The sum of the ages of Lindsey and Meghan is y, and Lindsey is exactly 9 years older than Meghan. Natalie is how many

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The sum of the ages of Lindsey and Meghan is y, and Lindsey is exactly 9 years older than Meghan. Natalie is how many years older than Meghan?

(1) In y years, Meghan will be exactly three times as old as Natalie is now.

(2) Lindsey is exactly 6 years older than Natalie.



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Let Lindsey's age = L
Let Meghan's age = m
Let Natalie's age = n
L + M = y - - - eqn (1)
L = M + 9 - - - eqn (2)
Target question => Natalie is how many years older than Meghan?
i.e What's n-m?
Statement 1: In y years, Meghan will be exactly three times as old as Natalie is now.
m + y = 3n - - - eqn (3)
Substituting Eqn. (2) in Eqn. (1)
m + 9 + m = y
2m + 9 = y - - - eqn (4)
Substituting Eqn. (4) in Eqn. (3)
m + (2m+9) = 3n
3m + 9 = 3n
3n - 3m = 9
$$\frac{3\left(n-m\right)}{3}=\frac{9}{3}$$
n - m = 3
Conclusively, Natalie is 3 years older than Meghan, hence statement 1 is SUFFICIENT.

Statement 2: Lindsey is exactly 6 years older than Natalie.
L - n = 6 - - - eqn (5)
Substituting Eqn. (2) in Eqn. (5)
m + 9 - n = 6
m - n = 6 - 9
m - n = -3
(multiply althrough by -1)
n - m = 3
In conclusion, Natalie is 3 years older than Meghan. Therefore, statement 2 is SUFFICIENT.
Since each alone is SUFFICIENT, option D is correct.