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If x is a positive integer, which one of the following could be the re
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03 Nov 2024, 01:16
03 Nov 2024, 01:16
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Question Stats:
100% (00:38) correct
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If x is a positive integer, which one of the following could be the remainder when \(73^x\) is divided by 10?
Indicate all such remainders.
A. 0
B. 1
C. 2
D. 3
E. 4
F. 5
G. 6
H. 7
I. 8
J. 9
Indicate all such remainders.
A. 0
B. 1
C. 2
D. 3
E. 4
F. 5
G. 6
H. 7
I. 8
J. 9
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Official Answer
B,D,H,J
Re: If x is a positive integer, which one of the following could be the re
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27 May 2025, 11:59
27 May 2025, 11:59
Expert Reply
OFFICIAL EXPLANATION
1, 3, 7, and 9 only. .
As with multiplication, when an integer is raised to a power, the units digit is determined solely by the product of the units digits. Those products will form a repeating pattern. Here, $\(3^1=\underline{3}, 3^2=\underline{9}, 3^3=\)$ $\(27,3^4=81\)$, and $\(3^5=243\)$.
Here the pattern returns to its original value of 3 and any larger power of 3 will follow this same pattern: $\(3,9,7\)$, and then 1 . Thus, the units digit of $\(73^x\)$ must be $\(1,3,7\)$, or 9 . When dividing by 10 , the remainder is the units digits, so those same values are the complete list of possible remainders.
1, 3, 7, and 9 only. .
As with multiplication, when an integer is raised to a power, the units digit is determined solely by the product of the units digits. Those products will form a repeating pattern. Here, $\(3^1=\underline{3}, 3^2=\underline{9}, 3^3=\)$ $\(27,3^4=81\)$, and $\(3^5=243\)$.
Here the pattern returns to its original value of 3 and any larger power of 3 will follow this same pattern: $\(3,9,7\)$, and then 1 . Thus, the units digit of $\(73^x\)$ must be $\(1,3,7\)$, or 9 . When dividing by 10 , the remainder is the units digits, so those same values are the complete list of possible remainders.
gmatclubot
Re: If x is a positive integer, which one of the following could be the re [#permalink]
27 May 2025, 11:59
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