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For which of the following values of x is the units digit of
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03 Dec 2019, 02:33
03 Dec 2019, 02:33
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Question Stats:
72% (01:15) correct
27% (01:27) wrong based on 58 sessions
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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
Kudos for the right answer and explanation
A. 12
B. 13
C. 14
D. 15
E. 16
Kudos for the right answer and explanation
Re: For which of the following values of x is the units digit of
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04 Dec 2019, 18:10
04 Dec 2019, 18:10
1
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
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
Re: For which of the following values of x is the units digit of
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04 Dec 2019, 22:56
04 Dec 2019, 22:56
1
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.
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.
