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by ayushiiitm » Thu Jul 22, 2010 9:51 am
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

OA:A
I am usually stumped, as i see numbers placed to number line. Can experts elaborate on the approach to solve questions in which one has to perceive number on 'number line'
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Source: — Data Sufficiency |
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by clock60 » Thu Jul 22, 2010 10:38 am
my try
is z>(x+10)/2, or 2z>x+10

(1) st1 can be transformed in math terms like this
(10-z)<(z-x), from here 2z>(10+x) sufficient

(2)here let us plug numbers
if z=5x, is 5x>(x+10)/2, 10x>x+10. 9x>10 is x>10/9
we are not given fixed value for x so st2 insufficient

just for checking
x=1 z=5.
here 5<(1+10)/2. (5<5.5) the answer is no

x=2 z=10, 10>(2+10)/2 (10>6) the answer is yes
hope my approach is valid
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by outreach » Thu Jul 22, 2010 10:58 am
this problem is discussed before

https://www.beatthegmat.com/gmatprep-num ... 35516.html
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