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 Post subject: Exponent QuestionPosted: Thu Dec 08, 2011 1:23 pm

Joined: Mon Oct 31, 2011 2:36 pm
Posts: 4
If X is a positive integer, what is the units digit of (24)^5+2X (36)^6 (17)^3?

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 Post subject: Re: Exponent QuestionPosted: Sat Dec 10, 2011 11:58 am

Joined: Thu Feb 12, 2009 6:32 pm
Posts: 497
This seems to be an example where the answer choices would help TREMENDOUSLY! One would assume that only one answer among them is possible. Lacking them, let me speak generally about this one.

You'll want to look in the Algebra book at the unit's trick for exponents. As you'll see, the expressions from the problem will necessarily have the following ones digits:

24^5: ends in 4
36^6: ends in 6
17^3: ends in 3

So, since we only care about the ones digits here, this yields:

(----4) + 2x(-----6)(------3)

Further simplifying, only considering ones digits:

(----4) + (-----6)x

So, it's an even plus an even, which must be even. Otherwise I don't see how we can go further without the choices.

[IF you meant that the first expression is 24^(5+2x), then we must consider only the odd exponent ones digits of this expression, which for anything ending in 4 is always 4! This yields the much easier to consider ones digits of:

(----4)(-----6)(------3),

in which case the answer is clearly 2!]

-Brian K., Instructor, bkalar@veritasprep.com

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