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Here is the first post, everyone is wellcomed to reply in [#permalink ]
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.

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yezz on 15 Aug 2009, 12:35, edited 2 times in total.

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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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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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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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5)Is y<(x+z)/2?
1. y-x < z-y
2 z-y > (z-x)/2

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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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7)if ab/cd <0, is bc>ad?
st1 cd>ab
st2 b<c<0

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8) If n is not equal to 0, is |n| < 4 ?
(1) n^2 > 16
(2) 1/|n| > n

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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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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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11) Is x>1?
1). x^2<x
2). x<rootx

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Re: The Inequality Thread [#permalink ]
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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Re: The Inequality Thread [#permalink ]
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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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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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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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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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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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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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