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number properties

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number properties

by sud21 » Sat Jan 21, 2012 9:07 pm
If 8.xxx * 10^(-1) + 7.xxx * 10^(-2) + 3.xxx * 10^(-3) + 2.xxx * 10^(-1)=N, the most left nonzero digit of N is which digit?
Units' digit
Tens' digit
Hundreds' digit
Thousands' digit
Ten thousands' digit
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by abby17 » Sun Jan 22, 2012 12:45 am
N will be of the form 1.abcdef
Value of a,b,c,d,e,f will be dependent on the value of x.
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by Mike@Magoosh » Sun Jan 22, 2012 12:45 pm
Hi, there. I'm happy to give my 2¢ on this. :)

We want the most left nonzero digit of N. Notice, the question is not even asking about the left most digit to the right of the decimal point. It's asking about the left most digit in the entire number.

When we add 8.xxx * 10^(-1) + 2.xxx * 10^(-1), we get a result greater than one. There's no way that the sum will be even greater than 2 --- it certainly will come nowhere near to 10.

I agree with abby17 that the sum will be of the form 1.abcdef. I agree with abby17 that the right most digit, f, will depend on the value of x. BUT, the left most digit would be the units digit of 1.

Therefore, the answer is (A) the units digit.

Does that make sense? Please let me know if you have any questions on what I've said.

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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