Is |x5|>4?

m09 q19

Is \(|x-5|>4\)?

Is \(|x-5|>4\)? --> is \(x<1\) or \(x>9\)?

(1) x^2-4>0 --> x^2>4 --> |x|>2 --> x<-2 or x>2, so we can have an YES answer as well as a NO answer (consider x=-5 and x=5). Not sufficient.

(2) x^2-1<0 --> x^2<1 --> |x|<1 --> -1<x<1. Sufficient.

Answer: B.
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IxI > a means x > a or x<-a
keeping that in mind , solve for the stem ie Ix-5I >4
you will get x > 9 or x <1 hence the question is "Is x > 9 or x <1"

1. Solve for Statement 1: (x-2)(x+2) >0 that means the range is x>2 or X <-2 visualize this on number line you will know certainly end up eliminating Statement 1

2. Similarly solve for statement 2: (x-1)(x+1)<0
this means that -1<x<1
hence is sufficeient as the the range is less than what asked in the question....

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https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/01 ... s-part-ii/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/07 ... -and-sets/

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Archit

Stmnt 1

x^2> 4

x>2 OR x<-2

0 or -3 could satisfy the condition for example however 3 cannot not

Stmnt 2

X^2< 1

-1< x <1

Suff

B

But doesn't x<-2 mean that x is always < 1?

Yes, if x is less than -2, then it's definitely less than 1 also.
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Yes, if x is less than -2, then it's definitely less than 1 also.[/quote]



So this means statement A is also sufficient. No? One of the alternatives is sufficient as well as it is in statement B

So this means statement A is also sufficient. No? One of the alternatives is sufficient as well as it is in statement B[/quote]

The question asks is \(x<1\) or \(x>9\)?

(1) says: x < -2 or x > 2. If x = -5, then answer is YES but if and x = 5, the answer is NO. Not sufficient.
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The answer should be E. Because we are not considering x<9. As per the question stem, we need to find whether 9<x<1 or not. As per statement B, we are getting -1<x<1. How we can say it is satisfying the answer?

First of all, the question asks whether \(x<1\) or \(x>9\).

(2) says that \(-1 < x < 1\). So, we have a NO answer to the question. That's why it's sufficient.
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first from the given question, see in what range of numbers |x-5| > 4

we get that X>9 and X < 1 .

statement 1 says , X^2 - 1 > 0 , this means X> 2 and X < -2 , these x values doesn't come under the range of our required, so some time the answer will be yes and some times no , so insufficient

statement 2 says X^2-1 < 0 , this means x lies btw -1 and 1, this is partly included in the total range of required values so m yes

so the correct option B.

We have a definite YES answer. -1 < x < 1 is part of x < 1.

IanStewart

I was looking for absolute value problems and found this one, which I'm stumped by.

(2) bunuel said for statement 2 above that -1 < x < 1, so we have a NO answer.
But my question is, the stem asks if x<1 or x>9, so doesn't this answer yes x<1?

On a separate thread, bunuel answered regarding statement 1
(1) bunuel said x < -2 or x > 2. If x = -5, then answer is YES but if and x = 5, the answer is NO. Not sufficient
But my question is if x < -2, then it's definitely less than 1 also so it's that enough to be sufficient? Why do we need to consider two cases shared in the example above of if x= -5 then yes but if x = 5, then no?

|x-5|>4 can have two cases
1) x-5>4.....x>9
2) 5-x>4....x<1
So if \(1\leq{x}\leq{9}\), answer is NO, otherwise YES.

(1) \(x^2 −4>0..........x^2>4..........|x|>2\)
SO, two possibilities
a) x<-2..........We can say for sure that \(1\leq{x}\leq{9}\) is NOT true, so answer is yes.
b) x>2...........If \(2<{x}\leq{9}\), answer is NO, but if x>9, answer is yes.
Insuff

(2) \(x^2−1<0.......x^2<1......|x|<1.......-1<x<1\)
None of the value of x fall in \(1\leq{x}\leq{9}\), so answer is surely yes.
Suff

B
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Asked: Is |x−5|>4?
Case 1: x-5 >4
x > 9
Case 2: x-5 <-4
x < 1
Combining case 1 & case 2:
1<x<9

(1) x^2 −4>0
(x-2)(x+2)>0
x<-2 or x>2
NOT SUFFICIENT

(2) x^2−1<0
(x+1)(x-1) < 0
-1 < x < 1
|x-5| <4
SUFFICIENT

IMO B

There are a couple of issues with this question and the replies:



Statement 1 here says x^2 > 4, while Statement 2 says x^2 < 1. Clearly x^2 cannot simultaneously by greater than 4 and less than 1, so there's no way both Statements can be true. In any real GMAT DS question, it always needs to make sense to consider the two Statements together, so the question is not properly designed.



Bunuel, I think you might want to correct this -- Statement 2 ensures that x < 1, so on its own it ensures the answer to the original question is 'yes', not 'no'.

That post isn't correct; you are right that Statement 2 gives us a 'yes' answer to the question.



From Statement 1, all you know about x is that it is some unknown number that is not between -2 and 2. The question then becomes (at least if we're trying to get a 'yes' answer to the question) : from that information alone, can you be sure that the value of x is not between 1 and 9? And you can't be sure, because if x is not between -2 and 2, then x can still be, say, 5, and then x is between 1 and 9, but x can also be -1000, and then x is not between 1 and 9.

If instead Statement 1 told us "x < -2", then it would certainly be sufficient alone, because it would then be impossible that x is equal to a number somewhere between 1 and 9.

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