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Let's work on the stem first. For which values of \(x\) inequality \(|x - 6| > 5\) is true?

If \(x \lt 6\), then \(-x+6 \gt 5\) or \(x \lt 1\).

If \(x \geq 6\), then \(x-6 \gt 5\) or \(x \gt 11\).

So we have that inequality \(|x - 6| \gt 5\) holds true for \(x \lt 1\) and \(x \gt 11\).

(1) \(x\) is an integer. Clearly not sufficient. \(x\) can be 12 and the inequality holds true as we concluded OR \(x\) can be 5 and inequality doesn't hold true.

(2) \(x^2 \lt 1\). So, \(-1 \lt x \lt 1\), as all \(x\)-es from this range are in the range \(x \lt 1\), hence inequality \(|x - 6| \gt 5\) holds true. Sufficient.

I use number line for Inequality problems as i find it more acurate |x - 6|>5 or |x - 6|-5>0 expression is 0 for 1 and 11 divides number line in 3 segments x<1, 1<x<6, x>11 now expression is positive for x>11 and x<1 while for 1<x<11 is negative.

(1) x is an integer- not sufficient (2) x^2< 1 or -1<x<1 which is sufficient since expression is positive for all values for x<1

Why are the questions containing $ symbols and many other Questions have terms like "Frac" etc. Its very difficult to understand the Question itself. May I know if the real GMAT test will also have them?

Why are the questions containing $ symbols and many other Questions have terms like "Frac" etc. Its very difficult to understand the Question itself. May I know if the real GMAT test will also have them?

Can you please post a screenshot of a question with these symbols? You should not get them.
_________________

(2) x2<1. So, −1<x<1, as all x-es from this range are in the range x<1, hence inequality |x−6|>5 holds true. Sufficient.

I dont understand this statement. Because -1<x<1 means X=0 Or x=.25 and any other valu. But question inference say that x<1 or X>11. So -1<x<1 how x satisfy x>11. I am not clear about this. Would any one like to help me.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. (2) x2<1. So, −1<x<1, as all x-es from this range are in the range x<1, hence inequality |x−6|>5 holds true. Sufficient.

I dont understand this statement. Because -1<x<1 means X=0 Or x=.25 and any other valu. But question inference say that x<1 or X>11. So -1<x<1 how x satisfy x>11. I am not clear about this. Would any one like to help me.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. (2) x2<1. So, −1<x<1, as all x-es from this range are in the range x<1, hence inequality |x−6|>5 holds true. Sufficient.

I dont understand this statement. Because -1<x<1 means X=0 Or x=.25 and any other valu. But question inference say that x<1 or X>11. So -1<x<1 how x satisfy x>11. I am not clear about this. Would any one like to help me.

The question asks whether x<1 and x>11.

(2) says that −1<x<1, so we can say that yes, x is less than 1, which makes this statement sufficient.
_________________

Let's work on the stem first. For which values of \(x\) inequality \(|x - 6| > 5\) is true?

If \(x \lt 6\), then \(-x+6 \gt 5\) or \(x \lt 1\).

If \(x \geq 6\), then \(x-6 \gt 5\) or \(x \gt 11\).

So we have that inequality \(|x - 6| \gt 5\) holds true for \(x \lt 1\) and \(x \gt 11\).

(1) \(x\) is an integer. Clearly not sufficient. \(x\) can be 12 and the inequality holds true as we concluded OR \(x\) can be 5 and inequality doesn't hold true.

(2) \(x^2 \lt 1\). So, \(-1 \lt x \lt 1\), as all \(x\)-es from this range are in the range \(x \lt 1\), hence inequality \(|x - 6| \gt 5\) holds true. Sufficient.

Answer: B

I can`t understand why the option C is not the right answer. According to S2, x can only be anything within -0.99 to 0.99 as -1<x<1. While we take S1, we can say that there is only one integer which is O. Therefore, we can find a certain value for x.

Let's work on the stem first. For which values of \(x\) inequality \(|x - 6| > 5\) is true?

If \(x \lt 6\), then \(-x+6 \gt 5\) or \(x \lt 1\).

If \(x \geq 6\), then \(x-6 \gt 5\) or \(x \gt 11\).

So we have that inequality \(|x - 6| \gt 5\) holds true for \(x \lt 1\) and \(x \gt 11\).

(1) \(x\) is an integer. Clearly not sufficient. \(x\) can be 12 and the inequality holds true as we concluded OR \(x\) can be 5 and inequality doesn't hold true.

(2) \(x^2 \lt 1\). So, \(-1 \lt x \lt 1\), as all \(x\)-es from this range are in the range \(x \lt 1\), hence inequality \(|x - 6| \gt 5\) holds true. Sufficient.

Answer: B

I can`t understand why the option C is not the right answer. According to S2, x can only be anything within -0.99 to 0.99 as -1<x<1. While we take S1, we can say that there is only one integer which is O. Therefore, we can find a certain value for x.

Please correct me if i am wrong.

Thanks in advance.

The question does not ask to find the value of x. The question asks whether x<1 and x>11.

(2) says that −1<x<1, so we can say that yes, x is less than 1, which makes this statement sufficient.
_________________

In Stmt II I think that the range -1<x<1 satisfies only one of the two conditions. In this case x<1. what about x>11? Are you implying that x<1<11? Kindly explain.

In Stmt II I think that the range -1<x<1 satisfies only one of the two conditions. In this case x<1. what about x>11? Are you implying that x<1<11? Kindly explain.

\(|x - 6| \gt 5\) is true if x<1 or x>11.

(2) says that −1<x<1, so we can say that yes, x is less than 1, thus \(|x - 6| \gt 5\) holds true.
_________________