Carol's B-day

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islands80: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Tue May 04, 2010 12:18 pm

by islands80 » Tue Apr 24, 2012 11:53 pm

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

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 24, 2012 11:53 pm

shantanu86: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Sun Mar 11, 2012 8:57 pmFollowed by: 1 member; Location: India; Thanked: 16 times

by shantanu86 » Wed Apr 25, 2012 1:12 am

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.

If you feel like it, hit thanks

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Apr 25, 2012 2:51 am

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

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Apr 25, 2012 8:55 am

islands80 wrote: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!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

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jrakhe: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sun Apr 22, 2012 11:22 am

by jrakhe » Wed Apr 25, 2012 4:00 pm

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

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Fri Apr 27, 2012 10:32 am

(D) QED

Follow your passion, Success as perceived by others shall follow you

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