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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- ayushiiitm
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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
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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