Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Oct 2016, 05:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Jun 2009
Posts: 29
Followers: 0

Kudos [?]: 89 [4] , given: 1

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

### Show Tags

08 Nov 2009, 21:32
4
KUDOS
16
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:28) correct 46% (01:28) wrong based on 998 sessions

### HideShow timer Statistics

If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

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

(2) z = 5x
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Mar 2012, 01:57, edited 1 time in total.
Edited the question and added the OA
Senior Manager
Joined: 18 Aug 2009
Posts: 328
Followers: 8

Kudos [?]: 279 [2] , given: 13

Re: x is a positive number less than 10 [#permalink]

### Show Tags

08 Nov 2009, 21:37
2
KUDOS
1
This post was
BOOKMARKED
amitgovin 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

*********************************

IMO A

1) The distance between Z and 10 is lesser than distance between Z and X. So Z is greater than the center of the line segment X to 10. That means Z is greater than the average of X and 10. Sufficient.
2) Z = 5X
If X=1, then Z = 5. Avg of X and 10 = 5.5. So Z<Avg.
If X=2, then Z = 10. Avg of X and 10 = 6. So Z>Avg.
Statement is Insufficient.
Director
Joined: 01 Apr 2008
Posts: 897
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 28

Kudos [?]: 602 [1] , given: 18

Re: x is a positive number less than 10 [#permalink]

### Show Tags

09 Nov 2009, 08:01
1
KUDOS
1
This post was
BOOKMARKED
Yup A.

stmt1:
|10-z| < |z-x| , here x and z are +ve ( as Z is closer to 10 than to x, and x is +ve )
10-z < z-x
=> z > Av of 10 and x.

stmt2:
x=1, z=5, 5 < 5.5
x=2, z=10, 10 > 6
Math Expert
Joined: 02 Sep 2009
Posts: 35320
Followers: 6648

Kudos [?]: 85829 [10] , given: 10254

### Show Tags

21 Oct 2010, 16:14
10
KUDOS
Expert's post
8
This post was
BOOKMARKED
amp0201 wrote:
Hi,

Can anyone please suggest me the solution. I arrived at B, but unfortunately it was wrong. Thanks.

If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

Given: $$0<x<10$$.
Q: is z greater than the average of x and 10? Or: is $$z>\frac{10+x}{2}$$? --> $$2z>10+x$$?

(1) On the number line, z is closer to 10 than it is to x --> $$|10-z|<|z-x|$$ --> as z is closer to 10 than it is to x, then z>x, so $$|z-x|=z-x$$ --> two cases for 10-z:

A. $$z\leq{10}$$ --> $$|10-z|=10-z$$ --> $$|10-z|<|z-x|$$ becomes: $$10-z<z-x$$ --> $$2z>10+x$$. Answer to the question YES.

B. $$z>{10}$$ --> in this case $$2z>20$$ and as $$x<10$$, then $$x+10<20$$, hence $$2z>10+x$$. Answer to the question YES.

OR another approach:
Given:
x-----average-----10----- (average of x and 10 halfway between x and 10).

Now, as z is closer to 10 than it (z) is to x, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES.

Sufficient.

(2) z = 5x --> is $$2z>10+x$$? --> is $$10x>10+x$$? --> is $$x>\frac{10}{9}$$. We don't now that. Not sufficient. (we've gotten that if $$x>\frac{10}{9}$$, then the answer to the question is YES, but if $$0<x\leq{\frac{10}{9}}$$, then the answer to the question is NO.)

Similar question: 600-level-question-95138.html?hilit=number%20line%20closer
_________________
Manager
Joined: 18 Aug 2010
Posts: 90
Followers: 1

Kudos [?]: 8 [0], given: 22

### Show Tags

19 Apr 2011, 14:07
hello Bunuel,

how did u get Z>10 ? above in red. from your inequality i got 10>x

thx
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6972
Location: Pune, India
Followers: 2033

Kudos [?]: 12783 [4] , given: 221

Re: x is a positive number less than 10 [#permalink]

### Show Tags

19 Apr 2011, 16:29
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
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

Attachment:

Ques2.jpg [ 4.71 KiB | Viewed 18000 times ]

So x is somewhere between 0 and 10 and average of x and 10 is between x and 10.
z can be in any of the 5 regions as shown.

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

In which regions is z closer to 10 than to x? Only the two rightmost regions. There, z is greater than the average of x and 10. Sufficient.

