looks easy, complex underneath (I think)

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deagez: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun Dec 28, 2008 2:52 am; Location: Denver; Thanked: 2 times

looks easy, complex underneath (I think)

by deagez » Sat Jul 25, 2009 10:30 am

This type of problem is why I hate data sufficiency like I hate North Korea.

if x is positive, is x>3?

- (x-1)^2 > 4
- (x-2)^2 > 9

OA is D (each statement alone is sufficient)

Ok so first one makes since: if x >3 (say 4) it will make since 9>4, but if x is 3 then 4 is not > 4

However, the second makes is not so clear cut to me. if X is 4, then 4 is not > 9,, so to make sense here X has to be 6 or higher to make the equation equal 16 > 9

I mean how on earth is the second one sufficient?
If anyone can help me with how I need to properly think about this I would appreciate it, because I am apparently not taking the correct approach here

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 25, 2009 10:30 am

Spaceman Spiff: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Fri Apr 03, 2009 7:23 pm; Location: Los Angeles; Thanked: 1 times; GMAT Score:780

by Spaceman Spiff » Sat Jul 25, 2009 11:03 am

1) (X-1)^2>4

-2 < X - 1 < 2

-1 < X < 3

sufficient

2) (x-2)^2 < 9

-3 < X - 2 < 3

-1 < X < 5

Not sufficient

IMO A.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: looks easy, complex underneath (I think)

by Stuart@KaplanGMAT » Sat Jul 25, 2009 11:33 am

deagez wrote:This type of problem is why I hate data sufficiency like I hate North Korea.

if x is positive, is x>3?

- (x-1)^2 > 4
- (x-2)^2 > 9

OA is D (each statement alone is sufficient)

Ok so first one makes since: if x >3 (say 4) it will make since 9>4, but if x is 3 then 4 is not > 4

However, the second makes is not so clear cut to me. if X is 4, then 4 is not > 9,, so to make sense here X has to be 6 or higher to make the equation equal 16 > 9

I mean how on earth is the second one sufficient?
If anyone can help me with how I need to properly think about this I would appreciate it, because I am apparently not taking the correct approach here

You're making a very common misinterpretation error. DS is often more about understanding how the questions work than doing math.

As always, let's start with Step 1 of the Kaplan Method for DS: focus on the question stem.

If x is postive, is x > 3?

As soon as you see "is" in the question, you know there are two possible answers: Yes and No. If we always get a "yes" answer, we have sufficiency; if we always get a "no" answer, we have sufficiency; if we get a "maybe yes or maybe no" or "sometimes" or "not sure", we have insufficiency.

So, if x is never greater than 3, that's sufficient; if x is always greater than 3, that's sufficient.

Let's just focus on statement (2):

(2) (x-2)^2 > 9

You approached it by picking numbers, a great way to go in DS. However, when we pick numbers we have to follow TWO key steps:

1) pick permissible numbers; and then
2) plug those numbers back into the original question.

A lot of people mess up step 1. We have to remember that the rules we're given (both in the question stem and the statements) are immutable laws of the universe. All numbers we choose MUST follow those laws.

The first number you chose is 4. As you correctly noted, 4 does not follow the law. Therefore, we completely ignore 4 for the rest of the exercise. 4 is dead to us, we rip our clothing and move on.

You then determined that x has to be at least 6 - which isn't actually true. 6 is the smallest possible integer value of x, but nowhere does it say that x must be an integer. In fact, x can be any number greater than 5.

Regardless (that particular slip us is irrelevant on this question, but won't be on others), if you see that x must be at least 6, you should conclude that (2) is sufficient. After all, if x>=6, x is ALWAYS bigger than 3. Since we get an "ALWAYS", (2) is sufficient.

You actually interpreted the question as "could x be every number bigger than 3?". You saw that x could not equal 4 and you took that as a "no" answer to the question. It was that misinterpretation that cost you the point.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sat Jul 25, 2009 11:38 am

Spaceman Spiff wrote:1) (X-1)^2>4

-2 < X - 1 < 2

-1 < X < 3

sufficient

2) (x-2)^2 < 9

-3 < X - 2 < 3

-1 < X < 5

Not sufficient

IMO A.

Some wacky math going on here!

If (x-1)^2 > 4, then we get:

+(x-1) > 2 or -(x-1) > 2

x > 3 or x < -1

Since we know that x is positive, we can ignore the second option and conclude that x is ALWAYS greater than 3... sufficient.

(2) (x-2)^2 > 9

(You flipped the inequality.)

Using the same algebra as we did for (1), we get:

+(x-2) > 3 or -(x-2) > 3

x > 5 or x < -1

Again, x must be positive, so x > 5. If x > 5, is x > 3? DEFINTELY YES... sufficient.

Each of (1) and (2) is sufficient alone: choose D.

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Spaceman Spiff: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Fri Apr 03, 2009 7:23 pm; Location: Los Angeles; Thanked: 1 times; GMAT Score:780

by Spaceman Spiff » Sat Jul 25, 2009 1:17 pm

I must have been hung over when I wrote that!

Thanks for the correction

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woo: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Sat Jan 03, 2009 11:34 pm

I know this is DS forum but,...

by woo » Sat Aug 01, 2009 8:29 pm

I found a sentence correction related point to make

In the original post, it should say as I hate North Korea, I think.

Right?

Now, about the DS problem...

(x-1)^2>4 is same as
x^2-2x+1-4>0
(x-3)(x+1)>0
therefore, x> 3, -1 but the original condition says x is positive.
Therefore x>3 thus, sufficient.

Same approach applies to the second condition.