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a manhattan data question

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a manhattan data question

by diebeatsthegmat » Sun Aug 22, 2010 12:00 pm
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

hi guys, can you explain for me why the answer is A but not E bc from statement if z=9 ( also close to 10) and x=8 thus 9=(10+8)/2??
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by skprocks » Sun Aug 22, 2010 12:09 pm
diebeatsthegmat wrote: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

hi guys, can you explain for me why the answer is A but not E bc from statement if z=9 ( also close to 10) and x=8 thus 9=(10+8)/2??
Solution: From Statement 1 we can say that min. value of z=6 when X=1.This shall meet the criterion that Z shall be closer to 10 as compared to the distance between X and 10.
And unless Z < 6, Z > (x+10)/2

Stmt2: z=5x Take the case x=1,z=5 so z<(x+10)/2 i.e. 5<5.5
Take Z=10,X=2 Z> (x+10)/2 i.e. 10 > 6
Hence,Stmt 2 is Insufficient So, OA is A and not E Hope it helps!!
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by Makushr1 » Sun Aug 22, 2010 12:17 pm
diebeatsthegmat wrote: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

hi guys, can you explain for me why the answer is A but not E bc from statement if z=9 ( also close to 10) and x=8 thus 9=(10+8)/2??
(1) states that Z is CLOSER to 10 than x, which means if Z is 9, X must be less than (but not equal to) 8. Closer is the key word here.

Hope that helps.
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