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The average (arithmetic mean) salary in a firm increased by 20% after

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The average (arithmetic mean) salary in a firm increased by 20% after [#permalink]

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The average (arithmetic mean) salary in a firm increased by 20% after a number of new employees were hired. How many people joined the firm?

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
(2) There were 10 people in the firm initially.
[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) salary in a firm increased by 20% after [#permalink]

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duahsolo wrote:
The average (arithmetic mean) salary in a firm increased by 20% after a number of new employees were hired. How many people joined the firm?

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
(2) There were 10 people in the firm initially.



Hi,

The main statement tells us that the AVG salary increased by 20%•••••

Let's see the statements

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
the difference in AVG salary is 40% and this results in an increase of 20% overall..
This means the new avg salary is AVERAGE of the two average salaries..
So the old and new people are the same..

But nothing about numeric value
Insufficient

(2) There were 10 people in the firm initially
Nothing about the new people joining..
Insufficient

Combined..
From statement I, we get new is EQUAL to old..
Statement II gives us the value of old, so new also is also 10
Sufficient
C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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The average (arithmetic mean) salary in a firm increased by 20% after [#permalink]

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New post 13 Feb 2017, 07:40
chetan2u wrote:
duahsolo wrote:
The average (arithmetic mean) salary in a firm increased by 20% after a number of new employees were hired. How many people joined the firm?

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
(2) There were 10 people in the firm initially.



Hi,

The main statement tells us that the AVG salary increased by 20%•••••

Let's see the statements

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
the difference in AVG salary is 40% and this results in an increase of 20% overall..
This means the new avg salary is AVERAGE of the two average salaries..
So the old and new people are the same..

But nothing about numeric value
Insufficient

(2) There were 10 people in the firm initially
Nothing about the new people joining..
Insufficient

Combined..
From statement I, we get new is EQUAL to old..
Statement II gives us the value of old, so new also is also 10
Sufficient
C


Hi Chetan2u,

Could you kindly explain the highlighted portions further?
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Re: The average (arithmetic mean) salary in a firm increased by 20% after [#permalink]

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New post 13 Feb 2017, 07:59
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Expert's post
duahsolo wrote:
chetan2u wrote:
duahsolo wrote:
The average (arithmetic mean) salary in a firm increased by 20% after a number of new employees were hired. How many people joined the firm?

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
(2) There were 10 people in the firm initially.



Hi,

The main statement tells us that the AVG salary increased by 20%•••••

Let's see the statements

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
the difference in AVG salary is 40% and this results in an increase of 20% overall..
This means the new avg salary is AVERAGE of the two average salaries..
So the old and new people are the same..

But nothing about numeric value
Insufficient

(2) There were 10 people in the firm initially
Nothing about the new people joining..
Insufficient

Combined..
From statement I, we get new is EQUAL to old..
Statement II gives us the value of old, so new also is also 10
Sufficient
C


Hi Chetan2u,

Could you kindly explain the highlighted portions further?


Say initially it was X, new it was X+40%.. final it is given as X+20%..
Average of X and X+40 is (X+X+40)/2=X+20..
For this to happen there has to be same number of people with X and with X+40...

Basically this is from weighted average method..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: The average (arithmetic mean) salary in a firm increased by 20% after [#permalink]

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New post 14 Feb 2017, 16:03
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Expert's post
duahsolo wrote:
The average (arithmetic mean) salary in a firm increased by 20% after a number of new employees were hired. How many people joined the firm?

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.
(2) There were 10 people in the firm initially.


We can let the number of original employees = D and the number of new employees = N. We can also let the average salary of the original employees = a and the average salary of the new employees = s.

We are given that the average (arithmetic mean) salary in the firm increased by 20% after a number of new employees were hired. Thus, the new average salary is 1.2a. However, in terms of a, s, D, and N, the new average salary is (aD + sN)/(D + N). Thus 1.2a = (aD + sN)/(D + N). We must determine the value of N.

Statement One Alone:

The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.

This means s = 1.4a. So the equation 1.2a = (aD + sN)/(D + N) becomes 1.2a = (aD + (1.4a)N)/(D + N). We can simplify this equation by dividing both sides of the equation by a, and we have:

1.2 = (D + 1.4N)/(D + N)

However, since we don’t know the value of D, we can’t determine the value of N. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

There were 10 people in the firm initially.

Since D = 10, the equation 1.2a = (aD + sN)/(D + N) becomes:

1.2a = (10a + sN)/(10 + N)

However, since we don’t know the values of a and s, we can’t determine the value of N. Statement two alone is not sufficient.

Statements One and Two Together:

Using the information from statements one and two, we know that:

1.2 = (D + 1.4N)/(D + N) and D = 10.

Thus:

1.2 = (10 + 1.4N)/(10 + N)

1.2(10 + N) = 10 + 1.4N

12 + 1.2N = 10 + 1.4N

2 = 0.2N

N = 2/0.2 = 20/2 = 10

Answer: C
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Re: The average (arithmetic mean) salary in a firm increased by 20% after   [#permalink] 14 Feb 2017, 16:03
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