jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?
a) 4
b) -1
c) -5
A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only
'If we let x = 1, then (1 - 3) = -2 is in the set. If -2 is in the set, then (-2 - 3) = -5 is in the set. We can see that if we keep subtracting 3, we will get terms such as -8, -11, -14, etc. We see that -5 is definitely in the set, but -1 isn’t, since if 1 and -2 are in the set, then any numbers between them can’t be in the set.
Note: some people might argue that 4 is also in the set, since if we let x - 3 = 1, then x = 4. Of course, the answer choices don’t have ‘a and c only’ as an option. The problem says: “if x is in the set, then x - 3 is also in the set.” The problem doesn’t say: “if x - 3 is in the set, then x is also in the set.” So, when the problem says “if the number 1 is in the set,” we have to assume that 1 is the value of x, and we have to subtract 3 and keep subtracting 3 to get subsequent terms. We can’t assume that 1 is the value of x - 3.
Answer: C
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