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# If x is a positive integer, what is the units digit of

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Director
Joined: 08 Jun 2015
Posts: 518
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
Re: If x is a positive integer, what is the units digit of [#permalink]

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08 Jul 2018, 00:25
+1 for option D. The power of 4 and 9 will be fixed. We need to find out what the last digits of 33 and 17 will be .. If even the last digit of 33 will be 9 and 7 if odd. For 17 it will be 3 if odd and 1 if even respectively. The product comes to 4*7*1 = 8. Option D it is !
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Manager
Joined: 04 Aug 2010
Posts: 180
Schools: Dartmouth College
Re: If x is a positive integer, what is the units digit of [#permalink]

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08 Jul 2018, 04:14
MA wrote:
If x is a positive integer, what is the units digit of $$(24)^{(2x + 1)}*(33)^{(x + 1)}*(17)^{(x + 2)}*(9)^{(2x)}$$ ?

A. 4
B. 6
C. 7
D. 8
E. 9

The rightmost factor -- $$9^{2x}$$ -- will have a units digit of 1 for any nonnegative value of $$x$$.
Thus, the rightmost factor can be ignored.

All of the remaining exponents will be positive integers even if $$x=0$$.
Thus, we can solve by letting $$x=0$$ and raising the units digits of the first 3 factors to the resulting exponents:
$$4^1 * 3^1 * 7^2 = 12 * 49$$ = integer with a units digit of 8.

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Re: If x is a positive integer, what is the units digit of   [#permalink] 08 Jul 2018, 04:14

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