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).
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We can look at this as a cause and effect problem. "x" is the cause and "x-3" is the effect. i.e. We are given that is "x" is in the set "x-3" is also in the set. The reverse need not necessarily be true. We cannot take the effect to be the cause.

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

the answer is III only, means -5.

They are reasoning that, 1 in the set, so -2 also in the set, so -5 also in the set, so -8 also in the set.

I wonder why 4 can't be in the set??? let consider 1 is x-3, not x, hence x = 4.
What is the trap of GMAT here?

(I always have problem with the trap of gmat)

I call them Verbal diaorea of GMAT. You have to follow these verbal vomits carefully. When they say x-3 is there only x-3 is guaranteed to be there nothing else. And so here you can not travel to the side of the stream.

that's true, I have no problem with math, but I have quite problem with those kinds of "Verbal diaorea of GMAT". Hope exercises will help much. Thanks

It does not make logical sense to only have -5 and 4 is not the correct answer.

Can't we take that 1 is the result of X -3 ? In which case, X = 4.

I cant agree with -5 more because it is one more "jump"

X = 1 .... 2nd number is ( -2 ) is fine with me.
But the question did not say that "X - 6" also exists? Because X is still 1, and did not "move on" to become -2.

Agree its a bit of a "throw you off if you did not buy our official guide" even if you had maths as your bach degree.

Hope this kind of stuff don't pop up for my coming exam, but it cant be helped =)

'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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1 is in the set, so: 1-3=-2; -2-3=-5 are in the set.

There is no chance that any positive number other than 1 will be in the set according to the given condition.
And the negative value is also increasing.

The answer is \(C\)
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For x: x-3 is in the set

For 1: 1 - 3 = -2 is in the set

For -2: -2 - 3 = -5 is in the set

We aren't sure of other numbers.

Answer C
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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
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