## For a certain set of numbers, if x is in the set, then x - 3

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### For a certain set of numbers, if x is in the set, then x - 3

by BTGmoderatorDC » Thu Sep 26, 2019 5:17 pm
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

OA C

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by [email protected] » Sun Sep 29, 2019 6:16 pm
BTGmoderatorDC 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

OA C

Source: GMAT Prep
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.

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by swerve » Wed Oct 02, 2019 7:06 am
BTGmoderatorDC 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

OA C

Source: GMAT Prep
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.

Hence, the correct answer is C.

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### Re: For a certain set of numbers, if x is in the set, then x - 3

by [email protected] » Fri Apr 29, 2022 6:56 am
BTGmoderatorDC wrote:
Thu Sep 26, 2019 5:17 pm
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

OA C

Source: GMAT Prep
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