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

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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 Scott@TargetTestPrep » 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.

Answer: C

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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 Brent@GMATPrepNow » 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

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
Brent Hanneson - Creator of GMATPrepNow.com
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