number properties

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Wed Jan 25, 2012 7:02 pm

If x is unit digit, y is tenth digit of a certain number, what x and y of (123,456,789)^2?
I. x = 1, II. Y=2 ,III Y=4
A) I
B) II
C) III
D) I,II
E) I, III

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Source: Beat The GMAT — Problem Solving | Wed Jan 25, 2012 7:02 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jan 25, 2012 8:23 pm

sud21 wrote:If x is unit digit, y is tenth digit of a certain number, what x and y of (123,456,789)^2?

I guess it should be tens digit.

As the number ends with 9, the square of the number will end with 1. Hence, x = 1.

Now, we have to calculate the tens digit of 123456789Â².

123456789Â² = (123456780 + 9)Â² = (123456780Â² + 2*123456780*9 + 9Â²)
Now the underlined term in the above expression will end with 00. Hence, it won't contribute in determining the tens digit or y of the given term.

Hence, y of 123456789Â² = y of (2*123456780*9 + 9Â²) = y of (18*123456780 + 81) = y of (...40 + 81) = y of (...21) = 2

The correct answer is D.

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