Modulus Doubt

[das.ashmita]

Hi Experts
I have a basic doubt.

Is |x−6|>5 ?
(1) x is an integer
(2) x^2<1


|x-6|>5
If x<6, then −x+6>5 or x<1.
If x≥6, then x−6>5 or x>11.

In this question, do we need to find if the options fulfill both x<1 and x>11 or any one would suffice?

[rijul007]

Is |x−6|>5 ?
(1) x is an integer
(2) x^2<1

You can solve this question by simply plugging in nos

Is |x−6|>5 ?

Statement 1
x is an integer

If x = 0
Is |x−6|>5 ? Yes

If x = 1
Is |x−6|>5 ? No

Not sufficient


Statement 2
x^2<1
-1 < x < 1

x = -0.9
|x−6| = 6.9
Is |x−6|>5 ? Yes

x = 0
|x−6| = 6
Is |x−6|>5 ? Yes

x = 0.9
|x−6| = 5.1
Is |x−6|>5 ? Yes

Sufficient

Option B

|x-6|>5
If x<6, then -x+6>5 or x<1.
If x≥6, then x-6>5 or x>11.

In this question, do we need to find if the options fulfill both x<1 and x>11 or any one would suffice?

If you have to go the conventional way,
you know that |x-6|>5 is true only if x<1 OR x>11


A statement would be sufficient if it gives range of values of x that
satisfies x<1 or x>11 but does not satisfy 1<=x<=11
OR
satisfies 1<=x<=11 but does nor satisfy x<1 and x>11


But the best approach is to identify a pattern and plug numbers.

[pemdas]

Hi Experts
I have a basic doubt.

Is |x−6|>5 ?
(1) x is an integer
(2) x^2<1

usually I avoid squaring both sides for mod, but here it clearly specifies x (all real values) and the right-hand-side > 5 > 1. So squaring both sides doesn't involve additional issues here at all. Restating question: Is x^2-12x+36>5 or x^2-12x+31>0? The question asks whether our function is greater than 0 with the given two statements (individually or combined).

st(1) x is an integer. If we try most integers we end with > true about always, but we select 8, this will return 64-96+31<0 Not Sufficient
st(2) x^2<1 implies -<1<x<1 is always true, therefore Sufficient

answer b