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# If x is a positive number less than 10, is z gater than the

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Senior Manager
Joined: 10 Mar 2008
Posts: 331
If x is a positive number less than 10, is z gater than the [#permalink]

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11 Sep 2008, 12:38
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If x is a positive number less than 10, is z gater than the average of x and 10?

1) on the number line, z is closer to 10 than to x

2) z=5x

--== Message from GMAT Club Team ==--

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Senior Manager
Joined: 31 Jul 2008
Posts: 270

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11 Sep 2008, 16:40
E

A cant be as :

suppose x=8 so average of x and 10 = 9 also if z=9 (as Z is closer to 10)

z=avg of x and 10 , hence insufficient .

B

suppose x=1

then 5x=5

hence not B
Manager
Joined: 09 Jul 2007
Posts: 235

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11 Sep 2008, 16:49
IMO A.

1 ) The mid point between X and 10 is the avg . and Z id more than the midpoint.. so z is greater than the avg

2 ) z =5x => consider x=.1 or x= 5 => not sufficient

statement 1 means => z-x > 10-z => 2z> 10-x => z > (10-x)/2
Senior Manager
Joined: 09 Oct 2007
Posts: 456

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11 Sep 2008, 17:45
stallone wrote:
E

A cant be as :

suppose x=8 so average of x and 10 = 9 also if z=9 (as Z is closer to 10)

z=avg of x and 10 , hence insufficient .

B

suppose x=1

then 5x=5

hence not B

The fact that Z is closer to 10 than to x means that it's greater than the mean of x+10.
VP
Joined: 17 Jun 2008
Posts: 1285

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11 Sep 2008, 18:56
vksunder wrote:
If x is a positive number less than 10, is z gater than the average of x and 10?

1) on the number line, z is closer to 10 than to x

2) z=5x

IMO A

Given : 0<x<10
Q:isZ > (x+10)/2

(1) z-x>10-z=> z>(10+x)/2 when z >0
if z<0 then x-z >10-z is not possible since given is that x<10

SUFFI

(2)z=5x since x>0 z>0 now again when x=2/5 then z<(x+10)/2
when x=5 then z>(x+10)/2
hence INSUFFI

IMO A
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Its Now Or Never

Intern
Joined: 08 Sep 2008
Posts: 1

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11 Sep 2008, 19:29
In my tric is that
1.i taken z=8
x=7
so,result is 8>8.5 yes.
then i got it z=9.5
x=9
so.........
9.5>9.5
no. in sufficiunt
i m rigth or wrong.......????????///
Senior Manager
Joined: 09 Oct 2007
Posts: 456

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11 Sep 2008, 19:47
tina10 wrote:
In my tric is that
1.i taken z=8
x=7
so,result is 8>8.5 yes.
then i got it z=9.5
x=9
so.........
9.5>9.5
no. in sufficiunt
i m rigth or wrong.......????????///

Tina, if x=7, then Z has to be greater than 8.5 (x+10's average)
VP
Joined: 17 Jun 2008
Posts: 1477

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12 Sep 2008, 04:59
stallone wrote:
E

A cant be as :

suppose x=8 so average of x and 10 = 9 also if z=9 (as Z is closer to 10)

z=avg of x and 10 , hence insufficient .

In this example, z is equidistant from x as well as from 10.....whereas the stmt says that z should be closer to 10 than to x.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS: Inequalities   [#permalink] 12 Sep 2008, 04:59
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