Averages question

sukh wrote:The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people? (A) 179 cm and 172 cm (B) 181 cm and 169 cm (C) 173 cm and 178 cm (D) 176 cm and 176 cm (E) 174 cm and 177 cm

This is essentially a weighted averages question.
We can avoid lengthy calculations by considering the following analogous scenario:

Let's say, we have a flask containing a solution that is 40% alcohol.
i) If we add to this flask a solution that is also 40% alcohol, the resulting mixture will still be 40% alcohol.
ii) If we take the original 40% solution and add a solution that is less than 40% alcohol, the resulting mixture will be less than 40% alcohol.
iii) If we take the original 40% solution and add a solution that is more than 40% alcohol, the resulting mixture will be more than 40% alcohol.

If we apply these concepts to the original question we can see that, in order to increase the average height, the two new people must have an average height that is greater than 175 cm.

In answer choice B, the average height is 175cm (since [181+169]/2 = 175). So, when these two people are added to the group, the average will remain at 175cm.

So, the answer is B

Cheers,
Brent

mayank.arora wrote:SO the answer is E??

Answer choice E: The average of 174 cm and 177 cm is 175.5 cm.
So, if we add these two people to the group (with an average height of 175cm), the average height will increase.

Our goal is to find the answer choice where the height does not increase.

Since answer choice B does not increase the average height, it is the correct answer.

Cheers,
Brent