Bunuel wrote:
If x and y are positive integers, what is the remainder when x^y is divided by 10?
(1) x = 26
(2) y^x = 1
Kudos for a correct solution.
Given: x and y are positive integers Target question: What is the remainder when x^y is divided by 10?This is a good candidate for
rephrasing the target question. Notice that 43 divided by 10 leaves remainder 3, and 127 divided by 10 leaves remainder 7, and 618 divided by 10 leaves remainder 8.
So, asking for the remainder when x^y is divided by 10 is the same as asking what the units digit of x^y is. So, .....
REPHRASED target question: What is the units digit of x^y ?Aside: See the video below for tips on rephrasing the target question Statement 1: x = 26 IMPORTANT: if y is a positive integer, then 26^y will always have units digit 6.
Notice that 26^1 = 2
6, and 26^2 = 67
6, and 26^3 = ????
6, 26^4 = ????
6, etc.
So, the answer to the REPHRASED target question is
the units digit of x^y is 6Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: y^x = 1There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 11 and y = 1 (notice that y^x = 1^11 = 1. In this case, x^y = 11^1 = 11. So, the answer to the REPHRASED target question is
the units digit of x^y is 1Case b: x = 12 and y = 1 (notice that y^x = 1^12 = 1. In this case, x^y = 12^1 = 12. So, the answer to the REPHRASED target question is
the units digit of x^y is 2Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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