while solving statement A, I took the following critical points to solve the eqn |z-x|>|z-10|
x<z<10 : True .. Also the answer
z>10: solving this I got x<10. which is information given in the question stem. I dint know how this can answer the ques. hence, considered A as insufficient .. Pl help
enigma123 wrote:
If x is a positive integer less than 10, is z less 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
Any idea guys how come the answer is A?
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.
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