Problem Solving

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

In the attached problem, why can't we assume if 1 is a number in the set, then x-3 = 1; x = 4?

You 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 x is in the set, then x-3 is also in the set"
Reversing the statement (to get "if x-3 is in the set, then x is also in the set") 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 conclude that if an animal has ears then that animal is a rabbit? No.

So, 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

Another analogy might look like this:

Sarah is shy, so if she goes to a party, her sister has to come, too.
So we know that if Sarah goes, then her sister will go.

Does it have to follow that if her sister goes, Sarah will go? Not necessarily. Maybe her sister isn't shy and doesn't mind going by herself.

Only if the statement said "if either sister goes, then the other one will go, too" should we assume both.

Likewise in this question, only if it says "if x is in the set, x-3 is in the set and vice versa" would we assume that 4 has to be in the set. Maybe 1 was the starting point (like a cascading/domino effect), and the set is only infinite in one direction.

Hi tanvis1120,

The question that you posted emphasizes a concept called "formal logic". It's an idea that's common on the LSAT but appears only in rare circumstances on the GMAT. Chances are good that you won't see it at all when you take the Official GMAT, so you shouldn't worry too much about it.

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