GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Sep 2018, 15:27

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49271
If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

20 Feb 2014, 01:15
3
28
00:00

Difficulty:

85% (hard)

Question Stats:

57% (01:47) correct 43% (02:05) wrong based on 800 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Data Sufficiency
Question: 103
Category: Arithmetic; Algebra Statistics; Inequalities
Page: 160
Difficulty: 650

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49271
If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

20 Feb 2014, 01:16
7
7
If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

Given: $$0<x<10$$.
Question: 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 questions to practice:
https://gmatclub.com/forum/if-x-is-a-po ... 28086.html
https://gmatclub.com/forum/if-y-is-a-ne ... 95138.html
https://gmatclub.com/forum/if-x-is-a-po ... 31322.html
https://gmatclub.com/forum/if-a-is-a-po ... 05650.html
https://gmatclub.com/forum/if-x-and-z-a ... 55651.html
_________________
##### General Discussion
Intern
Joined: 30 Jan 2014
Posts: 18
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

20 Feb 2014, 03:18
2
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

On st1 i'll draw a number line. 0----------------------x-----------------z---10
We can see that z will always be greater than the average. Sufficient

St2 say that z=5x. we'll choose 2 cases:
Case 1: x=2, so z=10. avarge is 6 and z is greater than the avarage.
Case 2: x=1, so z=5 avarge is 5.5 and z is smaller than the avarage. Insufficient

So ans is A.
_________________

Please +1 KUDO if my post helps. Thank you.

Manager
Joined: 20 Dec 2013
Posts: 245
Location: India
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

21 Feb 2014, 00:06
Option A.
From S1:Is z>(x+10)/2 (1)
(x+10)2 is basically the middle value between x and 10.
So,if z is closer to 10 than x it would imply z>the mid value of x and 10 which is the mean.
Sufficient.

From S2:If z=5x
Replacing in (1) Is 5x>x+10/2
Or Is 9x>10
If x=1 ans is true
If x=2.
Ans is false.Not suff.
Senior Manager
Joined: 13 Jun 2013
Posts: 277
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

21 Feb 2014, 03:59
2
Q Is z>(x+10)/2 ; provided that 0<x<10
(1) On the number line, z is closer to 10 than it is to x.

this means distance between z and x is greater than distance between z and 10 on the number line. hence we have
z-x>10-z
z>(x+10)/2
in the above case z is less than 10 and lies between x and 10. If z is greater 10, then it will definitely be greater than average of x+10. hence z is greater than average of x+10. therefore sufficient.

(2) z = 5x

z=5x assume x=1 average of 10 and 1 = 5.5 and z=5(1)
when x=3, average of 10 and 3= 6.5 and z=15

since two different answers are possible hence 2 alone is not sufficient hence correct answer is A
Director
Joined: 10 Mar 2013
Posts: 549
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

23 Aug 2015, 02:37
Statement 1: 0---X----Z--10 The average is the middle point between X (which is 0<x<10) and 10, and we are told that Z is closer to 10 that means Z>Average

Statement 2: 10x>x+10 (plugin 5x=z here z>(x+10)/2 --> 9x>10 ? If x=1 9<10 No, and if x=2 18>10 Yes NOT Sufficient
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Joined: 21 Jul 2015
Posts: 2
Location: India
Schools: Ryerson
GMAT 1: 560 Q44 V25
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

13 Dec 2015, 00:13
Hi,

i request your help to find out weather statement A is sufficient, when x=8 and Z =9 . Here z is closer to 10 than x, but the average of 10 and X will be equal to z.

Is this correct?

Thanks
Senior Manager
Joined: 18 Jun 2016
Posts: 267
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

13 Sep 2016, 02:50
syamukrishnan wrote:
Hi,

i request your help to find out weather statement A is sufficient, when x=8 and Z =9 . Here z is closer to 10 than x, but the average of 10 and X will be equal to z.

Is this correct?

Thanks

No, the Statement 1 says that - Z is closer to 10 than it is to x and not that z is closer to 10 than x is. Your's is the later case.
_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

CEO
Joined: 12 Sep 2015
Posts: 2865
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

05 Oct 2016, 11:25
2
Top Contributor
Bunuel 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

Here's my solution:

Target question: Is z greater than the mean of x and 10?

Statement 1: On the number line, z is closer to 10 than it is to x.
IMPORTANT: On the number line, the mean of two numbers will lie at the midpoint between those two numbers.
So, the mean of x and 10 will lie halfway between x and 10.
So, if z is closer to 10 than it is to x, then z must lie to the right of the midpoint between x and 10.
This means that z must be greater than the mean of x and 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 5x
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=1, z=5, in which case z is less than the mean of x and 10 (mean = 5.5)
Case b: x=4, z=20, in which case z is greater than the mean of x and 10 (mean = 7)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com

Current Student
Joined: 26 Jan 2016
Posts: 109
Location: United States
GPA: 3.37
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

05 Oct 2016, 13:23
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

I first rephrased the question to
z>(x+10)/2
2z>x+10
2z-10>x?
(This didn't help me w/ the question)

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

I just used guess and check for this one.
x=8 then (10+8)/2=9 if z is closer to 10 than to 8 it has to be more than 9 so yes
x=1 then (10+1)=11/2=5.5 5.5 is the midpoint between 1 and 10 (i.e. 5.5 is the average). In order for z to be closer to 10 it need to be more than 5.5. yes
suff

(2) z = 5x
again I plugged in numbers
x=1, z=5 then no z is not greater than the average
x=2, z=10 z is greater than the average

insuff
Intern
Joined: 28 Dec 2010
Posts: 23
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

31 Jul 2017, 18:23
Given:
x is a +ve integer and x< 10.

Is z > (x+10)/2 ?

Using the values of x we can find the range of the inequality.

case 1: when x = 1 (minimum value of x), z > 11/2 => z > 5.5

case 2: when x = 9 (maximum value of x ), z >19/2 => z > 9.5

From case 1 and case 2, we can rephrase the question as Is z > 5.5 ?

Taking Statement 2 first: -----------> NOT Sufficient
For x = 1, z = 5 is z >5.5 ---> No
For x = 2, z = 10 is z > 5.5. --> yes

Statement 1: It say's z is closer to 10 i.e. z> 5.5, therefore sufficient. Answer is A
SVP
Joined: 08 Jul 2010
Posts: 2314
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

27 Aug 2018, 08:10
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

0 < x < 10
Question : is z greater than the average (arithmetic mean) of x and 10?

Question : is z > (x+10)/2?
OR
Question : is z > Midpoint of x and 10 ?

Statement 1: On the number line, z is closer to 10 than it is to x.

i.e. z is to the right of "midpoint of 10 and x"

i.e. z is GREATER than x

SUFFICIENT

Statement 2: z = 5x

@x = 1, Midpoint = (1+10)/2 = 5.5 and z = 5 i.e. z < AVerage

@x = 2, Midpoint = (2+10)/2 = 6 and z = 10 i.e. z > AVerage

NOT SUFFICIENT

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Re: If x is a positive number less than 10, is z greater than th &nbs [#permalink] 27 Aug 2018, 08:10
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.