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In a ceratin group, the average (arithmetic mean) age of the

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Jan 09, 2020 9:53 pm
AAPL wrote:Magoosh

In a certain group, the average (arithmetic mean) age of the males is 28, and the average age of the females is 30. If there are 100 people in the group, how many of them are males?

1) The average age of all 100 people is 28.9
2) There are 10 more males than there are females

OA D
Let's take each statement one by one.

1) The average age of all 100 people is 28.9.

Say there are x males; thus, there are (100 - x) females.

=> 28x + 30(100 - x) = 28.9*100. We can get the unique value of x. Sufficient.

2) There are 10 more males than there are females.

Given that there are 100 people, and there are 10 more males than there are females, the no.of males = 55 and no. of females = 45. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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Re: In a ceratin group, the average (arithmetic mean) age of the

by deloitte247 » Sun Jan 12, 2020 12:49 pm
Average age of male = 28
Average age of female = 30
Total population = 100
So, if there are 100 people in the group, how many of them are males?
Statement 1: The average age of all 100 people is 28.9
$$\frac{Total\ age}{100}=28.9$$
Where total age = male's age + female's age
Since male's average = 28
$$Then,\ \frac{Total\ age\ of\ male}{no.\ of\ male}=28$$
Let the no. of male = x, then no. of female = 100 - x.
$$Therefore,\ \frac{male's\ age}{x}=28;\ \ \ \ \ \ male's\ age\ =\ 28x$$
$$\frac{female's\ age}{no.\ of\ female}=30;\ \ \ then\ \frac{female's\ age}{100-x}=30$$
$$female's\ age\ =\ 30\left(100-x\right)$$
Total age = (28x) + 30 (100-x)
$$\frac{\left(28x\right)+30\left(100-x\right)}{100}=28.9$$
$$28x+3000-30x=2890$$
$$2x=110$$
$$x=\frac{110}{2}=55$$
The no. of male = 55. Hence, statement 1 is SUFFICIENT.

Statement 2: There are 10 more males than females.
Total population = male + female
100 = m + f
if m = f+10, then f = m-10.
Therefore, 100 = m + m - 10
110 = 2m
m = 110/2 = 55 males
Statement 2 is also SUFFICIENT.

Since each statement alone is SUFFICIENT, the correct option is option D
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