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30 Dec 2019, 13:08
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B
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Difficulty:
35%
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Question Stats:
65% (01:13) correct
35%
(01:16)
wrong
based on 127
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If x and y are positive integers, what is the units digit of \(3^{4x+2y+6}\)?
(1) x = 1
(2) y = 2
Are You Up For the Challenge: 700 Level Questions
30 Dec 2019, 13:52
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Units digit of 3^(4x+2y+6)
(1) x = 1
3^(10+2y)=9^(5+y)
If y is odd, the units digit is 1. On the other hand, If y is even, the units digit is 9.
NOT SUFFICIENT
(2) y = 2
3^(10+4x)=9^(5+2x)
(5+2x) is always odd, thus the resulting units digit is 9.
SUFFICIENT
FINAL ANSWER IS (B)
Posted from my mobile device
(1) x = 1
3^(10+2y)=9^(5+y)
If y is odd, the units digit is 1. On the other hand, If y is even, the units digit is 9.
NOT SUFFICIENT
(2) y = 2
3^(10+4x)=9^(5+2x)
(5+2x) is always odd, thus the resulting units digit is 9.
SUFFICIENT
FINAL ANSWER IS (B)
Posted from my mobile device
30 Dec 2019, 20:21
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If x and y are positive integers, what is the units digit of \(3^{4x+2y+6}\)?
\(3^{4x}*3^{2y}*3^6\)
Unit place of \(3^{4x}\) will always be 1 as 3's cyclicity of 4(3^4 = 81)
Unit place of \(3^{2y}\) will be 9 when y is odd and 1 when y is even
Unit place of \(3^6\) will always be 9
Thus, unit place of \(3^{4x+2y+6}\) is either 1(1*9*9 = 81) OR 9(1*1*9=9)
Hence only 'y' governs the value of \(3^{4x+2y+6}\)
(1) x = 1
y is not defined.
INSUFFICIENT.
(2) y = 2
Unit place of \(3^{4x+2y+6}\) is 1.
SUFFICIENT.
Answer B.
\(3^{4x}*3^{2y}*3^6\)
Unit place of \(3^{4x}\) will always be 1 as 3's cyclicity of 4(3^4 = 81)
Unit place of \(3^{2y}\) will be 9 when y is odd and 1 when y is even
Unit place of \(3^6\) will always be 9
Thus, unit place of \(3^{4x+2y+6}\) is either 1(1*9*9 = 81) OR 9(1*1*9=9)
Hence only 'y' governs the value of \(3^{4x+2y+6}\)
(1) x = 1
y is not defined.
INSUFFICIENT.
(2) y = 2
Unit place of \(3^{4x+2y+6}\) is 1.
SUFFICIENT.
Answer B.
