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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
What is the units digit of 16^4 × 27^3?
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22 Feb 2021, 06:15
22 Feb 2021, 06:15
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Re: What is the units digit of 16^4 × 27^3?
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22 Feb 2021, 08:18
22 Feb 2021, 08:18
1
Solution:
We can use cyclicity here.
6 has a cyclicity of 1 i.e when you multiply 6 "n" number of times, you always get units digit 6
7 has a cyclicty if 4 i.e. \(7,7^2=49, 7^3=343, 7^4= 2401\)
Thus, 7 has 4 different units digit when multiplied by itself.
\(16^4 \)will also have a units digit of 6
\(27^3 \)will have a units digit 3
Hence, 6*3=18
IMO D
Hope this helps
We can use cyclicity here.
6 has a cyclicity of 1 i.e when you multiply 6 "n" number of times, you always get units digit 6
7 has a cyclicty if 4 i.e. \(7,7^2=49, 7^3=343, 7^4= 2401\)
Thus, 7 has 4 different units digit when multiplied by itself.
\(16^4 \)will also have a units digit of 6
\(27^3 \)will have a units digit 3
Hence, 6*3=18
IMO D
Hope this helps
What is the units digit of 16^4 × 27^3?
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22 Feb 2021, 09:42
22 Feb 2021, 09:42
1
The trick is to multiply only a unit digit, then keep the unit digit only.
16 ^ 1 = 16
16 ^ 2 = .....6 (6 * 6)
16 ^ 3 = .....6 (6 * 6)
16 ^ 4 = .....6 (6 * 6)
27 ^ 1 = 27
27 ^ 2 = .....9 (7 * 7)
27 ^ 3 = .....3 (9 * 7)
So, 6 * 3 = 18, the answer will be D.
16 ^ 1 = 16
16 ^ 2 = .....6 (6 * 6)
16 ^ 3 = .....6 (6 * 6)
16 ^ 4 = .....6 (6 * 6)
27 ^ 1 = 27
27 ^ 2 = .....9 (7 * 7)
27 ^ 3 = .....3 (9 * 7)
So, 6 * 3 = 18, the answer will be D.