2) z = 5x
Put x = 1
z = 5 but average of 1 and 10 is 5.5 so z is less than the average. Actually, this is where I stop and mark (A) as the answer without checking to see if there is a value of x for which z is greater than the average. Think, why?
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews SVP Joined: 16 Nov 2010 Posts: 1673 Location: United States (IN) Concentration: Strategy, Technology Followers: 34 Kudos [?]: 492 [2] , given: 36 Re: x is a positive number less than 10 [#permalink] ### Show Tags 19 Apr 2011, 21:50 2 This post received KUDOS @Karishma We stop in (2) because we've found something contrary to the answer in (1), while in earlier choice we had a definite answer. So the answer can't be B,C,D oe E. The goal in DS is to get No as answer first for the choices, or to find the inconsistencies. (1) ---------------0--------x-----Av--------10----z------------ ---------------0--------x-----Av------z--10---------------- From the diagram above, it's evident that the answer is Yes (2) is insufficient if x is very close to 0, then z may not be closer to 10 e.g, x = 0.1, then z = 0.5 if x = 2, then z = 10 (greater than average) Answer - A _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6972 Location: Pune, India Followers: 2033 Kudos [?]: 12783 [2] , given: 221 Re: x is a positive number less than 10 [#permalink] ### Show Tags 20 Apr 2011, 04:28 2 This post received KUDOS Expert's post subhashghosh wrote: @Karishma We stop in (2) because we've found something contrary to the answer in (1), while in earlier choice we had a definite answer. So the answer can't be B,C,D oe E. The goal in DS is to get No as answer first for the choices, or to find the inconsistencies. (1) ---------------0--------x-----Av--------10----z------------ ---------------0--------x-----Av------z--10---------------- From the diagram above, it's evident that the answer is Yes (2) is insufficient if x is very close to 0, then z may not be closer to 10 e.g, x = 0.1, then z = 0.5 if x = 2, then z = 10 (greater than average) Answer - A Yes, it is not possible to get inconsistent answers from the two statements i.e. we cannot have 'Yes. z is greater. Sufficient Alone.' from statement 1 and 'No. z is smaller. Sufficient Alone.' from statement 2. From statement 2, we will either get 'Yes. z is greater. Sufficient Alone.' or 'z can be smaller or greater so not sufficient alone' From statement 1, we got that z is greater than the average. From statement 2, we tried a value and we got that z is less than the average. Then there must be a value for which z is greater than the average too in statement 2. We don't even need to try it. Definitely statement 2 alone is not sufficient and answer is (A). _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 28 Feb 2012
Posts: 19
GMAT Date: 05-23-2012
WE: Information Technology (Consulting)
Followers: 0

Kudos [?]: 7 [0], given: 11

If x is a positive number less than 10, is z greater than th [#permalink]

### Show Tags

24 Apr 2012, 09:18
If x is a positive number less than 10, is z greater than the average(Arithmetic mean) of x and 10?
1. On the number line, z is closer to 10 than it is to x.
2. z = 5x.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 35320
Followers: 6648

Kudos [?]: 85829 [0], given: 10254

Re: If x is a positive number less than 10, is z greater than th [#permalink]

### Show Tags

24 Apr 2012, 10:28
gayathriz wrote:
If x is a positive number less than 10, is z greater than the average(Arithmetic mean) of x and 10?
1. On the number line, z is closer to 10 than it is to x.
2. z = 5x.

Thanks

_________________
Manager
Joined: 11 Apr 2011
Posts: 50
Followers: 0

Kudos [?]: 6 [0], given: 3

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

25 Apr 2012, 17:22
just wondering about statement 1, am i misunderstanding the question?

"on the number line, z is closer to 10 than it is to x"

z = 11
x = 8
so z is closer to 10 than x is

is 11 > (8+10)/2
11 > (18/2) becomes 11 > 9 so the answer is YES

z = 9
x = 8
so z is closer to 10 than x is

is 9 > (8+10)/2
9 > (18/2) becomes 9 > 9 so the answer is NO

or is the question stating z is closer to 10 than z is to x? i interpreted it as z is closer to 10 than 10 is to x.
Math Expert
Joined: 02 Sep 2009
Posts: 35320
Followers: 6648

Kudos [?]: 85829 [1] , given: 10254

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

25 Apr 2012, 21:18
1
KUDOS
Expert's post
chamisool wrote:
just wondering about statement 1, am i misunderstanding the question?

"on the number line, z is closer to 10 than it is to x"

z = 11
x = 8
so z is closer to 10 than x is

is 11 > (8+10)/2
11 > (18/2) becomes 11 > 9 so the answer is YES

z = 9
x = 8
so z is closer to 10 than x is

is 9 > (8+10)/2
9 > (18/2) becomes 9 > 9 so the answer is NO

or is the question stating z is closer to 10 than z is to x? i interpreted it as z is closer to 10 than 10 is to x.

