A set of numbers has the property that for any number t in the set

Responding to a pm:

Forget this question. Consider this:

If I go to the movies, my friend Disha must go with me. If Disha goes to the movies, Ari must go to the movies too.

So now what can you say if I tell you that I went to the movies?
You can say that Disha went too. And further, you can say that Ari went too.

What if I tell you Disha went to the movies? Does it mean I went too? If I go, Disha must go. But if Disha goes, is it necessary for me to go? No, she has no such hang ups. She can easily go with or without me. But if Disha goes, Ari must go too. So we can say that Ari went to the movies.

The question is very similar. If 't' is in the set, 't+2' must be in the set too. But is it essential for 't-2' to be in the set? No! Just like Disha doesn't need me, 't+2' doesn't need 't'. 't+2' needs only 't+4'.
If 't+2' is in the set, 't+4' must be picked too. If 't+4' is there, 't+6' must be there too and so on...

A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?

I. -3
II. 1
III. 5

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II , and III

The question is which of the following must be in the set, not could be in the set.

If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.

Answer: D.
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Question says that if t is in the set, 't+2' must be in the set. It doesn't say that 't+2' can be in the set only if t is in the set too.

Say, if I put 10 in the set, I have to put 12 and then 14 and then 16 etc. I don't necessarily have to put 8 in the set. 8 may or may not be there.

Similarly, if -1 is in the set, 1, 3 and 5 (and 7 etc) must be in the set. -3 may or may not be.

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A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must be in the set?

I. -3
II. 1
III. 5

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III


Why not -3?
"for any number t in the set, t + 2 is in the set"
--- > t + 2 = r
t = r -2
if -1 = r, t can be -3 ( -3 = -1 -2)

What's wrong with my logic?

Since -1 is in the set, 1 must be there
Since 1 is there, 3 must be there
Since 3 it there, 5 must be there

-1 may or may not be there

So answer is II and III (D)
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Tricky one ! The idea here is the *MUST* condition makes it strict to move forward from the seed number -1 since for any t , t+2 exists. The set could start from -1 and not have -3 in it.

But how could we assume that the set has n numbers in it when it is not given.. The set could also have -1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that -3 is also in that set, as they dint pinpoint that -1 is the starting number in that set. The starting number can also be -3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question..

Maybe I can explain this. Don't know how much of this will be helpful.

The point here is -1 is our reference number i.e. t= -1
Now, since the question is "MUST BE TRUE", we have to find numbers that "RESULT FROM" the operation t+2.

When you say that -3 is present (it could be), we are in fact saying that the operation t+2 "RESULTS IN" the number -1. So here we are making t+2 the reference value and -1 the result of the operation.

In a vague way, when we say Ron is Sam's brother, its not necessary that Sam is also Ron's brother. Sam could be Ron's sister too.

Hope so it clears some of your doubt.

I have trouble understanding this question. so the question says that if t is there then t+2 must be there. So -1 can be t or t+2. So if t+2=-1 then t=-3 therefore -3 is in the set. I know iam wrong somewhere in my concept. Can someone please clarify this to me . Thanks.

The question says, if some number is in the set, then 2 more than that number is also in the set. It does not say that if some number is in the set, then 2 less than that number is in the set. We know that -1 is in the set, so -1 + 2 = 1 must also be in the set. We cannot say whether -3 is in the set because we are not told that -1 -2 is in the set but that -1 + 2 must be in the set.
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Would the answer be E, Had the question have "could be" instead of "must be"?

I am confused why E is not the answer.

If -1 is the source integer in the set, so if -1 is the smallest integer in the set, then -3 will not be in the set. For example, the set could be {-1, 1, 3, 5, 7, ...}. So, again, knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set but we cannot be sure about the numbers less than -1.

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BUT who says that the set contains of 4 numbers? 5 COULD be in there but it is also possible that the set only contains of 3 numbers? or am I thinking too complex

Any number COULD be in the set but we are asked "which of the following MUST also be in the set?" and only II and III MUST be in the set.
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Based on the condition, for any number "t" in the set, "t + 2" is also in the set.

Doesn't this mean you can have a set like this:

{10, 12, 18, 20, 31, 33}

If we are given that -1 is in the set, we can only determine that 1 is also in the set.

Where am I going wrong here?

GK002, Basically, this set never ends and the set that you have suggested doesn't fulfil the condition. You're correct to say that if -1 is in the set, 1 will be in the set. But if 1 is in the set, we need 3. If 3 is in the set, we need 5 and this loop continues. The set will contain all the odd numbers.

A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?

I. -3
II. 1
III. 5

if -1 is there , then -1 + 2 = 1 should be there.
So if 1 is there, 1 +2 = 3 should be there.
Following the same pattern , we can say 1, 3 , 5 , 7.. should be there in set if -1 is there.

Ans is option (D) II and III only

Thanks,
Clifin J Francis
GMAT SME
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Well, I am not a Gmat expert but I have some ideas sometimes.
The important thing is "MUST". I have answered many questions and I have faced many questions that depend on "MUST".
So, there could be 1 in our list, because we already have -1, so according to the statement there must be t+2, so -1+2=1. That is a "MUST". Then, since we have 1 in our list, then there MUST be 3 (t+2 -> 1+2=3). Again, since we have 3 on our list, then we MUST have 5 (3+2).

However, when it comes to -3, we can not say that "-3 MUST be in our list". What if I say that the beginning number of the set is -1. So in that case there is no -3. In other words, -3 CAN BE in our list, not MUST BE.