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

I only

II only

III only

I and II

II and III

Now I am sorry, but the answer explained by GMAC is sad, at best. Here is the logic: It is given that 1 is in the set. Therefore 1-3= -2 is in the set. Since we know -2 is in the set then -5 is also in the set. This set doesn't contain 4 or -1!. Therefore it is not true 4 or -1 must be in the set.

This is the absolute worst question I have seen to date guys. I am sorry, but this is just ridiculous. How do you know that the number 1 is the x in the set? The question merely states that it is in the set. For example X=4. If 4-3 =1, Therefore 1 is also in this set.

Am I missing something here? Any experts want to attempt a go at this type of logic?

## Anyone want to Address this problem?

##### This topic has expert replies

### GMAT/MBA Expert

- Rich.C@EMPOWERgmat.com
- Elite Legendary Member
**Posts:**10347**Joined:**23 Jun 2013**Location:**Palo Alto, CA**Thanked**: 2867 times**Followed by:**506 members**GMAT Score:**800

For these types of questions, it's important to pay attention to the language. The prompt asks which of the following MUST also be in the set? Not what "could" be in the set, what "must" be in the set (according to whatever rules we've been given to work with).

We're told that if X is in the set, then (X-3) is also in the set. This tells us that the set is infinite (once we have a number, we would subtract 3 from that number, then from the next number and so on). We also know that our math moves "forwards", so we can't work backwards from a value, we can only move forwards (by subtracting 3, because that's the only rule we have to work with).

Since we're told that 1 is in the set, we can move forwards from there (by subtracting 3, as we're told to do).

Thus, we know that these numbers MUST be in the set:

1, -2, -5, -8, -11, -14, etc.

Other numbers could be in the set, but we don't know if they must be in the set.

Thus, Roman Numeral III is the only value that we know for sure MUST be in the set.

Final Answer: C

GMAT assassins aren't born, they're made,

Rich

- bpolley00
- Master | Next Rank: 500 Posts
**Posts:**192**Joined:**11 Jul 2012**Thanked**: 20 times**Followed by:**5 members**GMAT Score:**650

**wrong**. You can't just make something up that isn't even in the problem.

In fact, here is an obvious source of information on sets https://en.wikipedia.org/wiki/Set_(mathematics)

Not directing the direct language at you personally Rich, but if this test is going to be used as a determinant of how I am being evaluated, then the questions at the very least better be correct

-BP

### GMAT/MBA Expert

- Rich.C@EMPOWERgmat.com
- Elite Legendary Member
**Posts:**10347**Joined:**23 Jun 2013**Location:**Palo Alto, CA**Thanked**: 2867 times**Followed by:**506 members**GMAT Score:**800

I understand your frustration, so maybe I can rephrase the idea.

I think that you can agree that since the number 1 is in the set, then the number -2 is also in the set.

Since the number -2 is in the set, what MUST also be in the set? Think about what the prompt tells you (If X is in the set, then X-3 is also in the set). So, we could NOW say that if X = -2, then -5 MUST also be in the set.

Going on from there, if X = -5, then -8 MUST also be in the set, and so on.

So even though the prompt doesn't state that the set is infinite, the one rule that we have to work with means that the set will go on forever (with increasingly negative values).

GMAT assassins aren't born, they're made,

Rich

- bpolley00
- Master | Next Rank: 500 Posts
**Posts:**192**Joined:**11 Jul 2012**Thanked**: 20 times**Followed by:**5 members**GMAT Score:**650

I understand what you are saying, I really do. However, you could also set x=4 and then the set would be simply {4,1} and so on. Technically, the set doesn't need to have ANY of the numbers listed below as it could just be {1,-2} and that is IT. There is nothing in the problem that the set must contain more than 2 numbers and there is nothing implicitly stating it is an infinite set. I am sorry, but this question is, in my opinion, completely pathetic. I will be done with the test in two days and then I am moving on, but thanks for taking the time to offer your opinion sir.

-BP