Is |x5|>4? : Data Sufficiency (DS)

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01 Sep 2017, 18:33

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guerrero25

Is |x−5|>4?

(1) x^2 −4>0

(2) x^2−1<0

Please elaborate the approach . I got the answer wrong and did not quite get the OE.

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

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16 Sep 2017, 11:56

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

Bunuel

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17 Sep 2017, 02:38

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Alabama

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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17 Sep 2017, 04:55

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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

Bunuel

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17 Sep 2017, 05:01

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Alabama

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

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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20 Jan 2020, 22:23

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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?

Bunuel

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20 Jan 2020, 23:14

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sampad

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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22 Jan 2020, 06:45

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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.

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10 Sep 2020, 00:16

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Bunuel

sampad

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.

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

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10 Dec 2020, 21:47

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Bunuel

sampad

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.

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?

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10 Dec 2020, 22:09

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guerrero25

Is |x−5|>4?

(1) x^2 −4>0

(2) x^2−1<0

|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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10 Dec 2020, 23:54

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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

IanStewart

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11 Dec 2020, 08:25

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

guerrero25

Is |x−5|>4?
(1) x^2 −4>0
(2) x^2−1<0

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

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.

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'.

IanStewart

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11 Dec 2020, 08:31

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lstudentd

(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?

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

lstudentd

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?

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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