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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
For a certain set of numbers, if x is in the set, then x - 3 is also
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28 Apr 2022, 10:24
28 Apr 2022, 10:24
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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 ?
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: For a certain set of numbers, if x is in the set, then x - 3 is also
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29 Apr 2022, 06:55
29 Apr 2022, 06:55
1
GeminiHeat 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
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
Important: This IF-THEN statement only goes in one direction. That is, IF x is in the set, THEN x-3 is also in the set.
So, since we're told 1 is in the set, it must also be true that 1-3 (aka -2) is also in the set.
Now that we know -2 is in the set, it must also be true that (-2)-3 (aka -5) is also in the set.
Now that we know -5 is in the set, it must also be true that (-5)-3 (aka -8) is also in the set.
And so on. . . .
So, -5 is the only number (among the answer choices) that we KNOW must be in the set
Answer: C
Note: Some students will (incorrectly) conclude that the given information ALSO tells us that IF x-3 is in the set, THEN x is also in the set.
These students will (incorrectly) conclude that, if 1 is in the set, then 4 must also be in the set.
Think of it this way: If an animal is a dog, then that animal has ears (I think we all agree with us). We can't then take this statement and ALSO conclude that if an animal has ears, then that animal must be a dog
gmatclubot
Re: For a certain set of numbers, if x is in the set, then x - 3 is also [#permalink]
29 Apr 2022, 06:55
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