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Updated on: 08 Nov 2023, 07:18
Originally posted by jayoptimist on 30 Jul 2012, 07:45.
Last edited by Bunuel on 08 Nov 2023, 07:18, edited 4 times in total.
Last edited by Bunuel on 08 Nov 2023, 07:18, edited 4 times in total.
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C
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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?
I. 4
II. -1
III. -5
A. I only
B. II only
C. III only
D. I and II
E. II and III
PS00253
I. 4
II. -1
III. -5
A. I only
B. II only
C. III only
D. I and II
E. II and III
PS00253
I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer 
)
)
30 Jul 2012, 08:02
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jayoptimist
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
I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer
)
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
I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer
)Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 1 is in the set, then so must be 1-3=-2. Similarly, since -2 is in the set, then so must be -2-3=-5. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: C.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Similar questions to practice:
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html (rule #3).
26 Jul 2017, 16:32
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jayoptimist
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
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
