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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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.)

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

Drawing a number line can help you see the answer quickly.

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?
_________________

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.

@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.

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).
_________________

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.

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.

Please explain your answer choice. Thanks

Merging similar topics. Please ask if anything remains unclear.
_________________

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.
_________________

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.
_________________

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?

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.”

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

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.

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

gmatclubot

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

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...