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by ixjoec » Tue Nov 13, 2012 9:47 pm
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



answer is A



can anyone explain this to me?

if x is say 1 and z is 2, wouldn't the arithmetic average be greater than z?
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by FLUID » Tue Nov 13, 2012 11:47 pm
ixjoec wrote:


can anyone explain this to me?

if x is say 1 and z is 2, wouldn't the arithmetic average be greater than z?
You are contradicting to what it says in first statement. please read again.

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

Z is closer to 10 than it is to x

=> if Z is 2 units away from 10 (1.e) 8 then x would be atleast 3 units away from Z
which would be 5.

average of 5 and 10 is 7.5

so , Z which is 8 is > average of 5 and 10 which is 7.5

This holds good for other values as well.

So, (A) is the answer.
Thanks,

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by ixjoec » Wed Nov 14, 2012 8:56 pm
Oh....thanks for clearing that up.
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by Brent@GMATPrepNow » Thu Nov 15, 2012 7:42 am
ixjoec 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
Target question: Is z greater than the mean of x and 10?

Statement 1: On the number line, z is closer to 10 than it is to x.
IMPORTANT: On the number line, the mean of two numbers will lie at the midpoint between those two numbers.
So, the mean of x and 10 will lie halfway between x and 10.
So, if z is closer to 10 than it is to x, then z must lie to the right of the midpoint between x and 10.
This means that z must be greater than the mean of x and 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 5x
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=1, z=5, in which case z is less than the mean of x and 10 (mean = 5.5)
Case b: x=4, z=20, in which case z is greater than the mean of x and 10 (mean = 7)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
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by sana.noor » Wed Oct 02, 2013 4:39 am
i have a question here what if x= 8 z=9 then the average of x and 10 is equal to z
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by theCodeToGMAT » Wed Oct 02, 2013 4:53 am
sana.noor wrote:i have a question here what if x= 8 z=9 then the average of x and 10 is equal to z
If you do so, then you will violate the Statement 1 "1) On the number line, z is closer to 10 than it is to x. "

If x is 8 then z should be 9+ and not N
So, (8+10)/2 = 9 and Z is 9+ ..
SUFFICIENT
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