1. Good post? |

## Law of averages

The average height for a group of students is 164. If the average height of the female students is 160, is the number of the female greater than the number of the males?
1) The average of the males is 170
2) There are 20 female students.

2. Good post? |

## Re: Law of averages

only first one is enough cause if they are equal, then the total average should be 165. but since it is smaller than 165, number of females should be larger than number of males

3. Good post? |

## Re: Law of averages

dsaqwert, could you please explain further.

My approach:

Females/x = 160, where x is the number of females -> females' height is 160x
males/y= ?, where y is the number of males
females+males/x+y=164

from statement 1: males/y=170 -> males' height=170y

160x+170y/x+y =164
160x+170y=164x+164y
4x=6y
x=3/2 *y

Consequently, x>y, i.e. number of females is bigger than that of males -> statement 1 is enough

Statement 2 is not enough as we don't know the combined height or the average or the number of males.

4. Good post? |

## Re: Law of averages

A it is.

5. Good post? |

## Re: Law of averages

My ans is A similar approach to alex.

dsaqwert could you explain your approach or if their is a shorter logic to get to the ans.

6. Good post? |

## Re: Law of averages

Originally Posted by Jeeves
My ans is A similar approach to alex.

dsaqwert could you explain your approach or if their is a shorter logic to get to the ans.
ok, let;s make it more clear;

assume number of boys and girls are equal, and knowing that the average of girls is 160 and the average of boys is 170, what overall average would you expect.... yes 165 ([160x + 170x]/2x=165) however the overall average is 164, in other words number of girls should be more than number of boys to ensure that the overall average is closer to the girls' average

in other words (mathematically);
x=number of girls
y=number of boys
160x+170y=164(x+y)
6y=4x
x=1.5y
x>y