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Which of the following could be the units digit of 57n, where n is a positive integer? Indicate all such digits. A 0 B 1 C 2 D
Which of the following could be the units digit of 57n, where n is a positive integer? Indicate all such digits. A 0 B 1 C 2 D
admin
2017-10-16
26
问题
Which of the following could be the units digit of 57
n
, where n is a positive integer?
Indicate all such digits.
A 0
B 1
C 2
D 3
E 4
F 5
G 6
H 7
I 8
J 9
选项
答案
B,D,H,J
解析
The units digit of 57
n
is the same as the units digit of 7
n
for all positive integers n. To see why this is true for n = 2, compute 57
2
by hand and observe how its units digit results from the units digit of 7
2
. Because this is true for every positive integer n, you need to consider only powers of 7. Beginning with n=1 and proceeding consecutively, the units digits of 7, 7
2
, 7
3
, 7
4
, and 7
5
are 7, 9, 3, 1, and 7, respectively. In this sequence, the first digit, 7, appears again, and the pattern of four digits, 7,9, 3,1, repeats without end. Hence, these four digits are the only possible units digits of 7
n
and therefore of 57
n
.
The correct answer consists of Choices B(1), D(3), H(7), and J(9).
This explanation uses the following strategies.
Strategy 7: Find a Pattern
Strategy 12: Adapt Solutions to Related Problems
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本试题收录于:
GRE QUANTITATIVE题库GRE分类
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GRE QUANTITATIVE
GRE
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