In ten years, David will be four times as old as Aaron.

[VJesus12]

In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron?

A. 1-5
B. 6-10
C. 11-15
D. 16-20
E- 21-25

The OA is the option A.

I've got confused here. How should I set the equations to solve this PS question? Experts, I'd be thankful for your help here. <i class="em em-grinning"></i>

[regor60]

In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron?

A. 1-5
B. 6-10
C. 11-15
D. 16-20
E- 21-25

The OA is the option A.

I've got confused here. How should I set the equations to solve this PS question? Experts, I'd be thankful for your help here. <i class="em em-grinning"></i>

Let T= "Now". So T+10 will be ten years from now and T-20 is 20 years ago,.

Let A, D and E be their respective ages now.

Translate the first part as follows:
D+10 = 4(A+10).
Similarly, the second prompt translates as follows: D-20 = 2(E-20)
And the third part: D = E+7

Let's save the first equation, D+10=4(A+10) and try to find D so that we can solve for A.

Let's solve for E using the third equation,
E=D-7
Substitute this into the second equation:
D-20=2((D-7)-20). Solving for D = 34.

Plug D=34 into the first equation:
34+10=4(A+10)

4A=4 > A= 1, A

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Hi VJesus12,

We're told that in TEN years, David will be FOUR times as old as Aaron. TWENTY years ago, David was TWICE as old as Ellen. David is SEVEN years older than Ellen. We're asked how old Aaron is NOW. While this question can be solved Algebraically, it can also be solved by 'playing around' with the information and a bit of 'brute force' math.

Let's start with David - since he's referenced repeatedly. We know that he was alive 20 years ago AND at that time he was TWICE as old as Ellen. Thus, David is clearly older than 20. Let's see what happens if David is currently 30....

IF.... right now, David = 30, then....
20 years ago, David = 10 and Ellen = 5
However, this does NOT match with the fact that David is supposed to be SEVEN years older than Ellen, so we have to 'work back' and adjust the numbers to account for the 7 year difference in their ages...

IF.... 20 years ago, David = 14 and Ellen = 7, then David is TWICE Ellen's age AND seven years older than Ellen.
That would make David = 34 right now.

We're told that in 10 years, David will be FOUR times as old as Aaron...
In 10 years, David = 44 and Aaron = 11....
Thus, Aaron's age right NOW = 1

Final Answer: A

GMAT assassins aren't born, they're made,
Rich