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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] New post 08 Nov 2005, 03:40
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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, 13:07, edited 3 times in total.
EDITED THE QUESTION.
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 [#permalink] New post 08 Nov 2005, 04:48
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

So the answer is C.
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 [#permalink] New post 08 Nov 2005, 05:05
Nakib,
Looks like you are leaving out the fact that z is closer to 10 than to x.
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Re: number line problem [#permalink] New post 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.
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 [#permalink] New post 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.
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 [#permalink] New post 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
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 [#permalink] New post 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 ..
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 [#permalink] New post 08 Nov 2005, 06:55
I understand it in the way, that z is closer to 10 as x IS... (10-z < 10-x)
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Re: number line problem [#permalink] New post 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.

Hence B answers the Q.
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Re: number line problem [#permalink] New post 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.

Why is the answer B?
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Re: number line problem [#permalink] New post 30 Apr 2010, 09:01
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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.

Why is the answer B?


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.)

Answer: A.
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Re: number line problem [#permalink] New post 22 Oct 2010, 20:53
A it is.. :)
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Re: This one is from GMATPREP as well. DS: If x<10 and n is a [#permalink] New post 15 Oct 2013, 13:05
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Re: This one is from GMATPREP as well. DS: If x<10 and n is a   [#permalink] 15 Oct 2013, 13:05
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