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Perfect square

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Source: — Problem Solving |

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Re: Perfect square

by Ian Stewart » Fri Jul 10, 2009 8:38 am
tarun'susername wrote:the least number which should be subtracted from 10420 to make it perfect square is:

a> 189
b> 16
c> 256
d> 164
e> 36

?
If you can see that 100^2 = 10,000, then the nearest square to 10420 is going to be just larger than 100^2. You might try guessing it's 102^2 to see if you get something close to 10420. To compute this quickly:

102^2 = 102*102 = (100 + 2)*102 = 10200 + 204 = 10404

which is 16 less than 10420.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by tarun'susername » Mon Jul 13, 2009 6:18 am
Thanks Ian
I applied the same approach. But I was wondering if there is some precise mathematical technique to solve this question.
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Junior | Next Rank: 30 Posts
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by v » Wed Jul 15, 2009 1:39 am
I am agree with Ian.

Here is another approach to this...
You know (a+b)^2=a^2 + b^2 + 2ab
Put a=100 & try b=1,2,3,
for which value is less that 10420.
'
(100+2)^2=100^2 + 4 + 2*2*100
=10000 + 4 + 400 = 10404 very close.
So Ans is 16. "B"
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