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

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Director
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If x is a positive number less than 10, is z greater than [#permalink] New post 23 Jun 2007, 01:59
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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
Senior Manager
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Re: DS-AM [#permalink] New post 23 Jun 2007, 03:54
LM 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


Stmt 1: If z is closer to 10, then it (z) will be greater than the mean of 10 and x as x<10. SUFFICIENT

Stmt 2: mean= (10+x)/2=5+(x/2)
z=5x=(9x/2)+(x/2)
since all we know is x<10, we cannot say if 5<(9x/2). INSUFFICIENT

Answer: A
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Re: DS-AM [#permalink] New post 24 Jun 2007, 14:16
sumande wrote:
LM 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


Stmt 1: If z is closer to 10, then it (z) will be greater than the mean of 10 and x as x<10. SUFFICIENT

Stmt 2: mean= (10+x)/2=5+(x/2)
z=5x=(9x/2)+(x/2)
since all we know is x<10, we cannot say if 5<(9x/2). INSUFFICIENT

Answer: A


I agree with this. I think the answer's A, too.

The question doesn't say that z has to be between 0 and 10, just that it's closer to 10 than it is to x. So it's either between the mean and 10, or it's greater than 10, but both ways satisfy statement 1, and both ways are clearly higher than the average.

2 doesn't tell us anything. If x is .2, for example, z is 1, and the mean is 5.1, so the answer would be no. If x is 8, then then z is 40, and the average is 9, so that would be yes. that means, not sufficient.
Re: DS-AM   [#permalink] 24 Jun 2007, 14:16
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