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Here is the first post, everyone is wellcomed to reply in [#permalink] New post 15 Oct 2006, 13:28
Here is the first post, everyone is wellcomed to reply in the other thread named ( Inequality thread replies) Plz use the question stem.

OA and best OE will be posted by the end of each week.

Everyone is welcomed to add questions and reply to any post.



Is x negative?

1) x^3(1-x^2)<0

2) x^2-1<0

plz note that my answers below are not OA or OE it is my personal solutions. this thread was created 3 years ago. and i personally lost track of it.

Last edited by yezz on 15 Aug 2009, 12:35, edited 2 times in total.
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 [#permalink] New post 15 Oct 2006, 13:31
2) 0<|x|-4x<5 = ?

A. x<0
B. 0<x<1
C. -3/5<x<1
D. -3/5<x<0
E. -1<x<0
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 [#permalink] New post 15 Oct 2006, 13:32
3)[x] denotes largest integer less than or equal to x if [x] = -1, which one is true?

x=1
-2=<x<-1
-2<x<=-1
-1=<x<0
-1<x<=0
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Kudos [?]: 62 [0], given: 39

 [#permalink] New post 15 Oct 2006, 13:33
4)If a>b>c>0, is c <3?
(1) 1/a>1/3
(2) 1/a+1/b+1/c=1
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 [#permalink] New post 15 Oct 2006, 13:34
5)Is y<(x+z)/2?

1. y-x < z-y
2 z-y > (z-x)/2
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 [#permalink] New post 15 Oct 2006, 13:36
6) if a and b are positive, is 1/(1/a+1/b) less than ab?

1) a=2b
2) a+b > 1
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 [#permalink] New post 15 Oct 2006, 13:37
7)if ab/cd <0, is bc>ad?

st1 cd>ab

st2 b<c<0
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 [#permalink] New post 15 Oct 2006, 13:38
8) If n is not equal to 0, is |n| < 4 ?

(1) n^2 > 16

(2) 1/|n| > n
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 [#permalink] New post 15 Oct 2006, 13:40
9) a and b are positive numbers. Is a>b?

(1) ax>bx
(2) x*a^2+x*b^2<0

Last edited by yezz on 15 Oct 2006, 14:13, edited 1 time in total.
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 [#permalink] New post 15 Oct 2006, 14:12
10)If x and y are positive real numbers, is x > y?

i) x^3/y < 1

ii) (x^1/3)/y < 1
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 [#permalink] New post 16 Oct 2006, 08:20
11) Is x>1?

1). x^2<x

2). x<rootx
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Re: The Inequality Thread [#permalink] New post 14 Aug 2009, 04:05
yezz wrote:
Here is the first post, everyone is wellcomed to reply in the other thread named ( Inequality thread replies) Plz use the question stem.

OA and best OE will be posted by the end of each week.

Everyone is welcomed to add questions and reply to any post.



Is x negative?

1) x^3(1-x^2)<0

2) x^2-1<0

Good luck



Hey yezz

Where can I find the solution of these questions? I am unable to find the thread of replies....
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Kudos [?]: 62 [0], given: 39

Re: The Inequality Thread [#permalink] New post 15 Aug 2009, 11:40
[quote="yezz"]Here is the first post, everyone is wellcomed to reply in the other thread named ( Inequality thread replies) Plz use the question stem.

OA and best OE will be posted by the end of each week.

Everyone is welcomed to add questions and reply to any post.



Is x negative? is x<0

1) x^3(1-x^2)<0

2) x^2-1<0

from 1

x^3<x^5 either x>1 or -1<x<0.......insuff

from 2

from 2

x^2<1 ie: /x/<1 ie: -1<x<1....insuff

both

still insuff...E
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Re: [#permalink] New post 15 Aug 2009, 11:48
yezz wrote:
2) 0<|x|-4x<5 = ?

A. x<0
B. 0<x<1
C. -3/5<x<1
D. -3/5<x<0
E. -1<x<0



0<|x|-4x<5 = -4x</x/<5-4x split the inquality into 2

1) /x/< 5-4x , 5-4x>0 -4x>-5 , x<5/4

2) -4x</x/.............-4x<x or 4x>x

x(-4-1) < 0 Ie: x>0

4x>x thus 3x>0 thus x>0

at 1,2 solutions
0<x<5/4, b is the range that belong to our solution thus B
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Re: [#permalink] New post 15 Aug 2009, 11:55
yezz wrote:
3)[x] denotes largest integer less than or equal to x if [x] = -1, which one is true?

x=1
-2=<x<-1
-2<x<=-1
-1=<x<0
-1<x<=0



solution is
-1=<X<=0,
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Re: [#permalink] New post 15 Aug 2009, 12:06
yezz wrote:
4)If a>b>c>0, is c <3?
(1) 1/a>1/3
(2) 1/a+1/b+1/c=1


a,b,c r +ve

from 1

a<3 and since a>b>c thus sure c<3

from 2

since a>b>c>0 thus surely 1/a<1/b<1/c , assume all are equal then each is 1/3 however 1/b,1/c has to be less than 1/3 1/c>1/3 thus c<3..suff

D
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Re: [#permalink] New post 15 Aug 2009, 12:07
yezz wrote:
5)Is y<(x+z)/2?

1. y-x < z-y
2 z-y > (z-x)/2


is 2y<x+z

from 1

y-x-z+y<0

2y<x+z..........suff

from 2
2z-2y-z+x > 0

z+x>2y...suff

D
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Re: [#permalink] New post 15 Aug 2009, 12:24
yezz wrote:
8) If n is not equal to 0, is |n| < 4 ?

(1) n^2 > 16

(2) 1/|n| > n


is -4<n<4

from 1

/n/>4 ie: either n>4 or n<-4............suff

from 2

n/(/n/)<1 ....isnuff

A
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Re: [#permalink] New post 15 Aug 2009, 12:26
yezz wrote:
9) a and b are positive numbers. Is a>b?

(1) ax>bx
(2) x*a^2+x*b^2<0


is a-b>0

from 1

x(a-b)>0 ...depends on x ...insuff

from 2

x(a^2+b^2) < 0....x is -ve no idea about a,b...insuff

both

if x is -ve and x(a-b)>0 thus a-b<0...suff... C
Re:   [#permalink] 15 Aug 2009, 12:26
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