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DS Explanation is confusing me!

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Junior | Next Rank: 30 Posts
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by richs_ca » Wed Apr 16, 2008 6:37 pm
If a and b are positive integers, is 2 (Sq.rt of a+b) > 4(sq.rt of b)?

1) b > 3a
2) a + b > 3

The answer explanation says that i should simplify the problem by dividing by 2 and then to square both sides to get a + b > 4b.

However, I had always thought that if you divide one side by 2, you would need to do the same to the other side so it would be a + b > 2b.

So now I'm a little lost.

Help?

Thanks!!
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Source: — Data Sufficiency |
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by simplyjat » Wed Apr 16, 2008 9:39 pm
You missed squaring 2 on the right hand side of the equation

2(sqrt(a+b)) > 4(sqrt(b))
=> sqrt(a+b) > 2(sqrt(b)) {dividing both sides by 2}
=> a+b > 4b {taking square of both sides}
simplyjat
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by Neo2000 » Wed Apr 16, 2008 9:40 pm
When you divide by 2 on both sides you get

(Sq.rt of a+b) > 2(sq.rt of b)

If you square this you get a+b > 4b
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by richs_ca » Thu Apr 17, 2008 2:16 pm
Ah ha!! Got it - and it now seems so obvious.

Thank you very much!
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by gmat765 » Thu Apr 17, 2008 7:10 pm
and now it becomes clear
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