If r, s, and t are all positive integers, what is the remainder when 2rst is divided by 10?
(1) s is even
(2) rs = 4
When a number is divided by 10, the remainder is simply the units digit of that number. For example, 256 divided by 10 has a remainder of 6. This question asks for the remainder when an integer power of 2 is divided by 10. If we examine the powers of 2 (2, 4, 8, 16, 32, 64, 128, and 256...), we see that the units digit alternates in a consecutive pattern of 2, 4, 8, 6. To answer this question, we need to know which of the four possible units digits we have with 2rst.
(1) INSUFFICIENT: If s is even, we know that the product rst is even. Knowing that rst is even tells us that 2rst will have a units digit of either 4 or 6 (22 = 4, 24 = 16, and the pattern continues).
(2) SUFFICIENT: If rs = 4, then rst = 4t. Because t is an integer, rst must be a multiple of 4. Since every fourth integer power of 2 ends in a 6 (24 = 16, 28 = 256, etc.), we know that the remainder when 2rst is divided by 10 is 6.
The correct answer is B.
Can some one elaborate on this explanation....??
(1) s is even
(2) rs = 4
When a number is divided by 10, the remainder is simply the units digit of that number. For example, 256 divided by 10 has a remainder of 6. This question asks for the remainder when an integer power of 2 is divided by 10. If we examine the powers of 2 (2, 4, 8, 16, 32, 64, 128, and 256...), we see that the units digit alternates in a consecutive pattern of 2, 4, 8, 6. To answer this question, we need to know which of the four possible units digits we have with 2rst.
(1) INSUFFICIENT: If s is even, we know that the product rst is even. Knowing that rst is even tells us that 2rst will have a units digit of either 4 or 6 (22 = 4, 24 = 16, and the pattern continues).
(2) SUFFICIENT: If rs = 4, then rst = 4t. Because t is an integer, rst must be a multiple of 4. Since every fourth integer power of 2 ends in a 6 (24 = 16, 28 = 256, etc.), we know that the remainder when 2rst is divided by 10 is 6.
The correct answer is B.
Can some one elaborate on this explanation....??
