simplicity
1 worker in department, 99 in factory
$$\frac{(15,000+99·20,000)}{100}$$ = 19,950

99 workers in department, 1 in factory
$$\frac{(99·15,000+20,000)}{100}$$=15,050

Bunuel do you write these questions?
Department X of a factory has 100 workers. What is the average (arithm   [#permalink] 22 Oct 2018, 20:39
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