Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
What is the remainder when 7^8 is divided by 100?
A. 1
B. 2
C. 3
D. 4
E. 5
When an integer is divided by 100, the remainder will have the same units digit as the integer.
Thus, to determine which answer choice represents the remainder when 7� is divided by 100, we need to know the units digit of 7�.
When an integer is raised to consecutive powers, the resulting units digits repeat in a CYCLE.
7¹ --> units digit of 7.
7² --> units digit of 9. (Since the product of the preceding units digit and 7 = 7*7 = 49.)
7³ --> units digit of 3. (Since the product of the preceding units digit and 7 = 9*7 = 63.)
7� --> units digit of 1. (Since the product of the preceding units digit and 7 = 3*7 = 21.)
From here, the units digits will repeat in the same pattern: 7, 9, 3, 1.
The units digit repeat in a CYCLE OF 4.
Implication:
When an integer with a units digit of 7 is raised to a power that is a multiple of 4, the units digit will be 1.
Thus, 7� has a units digit of 1.
The correct answer is
A.
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