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Roman Numeral Question on Set of Numbers

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by gander123 » Sat Jan 12, 2013 4:07 am
Hey

QPS00253 GMAT Prep Pack 1

"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

OA: C

OA explanation:

"The rule for set membership is: If x is in the set, then x-3 is also in the set. It is given that 1 is in the set. Therefore, 1-3 = -2 is in the set. Also, since -2 is now known to be in the set, -2-3 = -5 is also known to be in the set. Similarly, since -5 is now known to be in the set, -8 is also known to be in the set. Note that the set could be {1,-2,-5,-8,...} and this does not contain either 4 or -1. Therefore, it is not true that either 4 or -1 must be in the set. Only -5 must be in the set."

My question:

I initally set x=1 and consequently x-3= - 2 then -5 is in the set and so forth.
BUT, I also set x-3 = 1 through which I obtained 4 is in the set.

Am I right in assuming that we do not necessarily have to set x-3 = 1 to obtain 4 is in the set, because the question stem asked us
which of the following must also be in the set?
?

So setting x-3 = 1 is a "COULD BE TRUE" value but not a "MUST BE TRUE" value?

Appreciate your feedback..

Cheers, Tobi
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by Brent@GMATPrepNow » Sat Jan 12, 2013 8:19 am
gander123 wrote:
I initally set x=1 and consequently x-3= - 2 then -5 is in the set and so forth.
BUT, I also set x-3 = 1 through which I obtained 4 is in the set.

Am I right in assuming that we do not necessarily have to set x-3 = 1 to obtain 4 is in the set, because the question stem asked us
which of the following must also be in the set?
?

So setting x-3 = 1 is a "COULD BE TRUE" value but not a "MUST BE TRUE" value?
Yes, x-3 = 1 "COULD BE TRUE" but x-3 = -1.95425 could be true as well. So, that doesn't help us much.

We're dealing with an if-then statement here, "If if x is in the set, then x-3 is also in the set"
You've taken this statement and reversed it to get: "if x-3 is in the set, then x is also in the set."
This reversal is not logically sound. Here's an example why.

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

In our question, the existence of x in the set guarantees the existence of x-3 in the set.
However, it is not necessarily the case that the existence of x-3 in the set guarantees the existence of x in the set.

I hope that helps.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by gander123 » Sun Jan 13, 2013 2:05 am
Thanks Brent! Good examples !
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