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  3. If x is a positive, single-digit integer such that 4x/3,2x, x, and x+2, and 3x-2

If x is a positive, single-digit integer such that 4x/3,2x, x, and x+2, and 3x-2

游客2024-01-14  59
问题 If x is a positive, single-digit integer such that 4x/3,2x, x, and x+2, and 3x-2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
选项 A、3
B、4
C、5
D、6
E、8
答案 C
解析 Since there are only nine single-digit, positive integers, and not all of them will yield integers when we use them in these algebraic expressions, let’s start with trying to find a value for x that will give us a list of consecutive integers. I won’t work, since 4/3×1 is not an integer. Same with 2. When we use 3, though, we get 4/3×3=4; that’s an integer. The other expressions give us 2×3=6, 3, 3+2=5, and 3×3-2=7. So our group includes 4, 6, 3, 5, and 7. They aren’t in order, but they don’t have to be according to the problem, and they are consecutive. But be careful! The problem asks for the median of the list, not the value of x. The median of the list 3, 4, 5, 6, 7 is 5.
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