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GMAT Set 10 Q10

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by Abhijit K » Tue Feb 24, 2015 2:59 am
A set of numbers has a property that for any number t in the set, t+2 is in the set, which of the following must also be in the set?

1.-3
2.1
3.5

a.1 only
b.2 only
c.1 and 2 only
d.2 and 3 only
e.1, 2 and 3
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by GMATGuruNY » Tue Feb 24, 2015 3:43 am
The problem should read as follows:
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
Since -1 is in the set, -1+2 = 1 is in the set.
Since 1 is in the set, 1+2 = 3 is in the set.
Since 3 is in the set, 3+2 = 5 is in the set.
Only options II and III must be in the set.

The correct answer is D.
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by Abhijit K » Tue Feb 24, 2015 3:56 am
if t =-3 wont -1 be in the set?
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by GMATGuruNY » Tue Feb 24, 2015 4:09 am
Abhijit K wrote:if t =-3 wont -1 be in the set?
Nothing in the prompt implies that t=-3 is in the set, so the portion in red is irrelevant.
The prompt indicates that only t=-1 is in the set and that -- for any value of t -- t+2 must also be in the set.
Thus, only odd integers GREATER than -1 MUST be in the set.
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by Brent@GMATPrepNow » Tue Feb 24, 2015 9:26 am
Abhijit K wrote:if t =-3 wont -1 be in the set?
Yes, IF -3 is in the set, THEN -1 will be in the set. However, we aren't told that -3 is in the set.

Some people take that fact that -1 is in the set, and conclude that -3 is also in the set. These people have reversed the order of the if-then statement.

It's not uncommon for people to do this.

The if-then statement here is "If if t is in the set, then t+2 is also in the set"
Reversing the statement (to get "if t+2 is in the set, then t is also in the set") is not logically sound.

Consider this example:
Let's say: If an animal is a rabbit, then that animal has ears.
Can we then conclude that if an animal has ears then that animal is a rabbit? No.

So, in our question, the existence of t in the set guarantees the existence of t+2 in the set.
However, it is not necessarily the case that the existence of t+2 in the set guarantees the existence of tx in the set.

I hope that helps.

Here's a similar question: https://www.beatthegmat.com/gmat-prep-pr ... 78170.html

Cheers,
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by Brent@GMATPrepNow » Tue Feb 24, 2015 9:33 am
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
ASIDE: It's possible that the set contains EVERY NUMBER in the universe. It's also possible that the set contains no numbers. The objective here is to determine what MUST be true (as opposed to what COULD be true).

Apart from the t and t+2 clue, the only other clue we're given is that -1 is in the set.
According to the other clue, since -1 is in the set, then (-1)+2 must also be in the set. So, 1 MUST be in the set.
Since 1 is in the set, then 1+2 must also be in the set. So, 3 MUST be in the set.
Since 3 is in the set, then 3+2 must also be in the set. So, 5 MUST be in the set.
Since 5 is in the set, then 5+2 must also be in the set. So, 7 MUST be in the set.
And so on...

So, we can be certain that the following numbers are in the set: -1, 1, 3, 5, 7, ....
Answer: C

Cheers,
Brent
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