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number system

by vipulgoyal » Mon Sep 02, 2013 9:27 pm
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

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

c
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by vinay1983 » Mon Sep 02, 2013 10:04 pm
Actually I had committed a mistake while solving this!

It is like this:

if x-3 is in the set, and if x is equal to 1 (note that X is 1 and part of the set!

then x-3=1-3=-2

then x= -2

so x-3= -2-3= -5 and so on

-2 , -5, -8, -11

Hence III is the answer choice.
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Tue Sep 03, 2013 6:15 am
vinay1983's solution is perfect. The only numbers we can be certain are in the set are -2 , -5, -8, -11 . . . etc


I thought I'd mention that a lot of students make the mistake of reversing the conditional (if-then) statement in this question. The statement says "If if x is in the set, then x-3 is also in the set." Many students mistakenly believe that this also implies that "if x-3 is in the set, then x is also in the set." (these students end up concluding that 4 must be 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 also conclude 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.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by vinay1983 » Wed Sep 04, 2013 1:25 am
Brent@GMATPrepNow wrote:vinay1983's solution is perfect. The only numbers we can be certain are in the set are -2 , -5, -8, -11 . . . etc


I thought I'd mention that a lot of students make the mistake of reversing the conditional (if-then) statement in this question. The statement says "If if x is in the set, then x-3 is also in the set." Many students mistakenly believe that this also implies that "if x-3 is in the set, then x is also in the set." (these students end up concluding that 4 must be 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 also conclude 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.

Cheers,
Brent
Brent Thanks!I am all smiles.felt very good to receive a "good" word from you.

Also I want to know in what condition can 4 be also a part of the sequence. THIS QUESTION CAN VERY WELL BE TURNED AROUND!
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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