Carol's B-day

[islands80]

If today is Carol's birthday, how old is Carol?

(1) 6 years ago she was half her present age.
(2) 3 years from now she will be 3 times as old as she was 7 years ago.

OA D

[shantanu86]

Let Carol's today's age be x.

Therefore we have-

(1) x= 2*(x-2) => x= 12 years

(2) x+3 = 3* (x-7) => x= 12 years

Thus, both are sufficient on their own.
[D] is the correct answer.

[neelgandham]

If today is Carol's birthday, how old is Carol?

Let Carol's age be x

(1) 6 years ago she was half her present age.

Carol's age 6 years ago = x-6 = (x/2)
Implies, 2x -12 = x, x = 12

(2) 3 years from now she will be 3 times as old as she was 7 years ago.

Carol's age 3 years from now = x+3
Carol's age 7 years ago = x-7
From the statement, x+3 = 3*(x-7). Implies x+3=3x-21 => 2x = 24 => x =12

We know that Statement I and Statement II are both sufficient to answer the question. IMO D

[Stuart@KaplanGMAT]

If today is Carol's birthday, how old is Carol?

(1) 6 years ago she was half her present age.
(2) 3 years from now she will be 3 times as old as she was 7 years ago.

OA D

Ooo, great question, since it gives us the opportunity to apply the most powerful rule known to DS experts across the universe: number of equations vs number of unknowns.

Here's the rule:

To solve for a system of n variables, one requires n distinct linear equations.

Or, somewhat simplified:

If you want to solve for n different variables, you need n different linear equations.

(Linear (for GMAT purposes) means no exponents other than 1 on any of the variable terms.)

Understanding and applying this rule allows you to answer many DS questions without doing any calculations. Let's apply it to this question!

Q: How old is Carol?

We think: we have 1 variable and 0 equations. If we get 1 linear equation involving only Carol, we're good to go!

(1) we can turn this into an equation. Running through a mini checklist:

Does it introduce any new variables? NO
Are there any non-linear terms? NO

1 linear equation, 1 unknown: SUFFICIENT; eliminate B, C and E.

(2) we can turn this into an equation. Running through a mini checklist:

Does it introduce any new variables? NO
Are there any non-linear terms? NO

1 linear equation, 1 unknown: SUFFICIENT; eliminate A.

Choose D!

Note that by applying this rule, we didn't actually have to waste time translating either statement (as long as we could recognize that no extra variables were introduced and that there were no non-linear terms).

Learn this rule; love this rule; live this rule!

[jrakhe]

Let's assume that Carol's current age is C

1)C-6=1/2*C => C = 12 (Sufficient)

2) C+3=3(C-7) => C=12 (Sufficient)

So answer is D

[ronnie1985]

(D) QED