In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and of the females, 120 pounds. What is the average weight of the people in the group?
(1) The group contains twice as many females as males.
(2) The group contains 10 more females than males.
OA A
Source: Official Guide
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
In a certain group of people, the average (arithmetic mean)
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Let no: of Males in the group is m and females be fBTGmoderatorDC wrote:In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and of the females, 120 pounds. What is the average weight of the people in the group?
(1) The group contains twice as many females as males.
(2) The group contains 10 more females than males.
OA A
Source: Official Guide
sum of weights of males = 180m
sum of weights of females = 120f
Average weight of all people in the group = (180m +120f)/m+f
from (1) f=2m
substituting f for m in average weight of all people in the group we get = (180m+ 120(2m))/m+2m = 140
Hence information in 1 is Sufficient
from (2) f = m+10
substituting f for m in the average weight of all people in he group we get = (180m+120(m+10))/2m+10 = (300m+1200)/2m+10
This information is NOT sufficient to answer the question.
Hence Answer is A
PS - As rule to calculate averages or sum of terms of two groups, we need information of no: of terms between groups in the form of proportion not as equation. Statement (1) in above questions gives information as proportion and statement (2) gives information on form of an equation.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
We can solve this question using weighted averagesBTGmoderatorDC wrote:In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and of the females, 120 pounds. What is the average weight of the people in the group?
(1) The group contains twice as many females as males.
(2) The group contains 10 more females than males.
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Given: In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and of the females, 120 pounds.
Target question: What is the average weight of the people in the group?
Statement 1: The group contains twice as many females as males.
This statement is SUFFICIENT because it provides us with information about the proportion of people in each group.
The above information tells us that, out of every three people, two are females and one is male.
In other words 2/3 of the group are female and 1/3 are male.
Adding this to our weighted average formula we get: average weight of the people in the group = (2/3)(120) + (1/3)(180)
Since we COULD evaluate this expression, we COULD answer the answer the target question with certainty
Statement 1 is SUFFICIENT
Statement 2: The group contains 10 more females than males.
This information does not tell us the proportion of people in each group (males and females)
For example, it could be the case that there are 14 people all together, with a breakdown of 12 females and 2 males. In this case, 12/14 of the people are females and 2/14 are males.
Or it could be the case that there are 16 people all together, with a breakdown of 13 females and 3 males. In this case, 13/16 of the people are females and 3/16 are males.
As you might imagine, the two scenarios, when plugged into are weighted averages formula, would yield different average weights for the group.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
