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

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Re: If x is a positive integer, what is the units digit of  [#permalink]

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New post 07 Jul 2018, 23:25
+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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Re: If x is a positive integer, what is the units digit of  [#permalink]

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New post 08 Jul 2018, 03:14
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 &nbs [#permalink] 08 Jul 2018, 03:14

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