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

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

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30 Sep 2005, 06:19
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If x is a positive number less than 10, is z greater than the arithmatic 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. I couldnt get the OE!! THanks!
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30 Sep 2005, 06:53
hmm, I would say A is sufficient

if Z is closer to 10, then it will pull closer to 10, while if x is furhter apart the avg is going to pull closer to X....

say if X is 5, then 10+5=15/2= 7.5

well we are told in I) that the Z is closer to 10 than to X...so

Z has to be greater than 7, cause if i z was say 7, it will be only 2 points away from 5 and 3 points away from 10...(1) tells us that z is closer to 10, than it is to X...so probably z=8 or 9 or something....

(II) x can be 1 then you will see the avg of 10 and x is 5.5, but z=5.

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30 Sep 2005, 07:04
A IMO too, good explanation frieshna12
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30 Sep 2005, 08:26
Oh yeah! I read it as z is closer to 10 than x....
Thanks for the explanation!
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03 Oct 2005, 20:03
I just have one problem.

If z=9 and x=8, Average of X and 10 will be equal to 9 which is equal to z. The question clearly asks if z will be greater than the average of x and 10. So am not too sure if A is sufficient. If it were greater than or equal to then , your argument is correct.

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03 Oct 2005, 20:07
Gmatsoon wrote:
I just have one problem.

If z=9 and x=8, Average of X and 10 will be equal to 9 which is equal to z. The question clearly asks if z will be greater than the average of x and 10. So am not too sure if A is sufficient. If it were greater than or equal to then , your argument is correct.

Hi Gmatsoon,

The statement 1) clearly says 'z is closer to 10 than to x' which means, you cannot consider z=9, x=8 as it would mean it is equidistant from x and 10 (by a value of 1).
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04 Oct 2005, 00:02
We're told that:

a) 0 < x < 10

We're asked whether z > (x+10)/2 ==> z > x/2 + 10

From statement 1, if z = 9 and x = 8, then x/2 + 10 = 14 and z < x/2 + 10
if z = 9 and x = 0, then x/2 + 10 = 10 and z < x/2 + 10

So z will always be smaller and we're able to answer the question. Statement 1 is therefore sufficient.

From statement 2, we can equate z/5 = x so x/2 + 10 = z/10 + 10 and we can't tell if z is greater than or less than x.

Ans: A

PS: If you're abe to answer yes or no for thsi question, then the statement is sufficient.

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04 Oct 2005, 00:02
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# If x is a positive number less than 10, is z greater than

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