Nice question to practice power & roots

[pankajks2010]

Hi,

read this piece by Vivian Kerr on power and roots:
https://www.beatthegmat.com/mba/2011/04/ ... ter-scores

Here's a DS question to practice it further:

Is 1 > |x-1|?

a)(x-1)^2 <= 1
b) x^2-1 > 0

[HSPA]

a) looks okay
b) x> -1 and x>1 so x>1 is the result

x = 2,3,4,5....
1 > |2-1| No.. 1>|3-1|No...

D for me

[pankajks2010]

a) looks okay
b) x> -1 and x>1 so x>1 is the result

x = 2,3,4,5....
1 > |2-1| No.. 1>|3-1|No...

D for me

HSPA...2 mistakes in 2 questions..come on boy..The correct answer is E.

Now just try the question again and if required go through the note written by Vivien..

[manpsingh87]

Hi,

read this piece by Vivian Kerr on power and roots:
https://www.beatthegmat.com/mba/2011/04/ ... ter-scores

Here's a DS question to practice it further:

Is 1 > |x-1|?

a)(x-1)^2 <= 1
b) x^2-1 > 0

lets just analyze |x-1|<1;
when x>1 |x-1|=(x-1), therefore (x-1)<1; x<2 therefore |x-1| will be less than 1 when x lies between 1 and 2 i.e. 1<x<2,

now when x<1, |x-1|=-(x-1), -x+1<1, x>0; hence |x-1| will be less than 1 when 0<x<1;

so, |x-1|<1 will be true for 1<x<2 and 0<x<1;

now consider statements 1 and 2:
1)(x-1)^2<=1; x(x-1)<=0 x<=0, x<=2, for x<=0 |x-1| doesn't holds true and for x<=2, consider two cases when x=2, |x-1|<1 won't hold true and for x<2, for some values it holds true (which lies in the two ranges 1<x<2 and 0<x<1) and for some it won't hence 1 alone is not sufficient to answer the question.

2)x^2-1>0, (x-1)(x+1)>0; x>1 and x>-1, similary here also different results are possible hence 2 alone is also not sufficient to answer the question.

combining 1 and 2 we have 1<x<=2, now the inequality |x-1|<1 holds true for all values except x=2,
and for the other values of x |x-1|<1 won't hold true hence answer should be E

[HSPA]

Oh my god.. enough math threads for today.. sorry as I think that I am brain dead for today, reading from morning on diff topics...

I saw... |x| = sqrt(x^2) but there is only x^2 ...

[pankajks2010]

first statement: (x-1)^2<=1 ---> -1<=(x-1)<=1 ---> 0<=x<=2
Now except for x=2, every value between 0-1.9 satisfies the required condition. Thus, first statement is insufficient

second statement: x^2-1>0 ----> either x<-1 or x>1
now, again by substituting different values (in the range, x<-1 or x>1) we get different results. Thus, this too is insufficient.

Thus, E

[GMATGuruNY]

Hi,

read this piece by Vivian Kerr on power and roots:
https://www.beatthegmat.com/mba/2011/04/ ... ter-scores

Here's a DS question to practice it further:

Is 1 > |x-1|?

a)(x-1)^2 <= 1
b) x^2-1 > 0

Rephrase the question stem:

|x-1| < 1
-1 < x-1 < 1
0 < x < 2

Question rephrased: Is 0 < x < 2?

Try to plug in values that satisfy both statements.

Statement 1: (x-1)² ≤ 1.
x = 2 works, because (2-1)² ≤ 1.
Is 0 < 2 < 2? No.

x = 1.5 works, because (1.5-1)² ≤ 1.
Is 0 < 1.5 < 2? Yes.

Since the answer can be both No and Yes, insufficient.

Statement 2: x²-1 > 0.
The values that were used in statement 1 -- x=2 and x=1.5 -- also satisfy statement 2.
Since these values showed that statement 1 was insufficient. they also show that statement 2 is insufficient.

Statements 1 and 2 combined:
Since x=2 and x=1.5 satisfy both statements, we know that even when we combine the 2 statements, the answer to the question stem can be both No and Yes.

The correct answer is E.