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

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

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08 Nov 2005, 04:40
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Oct 2013, 14:07, edited 3 times in total.
EDITED THE QUESTION.
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08 Nov 2005, 05:48
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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

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08 Nov 2005, 06:05
Nakib,
Looks like you are leaving out the fact that z is closer to 10 than to x.
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08 Nov 2005, 06:12
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.
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08 Nov 2005, 06:17
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.
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08 Nov 2005, 07:27
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
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08 Nov 2005, 07:43
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 ..
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08 Nov 2005, 07:55
I understand it in the way, that z is closer to 10 as x IS... (10-z < 10-x)
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08 Nov 2005, 11:37
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.

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29 Apr 2010, 16:08
If x = 1, z = 5, answer to the question is NO.
If x= 4, z = 20, answer to the question is YES.

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30 Apr 2010, 10:01
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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.)

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22 Oct 2010, 21:53
A it is..
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Re: This one is from GMATPREP as well. DS: If x<10 and n is a [#permalink]

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15 Oct 2013, 14:05
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Re: If x is a positive number less than 10, is z greater than th [#permalink]

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10 Feb 2015, 04:56
Hello from the GMAT Club BumpBot!

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

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11 Feb 2015, 05:07
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.

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

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24 Feb 2015, 12:27
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.

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

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24 Feb 2015, 12:32
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.

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

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06 Jun 2016, 07:35
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).

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Re: If x is a positive number less than 10, is z greater than th   [#permalink] 06 Jun 2016, 07:35
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