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24 Feb 2012, 16:50
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A
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Difficulty:
65%
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Question Stats:
59% (01:58) correct
41%
(02:39)
wrong
based on 679
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If x is a positive integer less than 10, is z greater than the average (arithmetic mean) of x and 10 ?
(1) The positive difference between z and x is greater than the positive difference between z and 10.
(2) z = 5x
(1) The positive difference between z and x is greater than the positive difference between z and 10.
(2) z = 5x
24 Feb 2012, 22:15
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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?
Given: \(0<x<10\). Question: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? --> \(2z>10+x\)?
(1) The positive difference between z and x is greater than the positive difference between z and 10 --> \(|z-x|>|z-10|\), which means that the distance between z and x is greater than the distance between z and 10:
x-----average-----10-----
(average of x and 10 halfway between x and 10).
Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES.
Sufficient.
(2) z = 5x --> is \(2z>10+x\)? --> is \(10x>10+x\)? --> is \(x>\frac{10}{9}\). We don't now that. Not sufficient. (we've gotten that if \(x>\frac{10}{9}\), then the answer to the question is YES, but if \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.)
Answer: A.
Similar questions to practice:
https://gmatclub.com/forum/if-x-is-a-po ... 67734.html (OG)
https://gmatclub.com/forum/if-y-is-a-ne ... 95138.html
https://gmatclub.com/forum/if-x-is-a-po ... 31322.html
https://gmatclub.com/forum/if-a-is-a-po ... 05650.html
https://gmatclub.com/forum/if-x-and-z-a ... 55651.html
Hope it helps.
Given: \(0<x<10\). Question: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? --> \(2z>10+x\)?
(1) The positive difference between z and x is greater than the positive difference between z and 10 --> \(|z-x|>|z-10|\), which means that the distance between z and x is greater than the distance between z and 10:
x-----average-----10-----
(average of x and 10 halfway between x and 10).
Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES.
Sufficient.
(2) z = 5x --> is \(2z>10+x\)? --> is \(10x>10+x\)? --> is \(x>\frac{10}{9}\). We don't now that. Not sufficient. (we've gotten that if \(x>\frac{10}{9}\), then the answer to the question is YES, but if \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.)
Answer: A.
Similar questions to practice:
https://gmatclub.com/forum/if-x-is-a-po ... 67734.html (OG)
https://gmatclub.com/forum/if-y-is-a-ne ... 95138.html
https://gmatclub.com/forum/if-x-is-a-po ... 31322.html
https://gmatclub.com/forum/if-a-is-a-po ... 05650.html
https://gmatclub.com/forum/if-x-and-z-a ... 55651.html
Hope it helps.
General Discussion
25 Feb 2012, 03:07
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Thanks Bunuel - I am struggling to understand this:
Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average.
Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average.
