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

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Manager
Joined: 17 Dec 2008
Posts: 162
If x is a positive number less than 10, is z greater than [#permalink]

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17 Feb 2009, 09:06
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If x is a positive number less than 10, is z greater than the average of x and 10?

(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

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SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York
Re: DS - Number line [#permalink]

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17 Feb 2009, 10:14
ConkergMat wrote:
If x is a positive number less than 10, is z greater than the average of x and 10?

(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

(1) Sufficient.
average.. = mid point of x and 10
if it is closer to 10.. z> average

(z)
avg = x+10/2

z= 5x

x=0.1 z=0.5 avg = 5.x
z<avg

when x = 5 z = 25 avg= 7.5
z> avg

not sufficient

A
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Manager
Joined: 11 Sep 2008
Posts: 56
Re: DS - Number line [#permalink]

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17 Feb 2009, 10:20
Agree w/ A

Here it is visually:

Number line:
1)===X===Z=10===

Visually, the Average: (X+10)/2 is clearly less than Z.

2) just pick numbers.
Manager
Joined: 10 Jan 2009
Posts: 107
Re: DS - Number line [#permalink]

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17 Feb 2009, 10:30
-------------------------------------
1) As z is closer to 10 than it is to x, we can have z > 10 or z < 10 on the condition that it stays closer to 10 than to x.

Case 1.

If z > 10, then the value of z will always be greater than average of x & 10.
For ex. z = 12 & x = 7 ---> Will satisfy option 1.

Now avg.(x+10) = 17/2 = 8.5, which is less than 12

Case 2.

Now let us see if z < 10.

If we consider z=9 & x=7, then avg.(x+10) = 17/2 = 8.5, which is less than 9. You can check by taking any legal values.

Another way of solving option 1:

We know that z > 10 will always satisfy, so we will consider only for z < 10.

As 10-z < z-x,
Therefore, 2z -x > 10
or, z > (x+10)/2

So, option 1 is sufficient.

-------------------------------------

2) z = 5x

So possible values for x = 1,2,...9

For x=1, z=5 So, avg(x+10) = 11/2 = 5.5, which is greater than z

For x=2, z=10 So, avg(x+10) = 12/2 = 6, which is less than z

So, option 2 is not sufficient.
-------------------------------------

So, only option 1 is sufficient to answer the question.

HTH
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Director
Joined: 01 Apr 2008
Posts: 828
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: DS - Number line [#permalink]

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22 Feb 2009, 04:56
x2suresh wrote:
ConkergMat wrote:
If x is a positive number less than 10, is z greater than the average of x and 10?

(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

(1) Sufficient.
average.. = mid point of x and 10
if it is closer to 10.. z> average

(z)
avg = x+10/2

z= 5x

x=0.1 z=0.5 avg = 5.x
z<avg

when x = 5 z = 25 avg= 7.5
z> avg

not sufficient

A

Hi x2suresh,
A says: Z is closer to 10 than Z is closer to X.
x can be 2, Z can be 3.

Average of x and 10 is 6 , Z < x.

x can be 2, Z can be 8.
Average of x and 10 is 6, Z > x.

What you say is correct if Z>5!! Please explain.
Senior Manager
Joined: 08 Jan 2009
Posts: 310
Re: DS - Number line [#permalink]

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22 Feb 2009, 05:28
Economist wrote:
x2suresh wrote:
ConkergMat wrote:
If x is a positive number less than 10, is z greater than the average of x and 10?

(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

(1) Sufficient.
average.. = mid point of x and 10
if it is closer to 10.. z> average

(z)
avg = x+10/2

z= 5x

x=0.1 z=0.5 avg = 5.x
z<avg

when x = 5 z = 25 avg= 7.5
z> avg

not sufficient

A

Hi x2suresh,
A says: Z is closer to 10 than Z is closer to X.
x can be 2, Z can be 3.

Average of x and 10 is 6 , Z < x.

x can be 2, Z can be 8.
Average of x and 10 is 6, Z > x.

What you say is correct if Z>5!! Please explain.

hi

A : Z is closer to 10 than to X.

By taking X =2 and Z=3 you have actually made Z closer to 10 when compared with X from 10.But the question says the distance b/w Z and 10 < distance b/w Z and X.

hope you got it.
Manager
Joined: 19 Aug 2006
Posts: 226
Re: DS - Number line [#permalink]

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22 Feb 2009, 21:41
Yup, only A.

B does not apply, because we can easily find a case when z<(x+10)/2 and also when z>(x+10)/2:

1. if x=1 => z=5x => so z=5
(1+10)/2 = 5.5 => 5<5.5

2. if x=3 => z=5x => so z=15
(3+10)/2 = 6.5 => 15>6.5
Manager
Joined: 04 Sep 2006
Posts: 113
Re: DS - Number line [#permalink]

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23 Feb 2009, 08:01
WHEN Z IS CLOSER TO 10 , WHAT ARE THE UPPER AND LOWER VALUES FOR Z

WILL THE VALUES OF Z BE 9.5 TO 10.5 OR 9 TO 11
Manager
Joined: 11 Sep 2008
Posts: 56
Re: DS - Number line [#permalink]

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23 Feb 2009, 08:28
vcbabu wrote:
WHEN Z IS CLOSER TO 10 , WHAT ARE THE UPPER AND LOWER VALUES FOR Z

WILL THE VALUES OF Z BE 9.5 TO 10.5 OR 9 TO 11

There is no limit. maybe x = 9.9, and z = 9.9999 or z = 150

The main point is that 1) tells you that z is closer to 10 than Z is to X, it shows you that (minimum): AVG(X,10)<Z

--== 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 - Number line   [#permalink] 23 Feb 2009, 08:28
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