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Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10

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Bunuel
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Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  20 Apr 2018, 06:14
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(1) |x + 2| < 10

(2) |x + 5| > 10
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DavidTutorexamPAL
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  20 Apr 2018, 06:30
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Bunuel wrote:
Is x = 4?

(1) |x + 2| < 10

(2) |x + 5| > 10


Instead of trying to explicitly solve, we'll just plug x=4 into our equation and see what happens.
This is an Alternative approach.

(1) |4+2| = 6 which is smaller than 10. So x = 4 works in the inequality.
So, (1) tells us that x could be 4. Can it be something else?
Let's try x = 3: |3+2| = 5 which is also smaller than 10.
That is, (1) tells us that x could be 4 but it could also be 3, and therefore this is not enough.
Insufficient!

(2) |4+5| = 9 which is not larger than 10. So in this case the answer to 'is x=4' is NO!
As this is a definite answer, then it is sufficient.

(B) is our answer.
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  20 Apr 2018, 07:10
DavidTutorexamPAL wrote:
Bunuel wrote:
Is x = 4?

(1) |x + 2| < 10

(2) |x + 5| > 10


Instead of trying to explicitly solve, we'll just plug x=4 into our equation and see what happens.
This is an Alternative approach.

(1) |4+2| = 6 which is smaller than 10. So x = 4 works in the inequality.
So, (1) tells us that x could be 4. Can it be something else?
Let's try x = 3: |3+2| = 5 which is also smaller than 10.
That is, (1) tells us that x could be 4 but it could also be 3, and therefore this is not enough.
Insufficient!

(2) |4+5| = 9 which is not larger than 10. So in this case the answer to 'is x=4' is NO!
As this is a definite answer, then it is sufficient.

(B) is our answer.


I got this one wrong!
Perfectly explained!!! :thumbup:
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DavidTutorexamPAL
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  20 Apr 2018, 11:59
Tulkin987 wrote:
DavidTutorexamPAL wrote:
Bunuel wrote:
Is x = 4?

(1) |x + 2| < 10

(2) |x + 5| > 10


Instead of trying to explicitly solve, we'll just plug x=4 into our equation and see what happens.
This is an Alternative approach.

(1) |4+2| = 6 which is smaller than 10. So x = 4 works in the inequality.
So, (1) tells us that x could be 4. Can it be something else?
Let's try x = 3: |3+2| = 5 which is also smaller than 10.
That is, (1) tells us that x could be 4 but it could also be 3, and therefore this is not enough.
Insufficient!

(2) |4+5| = 9 which is not larger than 10. So in this case the answer to 'is x=4' is NO!
As this is a definite answer, then it is sufficient.

(B) is our answer.


I got this one wrong!
Perfectly explained!!! :thumbup:


Glad to help :)
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pikolo2510
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  20 Apr 2018, 23:11
Statement 1: -
|x + 2| < 10
Case 1:-
When |x+2| >0
|x+2|=x+2

x+2<10
x<8

Case 2:-
When |x+2| <0
i.e. |x+2|= -x-2

Now
-x-2<10
x>-12

therefore, x lies between -12<x<8

x can be equal to 4 or x can be 5,6 or 7. Hence insufficient

Statement 2: -(
|x + 5| > 10
Case 1: -
When |x + 5| >0
then, |x + 5|=x + 5

Now,
x + 5>10
x>5

Case 2: -
When |x + 5|<0
then, |x + 5|=-x-5

Now,
-x-5>10
x<-15

There x>5 and x is <-15

Hence Now I can say that x can never be 4 as it does not lie in the above range. Hence sufficent

Answer is B
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  21 Apr 2018, 00:41
Bunuel wrote:
Is x = 4?

(1) |x + 2| < 10

(2) |x + 5| > 10


Here's a number line approach that can be used to skip any form of calculation -

Attachment:
number line.jpg
number line.jpg [ 39.51 KiB | Viewed 4099 times ]


Statement 1: this equation will yield \(-12<x<8\). Hence \(x\) may or may not be \(4\). Insufficient

Statement 2: this equation will yield \(x<-15\) or \(x>5\). In either case, \(x≠4\). Sufficient

Option B
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  03 May 2018, 00:41
1
Kudos
simple way
1. |X+2|<10
=> -10<X+2<10
=>-12<X<8
SO X CAN BE -11,-10,-9,-8...1, 2 ..7
SO X can or cannot be 4. Hence insufficient.
2. |x + 5| > 10
=> x+5>10 or X>5 hence X cannot be 4
or X+5 <-10 or X<-15 , hence x cannot be 4
Therefore Sufficient
Answer should be B
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push12345
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  07 May 2018, 06:06
I) x can take values from -12 to 8
So x can be or cannot be 4
Insufficient

II) x can take values outside of -15 to 5
X cannot be 4 for sure
So sufficient

B is answer

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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink] New post  05 May 2023, 07:10
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Re: Is x = 4? (1) |x + 2| < 10 (2) |x + 5| > 10 [#permalink]
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