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Bobby & Johnny

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Bobby & Johnny

by dipzzz » Sun Jun 24, 2012 2:24 am
Bobby and his younger brother Johnny have the same birthday. Johnny's age now is the same as Bobby's age was when Johnny was half old as Bobby is now. What is Bobby's age now?
1)Bobby is currently four times as old as he was when Johny was born.
2)Bobby was six years old when Johnny was born.

OA after few responses....
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Source: — Data Sufficiency |
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by jcnasia » Sun Jun 24, 2012 3:48 am
I'm going to first assign variables.

Bn = Bobby now
Jn = Johnny now
Bb = Bobby before
Jb = Johnny before

Then, from the prompt, I can write the following equations.

Jn = Bb
Jb = 1/2 * Bn

Statement 1:
I can write the following equations.

Bn = 4*(Bn - Jn) since (Bn - Jn) is the age difference between Bobby and Johnny
Bn = 4*(Bb - Jb)

Now, I have four equations and 4 unknowns. However, I still can't find a unique solution. I see, just by looking at the equations, that they can be solved by setting Bn = Bb = Jn = Jb = 0. And, Statement 2 tells me that it's possible for Bobby and Johnny to have different ages, so Statement 1 is insufficient.

Statement 2:
Again, I can write 2 new equations.

Bn = Jn + 6
Bb = Jb + 6

And again, I have four equations, but this time, there is a constant (6) so I can't solve them by setting them all equal to 0. So 4 equations and 4 unknowns: Statement 2 is sufficient.

Bn = 24, Jn = 18, Bb = 18, Jn = 12
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by Anurag@Gurome » Sun Jun 24, 2012 5:42 am
Refer to the post here >> https://www.beatthegmat.com/an-english-l ... tml#475041
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by [email protected] » Tue Jun 26, 2012 10:59 pm
Another simple solution:
Let Bobby's age now=B and Johnny's age now=J years. So the diff in their ages is=B-J

So, Johnny was half old as Bobby is now=B/2
Then, Bobby's age was=B/2+(B-J)
As per stem,
J=B/2+(B-J)
or, 2J=3B/2
or, 4J=3B

Statement 1: When Johnny was born Bobby's age was B-J
So, B=4(B-J)
or, 3B=4J
Insufficient.
Statement 2: B-J=6

So now we have 2 equation,
B-J=6 and
4J=3B
or 3B=4(B-6)
or B=24
Sufficient.
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