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For which of the following values of x is the units digit of

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For which of the following values of x is the units digit of [#permalink] New post 03 Dec 2019, 02:33
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For which of the following values of x is the units digit of the product \((2)(3^x)\) equal to 4?

A. 12

B. 13

C. 14

D. 15

E. 16


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Re: For which of the following values of x is the units digit of [#permalink] New post 04 Dec 2019, 18:10
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For this question, we should recognize that there is a pattern in the units digit for powers of 3.

3^1 = 3 (Units Digit = 3)
3^2 = 9 (Units Digit = 9)
3^3 = 27 (Units Digit = 7)
3^4 = 81 (Units Digit = 1)
3^5 = 243 (Units Digit = 3 --> the pattern restarts

The question asks for the value of x that would yield a units digit of 4 from the product if (2)(3^x). So, we know the units digit of 3^x must multiply by 2 and yield a result with a units digit of 4.

I think the easiest way is to figure out the units digit of each of the answer choices, using the pattern above --

A: 3^12 - Units Digit of 1 -- 2 x 1 = 2 Doesn't give us a units digit of 4
B: 3^13 - Units Digit of 3 -- 2 x 3 = 6 Doesn't give us a units digit of 4
C: 3^14 - Units Digit of 9 -- 2 x 9 = 18 Doesn't give us a units digit of 4
D: 3^15 - Units Digit of 7 -- 2 x 7 = 14 This one works!
E: 3^16 - Units Digit of 1 -- 2 x 1 = 2 Doesn't give us a units digit of 4

Answer is D
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Re: For which of the following values of x is the units digit of [#permalink] New post 04 Dec 2019, 22:56
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Here we are going to use the concept of rotation of unit digits of powers. Given question (2)(3^x) and observing the unit digit,
3^1 = 3 (2*3 = 6)
3^2 = 9 (2*9 = 18, unit digit is 8)
3^3 = 27(2*7 = 14, unit digit is 4, we found it)
3^4 = 81
The unit digit cycle of power if 3 repeats in a cycle of 4. As the options does not have 3, we have to find a number that givens remainder 3 when divided by 4(cycle of 4). Check options and 15 is only such number. Option D is the correct answer.
Re: For which of the following values of x is the units digit of   [#permalink] 04 Dec 2019, 22:56
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For which of the following values of x is the units digit of

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