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buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pm; Thanked: 13 times; Followed by:1 members; GMAT Score:710

GMAT Prep Practice - Set containing x and x-3

by buzzdeepak » Wed Feb 13, 2013 7:58 am

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

OA: C

Question:
[spoiler]If we consider x = 1, I understand -2, -5, -8 etc will be in the set.
But why can't we consider x-3 = 1, in which case 4 is a possibility as well?
So, the set would then have {..., -8, -5, -2, 1, 4}[/spoiler]

Please help
Thanks in advance...

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Source: Beat The GMAT — Problem Solving | Wed Feb 13, 2013 7:58 am

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Wed Feb 13, 2013 8:11 am

This is one of those relatively rare times in Quant that the GMAT actually tries to trick you semantically. Just because they say "if x is in the set, then x - 3 is also in the set," it doesn't necessarily mean that "if x - 3 is in the set, x is in the set." What if x = 1? We'd be able to prove that every number 3 less than x, and 3 less than that, and so on, is in the set. But can we prove that anything greater than x is in the set? Not necessarily.

It's certainly possible that 4 is in the set. Maybe x = 4, and then 1 is x - 3. Or maybe x = 13, and 4 is x - 3 - 3 - 3. But with these Roman numeral questions, make sure you distinguish between what's possible and what's necessary. If we know a certain number is in the set, we know about the values less than that number, but not necessarily the values greater than that number.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 13, 2013 8:25 am

It's not uncommon for people to reverse the order of if-then statements.

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

Brent Hanneson - Creator of GMATPrepNow.com

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buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pm; Thanked: 13 times; Followed by:1 members; GMAT Score:710