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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon May 23, 2011 10:12 pm
Akansha wrote:If x is a positive number less than 10, is z greater than average of x and 10?
a. z is closer to 10 than x on the number line
b. z = 5x

OA is A
Question is: If x < 10, then is z > (x + 10)/2)?

(1) z is closer to 10 than x on the number line implies that distance between z and 10 is less than the distance between z and x (see the number line below).
Image

So, z is more closer to 10 implies that average of x and 10 will be less than z.
So, z > (x + 10)/2) holds true.
So, (1) is SUFFICIENT.

(2) z = 5x does not give us the required info to decide whether z > (x + 10)/2) or not.
So, (2) is NOT SUFFICIENT.

The correct answer is A.
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by mmenifi » Tue May 24, 2011 7:57 am
What if x=8 and Z=9, in this case 9 is not > (8+10)/2.

any insights
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by djiddish98 » Tue May 24, 2011 8:31 am
In that case though, Z is not closer to 10 than x - it is an equal distance apart.
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by mmenifi » Tue May 24, 2011 8:35 am
Based on my previous comment A is also insufficient.
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by djiddish98 » Tue May 24, 2011 10:13 am
mmenifi wrote:What if x=8 and Z=9, in this case 9 is not > (8+10)/2.
Statement 1 says that Z is closer to 10 than x. In your example however, Z is as close to X as it is to 10. Hence, you can't use your example, since it doesn't comply with the statement.
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