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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 May 2006, 16:17
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If x is a positive number less than 10, is z greater than the average of x and 10

1. on the number line, z is closer to 10 than it is to x
2. z=5x
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30 May 2006, 16:32
A?

1. The average of x and 10 will be at the same distance from x and 10. Since is closer to 10, and x < 10, z has to be greater than average of x and 10. SUFF.

2. If x = 1 => z = 5; Average of x and 10 = 11/2 = 5.5 > z
If x = 2 => z = 10; Average of x and 10 = 12/2 = 6 < z.
INSUFF.
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30 May 2006, 17:12
giddi77 wrote:
A?

1. The average of x and 10 will be at the same distance from x and 10. Since is closer to 10, and x < 10, z has to be greater than average of x and 10. SUFF.

2. If x = 1 => z = 5; Average of x and 10 = 11/2 = 5.5 > z
If x = 2 => z = 10; Average of x and 10 = 12/2 = 6 < z.
INSUFF.

agree with giddi77, however z cannot be 10.

1. if st 1 is true, z is always greater than the average of x and 10.
2. if x = 0.2, z = 1 where as the avg of 10 and x is > than z. if x = 1.9, z = 9.55, which is > than the avg of x and 10.
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30 May 2006, 18:38
A it is.

More simple explanations

1. on the number line, z is closer to 10 than it is to x

x=9, so average of x and 10 = 9.5, z at least =9.6 suff to answer.

2. z=5x

x=9, z = 45 greater than average.
x=1, z = 5 less than average, not suff to answer.
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30 May 2006, 21:30
A

1) z is closer to 10 on the number line than to x and x is less than 10
In all cases of x from 0-9 if z is closer to 10 , it is greater than the average of 10 and x

2) z=5x

When x = 8 , AV = 9 and z = 40 hence z> AV
When x = 1 , AV = 5.5 and z =5 hence z< AV
therefor not suff
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07 Oct 2006, 23:19

1) Consider the example of X =9 and Z = 9.1

Z is closer to 10 compared to X

Avg of X and 10 = 19/2 = 9.5 > Z

2) Consider the example of X = 9 and Z = 9.6

Z is closer to 10 compared to X

Avg of X and 10 = 19/2 = 9.5 < Z

Senior Manager
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07 Oct 2006, 23:58
withme wrote:

1) Consider the example of X =9 and Z = 9.1

Z is closer to 10 compared to X

Avg of X and 10 = 19/2 = 9.5 > Z

2) Consider the example of X = 9 and Z = 9.6

Z is closer to 10 compared to X

Avg of X and 10 = 19/2 = 9.5 < Z

The first examplae has a wrong value for z the statement z is closer to as compared to x means that 10 - z<z-x
Therefor on a number line z will always be on right hand side of the mid pt of segment x-10 therefore z will be greater than the average.

Hope this helps

Yogesh
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08 Oct 2006, 01:35
If x is a positive number less than 10, is z greater than the average of x and 10

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

on the number line the average of any two numbers is exactly in the middle of the distance between them

so from stem all we need to know whether z lies in the half closer to 10 or that of x

from one

it is closer to 10 thus sure it is greater than the average ( either greater than 10 or just greater than 10+x / 2 ........suff

from two

z =5x z takes different places with different values of x......insuff

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08 Oct 2006, 04:36
A

Statement 1: If Z is closer to 10 than x, then that means Z is greater than half the distance between x and 10 on the number line. SUFF

Statement 2: If x=1, then not true, but if x=2, then true. INSUFF
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08 Oct 2006, 05:05
The average of any two numbers is the number equidistant from those two numbers.

Clearly 1 says z is closer to 10 which means Z will be definitely greater than the average.
So sufficient

Statement 2 is not sufficient...........(many ways already explained)\

So A
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08 Oct 2006, 05:05
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