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

 It is currently 21 Feb 2019, 16:43

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 30 Aug 2005
Posts: 177
If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

Updated on: 17 Dec 2017, 22:48
4
8
00:00

Difficulty:

95% (hard)

Question Stats:

46% (02:20) correct 54% (02:41) wrong based on 448 sessions

### HideShow timer Statistics

This one is from GMATPREP as well.
DS:

If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)

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

I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.

Thanks!

MODERATOR: EDITED THE QUESTION.

ORIGINAL QUESTION:

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-is-a-po ... 67734.html

Originally posted by rianah100 on 08 Nov 2005, 03:40.
Last edited by Bunuel on 17 Dec 2017, 22:48, edited 4 times in total.
EDITED THE QUESTION.
SVP
Joined: 28 May 2005
Posts: 1580
Location: Dhaka
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 04:48
1
I think it is C.

let's look at I) z is closer to 10 than x. and x is less than 10.

lest pick number if x= 1 and z=9 then (x+10)/2 = 5.5 which is less than z
how ever if x=1 and z=2 then (x+10)/2 = 5.5 which is more than z

simillarly using II) if x = 1 and z=5 then (x+10)/2 = 5.5 which is more than z

and if x = 3 and z=15 then (x+10)/2 = 6.5 which is less than z

but if we combine the both

z is greater than (x+10)/2

Manager
Joined: 30 Aug 2005
Posts: 177
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 05:05
Nakib,
Looks like you are leaving out the fact that z is closer to 10 than to x.
SVP
Joined: 24 Sep 2005
Posts: 1782
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 05:12
rianah100 wrote:
This one is from GMATPREP as well.
DS:

If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)

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

I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.

Thanks!

uhm, the bold part is easily misunderstood ....some can understand that z is closer to 10 than to x ...others may think: z is closer to 10 than x is . IMO, it is the latter one . They are totally different and thus lead to completely different outcomes.
SVP
Joined: 28 May 2005
Posts: 1580
Location: Dhaka
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 05:17
rianah100 wrote:
Nakib,
Looks like you are leaving out the fact that z is closer to 10 than to x.

If z is closer to 10 than to x, then answer will be obviously D.

but If z is closer to 10 than x, the answer will be C.
Intern
Joined: 30 Sep 2005
Posts: 20
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 06:27
I'm getting totally another answer: E

Number picking:

1 and 2 alone are clearly not sufficient.

But BOTH TOGETHER are also not sufficient:

x=1, z=5 (z closer to 10 and z = 5x) -> 5 < 5.5

BUT x=3, z=15 (conditions are also fullfilled) -> 15 > 6.5

It's not told that z < 10!!!

-> E
_________________

Looking for study partners:

http://www.gmatclub.com/phpbb/viewtopic.php?t=20834

SVP
Joined: 24 Sep 2005
Posts: 1782
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 06:43
lazy_k wrote:
I'm getting totally another answer: E

Number picking:

1 and 2 alone are clearly not sufficient.

But BOTH TOGETHER are also not sufficient:

x=1, z=5 (z closer to 10 and z = 5x) -> 5 < 5.5

BUT x=3, z=15 (conditions are also fullfilled) -> 15 > 6.5

It's not told that z < 10!!!

-> E

in which way do you understand statement 1?!! ...uhm, I'm not sure with the statement as my above post pointed out why ..
Intern
Joined: 30 Sep 2005
Posts: 20
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 06:55
I understand it in the way, that z is closer to 10 as x IS... (10-z < 10-x)
_________________

Looking for study partners:

http://www.gmatclub.com/phpbb/viewtopic.php?t=20834

Current Student
Joined: 23 Oct 2005
Posts: 239
Schools: Cranfield SOM
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

08 Nov 2005, 10:37
rianah100 wrote:
This one is from GMATPREP as well.
DS:

If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)

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

I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.

Thanks!

I don't know why there is an 'n' in the stem. Anyway.. I got B.

(1) assume x = 8, z = 8.1.
(x+10)/2 = 9
Hence z < (x+10)/2

If x = 1 and z is 8.
z > (x+10)/2
since (x +10)/2 = 5.5.

so insuff.

(2) If z = 5x

stem can be is 5x > (x+10)/2
which is 5x > x/2 + 5 which is always true.

Senior Manager
Joined: 19 Nov 2007
Posts: 396
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

29 Apr 2010, 15:08
If x = 1, z = 5, answer to the question is NO.
If x= 4, z = 20, answer to the question is YES.

_________________

-Underline your question. It takes only a few seconds!
-Search before you post.

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

30 Apr 2010, 09:01
1
3
vscid wrote:
If x = 1, z = 5, answer to the question is NO.
If x= 4, z = 20, answer to the question is YES.

Edited the question. the original question is below:

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. $$z<10$$ --> $$|10-z|=10-z$$ --> $$|10-z|<|z-x|$$ becomes: $$10-z<z-x$$ --> $$2z>10+x$$. Answer to the question YES.

B. $$z\geq{10}$$ --> $$|10-z|=z-10$$ --> $$|10-z|<|z-x|$$ becomes: $$z-10<z-x$$ --> $$z>10$$ --> now, as $$z>10$$, then $$2z>20$$ 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.)

_________________
Intern
Joined: 07 Sep 2014
Posts: 14
Location: United States
GMAT Date: 03-14-2015
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

11 Feb 2015, 04:07
rianah100 wrote:
This one is from GMATPREP as well.
DS:

If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)

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

I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.

Thanks!

MODERATOR: EDITED THE QUESTION.

ORIGINAL QUESTION:

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 take

is z>than the midpoint of x and 10

stated in the stem: x<10

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

M-midpint
case1
---------------------X----------M--z------10--------------------

case 2
---------------------X----------M---------10---z-----------------

In any of the case z is greater than the midpoint as it is closer to 10 than x
and
if it is on the midpoint then it is at equal distance from x and 10.

so SUFFICIENT.

STATEMENT 2) z=5x

if X=1 then Z=5 but average of x and 10=5.5
so Z<(X+10)/2 :NO

if X=4 then Z=20 but average of x and 10=7
so Z>(X+10)/2 :YES

so NOT SUFFICIENT.

Intern
Joined: 05 Dec 2013
Posts: 3
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

24 Feb 2015, 11:27
Please help me with statement (1). If x=8, and z=9, which z is closer to 10 on the number line, then 2(9)= 8 + 20.... So answer is "no". Every other scenarios make 2(z) > x+10 as "yes".... So I got this statement as Insufficient. What did I do wrong? Thanks.

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

24 Feb 2015, 11:32
freesoybean wrote:
Please help me with statement (1). If x=8, and z=9, which z is closer to 10 on the number line, then 2(9)= 8 + 20.... So answer is "no". Every other scenarios make 2(z) > x+10 as "yes".... So I got this statement as Insufficient. What did I do wrong? Thanks.

Posted from GMAT ToolKit

If x = 8 and z = 9, then z = 9 is NOT closer to 10 than it (z) is it x = 8. 9 is exactly in the middle of 8 and 10.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: If x is a positive number less than 10, is z greater than th  [#permalink]

### Show Tags

17 Dec 2017, 22:49
Re: If x is a positive number less than 10, is z greater than th   [#permalink] 17 Dec 2017, 22:49
Display posts from previous: Sort by