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Louise is three times as old as Mary. Mary is twice as

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by M7MBA » Fri Apr 05, 2019 11:42 am
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Louise is three times as old as Mary. Mary is twice as old as Natalie. If Louise is L years old, what is the average (arithmetic mean) age of the three women, in terms of L?

(A) L/3
(B) L/2
(C) 2L/3
(D) L/4
(E) L/6

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT
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by Brent@GMATPrepNow » Mon Oct 21, 2019 8:13 am
M7MBA wrote:Louise is three times as old as Mary. Mary is twice as old as Natalie. If Louise is L years old, what is the average (arithmetic mean) age of the three women, in terms of L?

(A) L/3
(B) L/2
(C) 2L/3
(D) L/4
(E) L/6
GIVEN: Louise is L years old

Louise is three times as old as Mary
This also means that Mary is 1/3 as old as Louise
Louise's age = L
So, Mary's age = (1/3)L = L/3

Mary is twice as old as Natalie.
This also means that Natalie is 1/2 as old as Mary
Mary's age = L/3
So, Natalie's age = (1/2)(L/3) = L/6

What is the average (arithmetic mean) age of the three women, in terms of L?
Average age = (sum of all 3 ages)/3

Sum of all 3 ages = L + L/3 + L/6
= 6L/6 + 2L/6 + L/6
= 9L/6
= 3L/2

So, average age = (3L/2)/3
= L/2

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Mon Oct 21, 2019 12:50 pm
M7MBA wrote:Louise is three times as old as Mary. Mary is twice as old as Natalie. If Louise is L years old, what is the average (arithmetic mean) age of the three women, in terms of L?

(A) L/3
(B) L/2
(C) 2L/3
(D) L/4
(E) L/6

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT
Given, Louise is three times as old as Mary
let the age of Mary be M,
Then L=3M or \(M=\frac{L}{3}\)
Given, Mary is twice as old as Natalie
Or, M=2N or \(N=\frac{N}{2} = \frac{L}{6}\)
Average age of L,M, and N in terms of \(L=\frac{M+N+L}{3} = \frac{1}{3}\left(\frac{L}{3}+\frac{L}{6}+L\right) = \frac{L}{2}.\)

Therefore, B
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by Scott@TargetTestPrep » Sun Oct 27, 2019 6:33 pm
M7MBA wrote:Louise is three times as old as Mary. Mary is twice as old as Natalie. If Louise is L years old, what is the average (arithmetic mean) age of the three women, in terms of L?

(A) L/3
(B) L/2
(C) 2L/3
(D) L/4
(E) L/6

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT
Solution:

We can let M and N be the ages of Mary and Natalie, respectively. Therefore, we have:

L = 3M

and

M = 2N

Since M = L/3 and N = M/2 = (L/3)/2 = L/6, the average age of the three women, in terms of L, is:

(L + L/3 + L/6)/3

Multiplying the expression by 6/6, we have:

(6L + 2L + L)/18

9L/18

L/2

Answer: B

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