Height of N People

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Height of N People

by theCodeToGMAT » Thu Sep 19, 2013 5:02 am
What is the average (arithmetic mean) height of the n people of a certain group?
(1) The average height of the n/3 tallest people in the group is 6 feet 2.5 inches, and the average height of the rest of the people in the group is 5 feet 10 inches
(2) The sum of the heights of the n people is 178 feet 9 inches


OA [spoiler][A][/spoiler]
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by Brent@GMATPrepNow » Thu Sep 19, 2013 6:13 am
theCodeToGMAT wrote:What is the average (arithmetic mean) height of the n people of a certain group?
(1) The average height of the n/3 tallest people in the group is 6 feet 2.5 inches, and the average height of the rest of the people in the group is 5 feet 10 inches

(2) The sum of the heights of the n people is 178 feet 9 inches


OA [spoiler][A][/spoiler]

Target question: What is the average height of the n people?

Statement 1: The average height of the n/3 tallest people in the group is 6 feet 2.5 inches, and the average height of the rest of the people in the group is 5 feet 10 inches
This tells us that the average height of 1/3 of the people is 6'2.5" and the average height of the other 2/3 of the people is 5'10"
So, we can use the weighted averages formula: average of entire group = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
We get: Group average = (1/3)(74.5 inches) + (2/3)(70 inches)
Of course, we don't need to perform any calculations beyond this. We need only recognize that we COULD use this euqation to find the group average.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the heights of the n people is 178 feet 9 inches
The average height = (sum of all heights)/n
Statement 2 gives us the sum of the heights, but we still need the value of n.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Aside: For more information on weighted averages, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

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by GMATGuruNY » Fri Sep 20, 2013 8:14 am
theCodeToGMAT wrote:What is the average (arithmetic mean) height of the n people of a certain group?
(1) The average height of the n/3 tallest people in the group is 6 feet 2.5 inches, and the average height of the rest of the people in the group is 5 feet 10 inches
(2) The sum of the heights of the n people is 178 feet 9 inches

OA [spoiler][A][/spoiler]
Statement 1:
Test TWO CASES.
If the average height is the same in each case, the statement is SUFFICIENT.
If the average height is NOT the same in each case, the statement is INSUFFICIENT.
To simplify the math, plug in easier values for the heights:
The average height of the n/3 tallest people in the group is 1 FOOT, and the average height of the rest of the people in the group is 2 FEET.

Case 1: n=3
Here, n/3 = 3/3 = 1, so 1 person is 1 foot tall, while the other 2 people are each 2 feet tall.
Average height for all 3 people = (1*1 + 2*2)/3 = 5/3.

Case 2: n=6
Here, n/3 = 6/3 = 2, so 2 people are each 1 foot tall, while the other 4 people are each 2 feet tall.
Average height for all 6 people = (2*1+ 4*2)/6 = 10/6 = 5/3.

Since the average height is the same in each case, SUFFICIENT.

Statement 2:
Without knowing the value of n, we cannot determine the average height.
INSUFFICIENT.

The correct answer is A.
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by faraz_jeddah » Sat Sep 21, 2013 2:12 am
theCodeToGMAT wrote:What is the average (arithmetic mean) height of the n people of a certain group?
(1) The average height of the n/3 tallest people in the group is 6 feet 2.5 inches, and the average height of the rest of the people in the group is 5 feet 10 inches
(2) The sum of the heights of the n people is 178 feet 9 inches


OA [spoiler][A][/spoiler]
Nice questions you have been posting lately. What is the source?
A good question also deserves a Thanks.

Messenger Boy: The Thesselonian you're fighting... he's the biggest man i've ever seen. I wouldn't want to fight him.
Achilles: That's why no-one will remember your name.

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by theCodeToGMAT » Sat Sep 21, 2013 5:44 am
faraz_jeddah wrote: Nice questions you have been posting lately. What is the source?
I am solving random questions.. The question I like, I post it.. :)
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