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If x is an integer greater than 1, what is the remainder whe

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If x is an integer greater than 1, what is the remainder whe

by Max@Math Revolution » Wed Apr 27, 2016 5:48 am
If x is an integer greater than 1, what is the remainder when x^4 is divided by 10?

1) x is not a multiple of 5.
2) x is a multiple of 2.


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed May 04, 2016 6:44 am
There is 1 variable (x) in the original condition. Therefore, there is high chance that D is the correct answer choice. In the case of the condition 1), the unit digit of x4 is always going to be 0, 1, 5, and 6. Hence, the answer becomes 1 and 6 and the answer is not unique. The condition, thus, is not sufficient.
In the case of the condition 2), we can get 0 and 6. The answers are not unique and the conditions are not sufficient. Using both the condition 1) and the condition 2), we get 6 as the remainder, and the answer is unique. Hence, the conditions are sufficient and the correct answer is C.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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