(1) says: "On the number line, z is closer to 10 than it is to x". Here "it" refers to z.

So, it's: "On the number line, z is closer to 10 than z is to x".

Similar question to practice: if-x-is-a-positive-number-less-than-10-is-z-less-than-the-131322.html

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12253
Followers: 542

Kudos [?]: 151 [0], given: 0

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

13 Oct 2013, 07:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12253
Followers: 542

Kudos [?]: 151 [0], given: 0

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

23 Oct 2014, 18:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Current Student
Joined: 25 Jul 2014
Posts: 43
GMAT 1: 640 Q V
GPA: 3.7
WE: Marketing (Pharmaceuticals and Biotech)
Followers: 0

Kudos [?]: 4 [0], given: 13

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

17 Dec 2014, 16:50
Hmm...I don't understand why the answer is A.

for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient?
Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 642 [0], given: 723

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

17 Dec 2014, 21:01
GMATAnnihilator wrote:
Hmm...I don't understand why the answer is A.

for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient?

The case you are considering with z=9,x=8 then z is equidistant from x and 10 both....So this is not valid.

Case 2 where z=2 ie. average of x+10 ----> (x+10)/2=2 or x+10=4 or x =-6...But we are told x is positive number less than 10...so x=-6 is not possible...

Hope it is clear
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Current Student
Joined: 25 Jul 2014
Posts: 43
GMAT 1: 640 Q V
GPA: 3.7
WE: Marketing (Pharmaceuticals and Biotech)
Followers: 0

Kudos [?]: 4 [0], given: 13

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

18 Dec 2014, 07:59
1
This post was
BOOKMARKED
WoundedTiger wrote:
GMATAnnihilator wrote:
Hmm...I don't understand why the answer is A.

for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient?

The case you are considering with z=9,x=8 then z is equidistant from x and 10 both....So this is not valid.

Case 2 where z=2 ie. average of x+10 ----> (x+10)/2=2 or x+10=4 or x =-6...But we are told x is positive number less than 10...so x=-6 is not possible...

Hope it is clear

Thanks Wounded Tiger...now where do I find that facepalm emoticon. I clearly misread the question... one of more deficiencies with timed exams... This will have to do: http://vignette3.wikia.nocookie.net/car ... 1217081420
Manager
Joined: 04 Oct 2013
Posts: 180
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Followers: 6

Kudos [?]: 113 [0], given: 29

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

04 Jan 2015, 10:26
Quote:
Hmm...I don't understand why the answer is A.

for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient?

For semplicity sake: rephrase the question into is 2z > 10 + x?

1) We know a few interesting things about x: it has to be smaller than 10; it can be a rational number; it is positive.
According to this statement --> if z=9 then x<8, say x=7,9 so that if 7,9 works any smaller value of x will work too. 2z=18 > 10+x. Thus z is always going to be greater than the average of 10 and x.

hope it helps
_________________

learn the rules of the game, then play better than anyone else.

Intern
Joined: 18 Apr 2015
Posts: 37
Followers: 0

Kudos [?]: 2 [0], given: 5

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

18 May 2015, 06:36
Hi Karishma,

This is regarding the number line approach that you have explained.Please share some problems where i could apply this technique.

Regards,

Kirti
Intern
Joined: 18 Apr 2015
Posts: 37
Followers: 0

Kudos [?]: 2 [0], given: 5

Re: If x is a positive number less than 10, is z greater than [#permalink]

### Show Tags

18 May 2015, 06:49
Hi Karishma,

How can we be sure that the average is not more than z.The pictorial representation suits your explanation but somewhere i am not able to convince myself with it.

Would be glad if we could discuss

Regards
Re: If x is a positive number less than 10, is z greater than   [#permalink] 18 May 2015, 06:49

Go to page    1   2    Next  [ 27 posts ]

Similar topics Replies Last post
Similar
Topics:
4 If both x and y are positive integers less than 90 and greater than 10 4 31 May 2016, 05:43
25 If x is a positive number less than 10, is z greater than th 11 20 Feb 2014, 01:15
8 If x is a positive number less than 10, is z less than the 16 25 Apr 2012, 11:22
14 If x is a positive integer less than 10, is z greater than 9 24 Feb 2012, 16:50
5 If a is a positive number less than 10, is c greater than 8 02 Dec 2010, 03:27
Display posts from previous: Sort by