x is a negative

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Jun 19, 2010 12:17 am

If x is a negative number, which of the following must be true?
I. x^5 < |x|
II. x < âˆš(-x)
III. x - 1/|x| < 0
(A) I, II and III
(B) I and II only
(C) II and III only
(D) I and III only
(E) None

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Source: Beat The GMAT — Problem Solving | Sat Jun 19, 2010 12:17 am

amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Sat Jun 19, 2010 12:32 am

sanju09 wrote:If x is a negative number, which of the following must be true?
I. x^5 < |x|
II. x < âˆš(-x)
III. x - 1/|x| < 0
(A) I, II and III
(B) I and II only
(C) II and III only
(D) I and III only
(E) None

I. x^5 < |x| x is negative xo x^5 will also be neagtuve < |x| (ia always positive)
II) x < âˆš(-x) not possible âˆš(-x)

III. x - 1/|x| < 0 =(-x +1/x) <0 as 1/x is less than x and withnegative sign it will be less than 0

so option D

Ideation without execution is delusion

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Sat Jun 19, 2010 1:31 am

I think A.

1 - for any value of negative x, x^5<abs(x)
2 - for any negative x, x is always less than sqrt (-x) since sqrt (-x) is positive
3 - for negative x, x - 1/abs(x) is always less than 0 since x and -1/ans(x) are both separately negative

Hence A

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Sat Jun 19, 2010 1:37 am

mj78ind wrote:I think A.

1 - for any value of negative x, x^5<abs(x)
2 - for any negative x, x is always less than sqrt (-x) since sqrt (-x) is positive (until and unless x is comples number this is not possible as squareroot of a negative number is not possible a gmat trap)
3 - for negative x, x - 1/abs(x) is always less than 0 since x and -1/ans(x) are both separately negative

Hence A

dude c the bold part

Ideation without execution is delusion

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Sat Jun 19, 2010 1:43 am

amising6 wrote:
mj78ind wrote:I think A.

1 - for any value of negative x, x^5<abs(x)
2 - for any negative x, x is always less than sqrt (-x) since sqrt (-x) is positive (until and unless x is comples number this is not possible as squareroot of a negative number is not possible a gmat trap)
3 - for negative x, x - 1/abs(x) is always less than 0 since x and -1/ans(x) are both separately negative

Hence A
dude c the bold part

@amising6
Nice observation the only issue is it is wrong. Say x = -6, then if you plug it in stmt 2 above we get -6 < Sqrt{-(-6)}

which boils down to -6 < sqrt(6), hence is always true and x does not have to be complex.

Cheers

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Sat Jun 19, 2010 1:55 am

yes agrreod oversight error i ignore that part
thanks

Ideation without execution is delusion

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