NTSE Stage 2 SAT 2016 Question Paper

Question : 59 of 100

Marks: +1, -0

The mean of three positive numbers is 10 more than the smallest of the numbers and 15 less than the largest of the three. If the median of the three numbers is 5, then the mean of squares of the numbers is

$108 2/3$
$116 2/3$
$208 1/3$
$216 2/3$

Validate

Solution:

\a > \b > \c

{\a+\b+\c}/3=\c+10=\a-15=\k

\b=5

\c=\k-10

\a=\k+15

\a+\b+\c=3\k

\k+15+5+\k-10=3\k

10=\k

∴

\a=10+15=25

\b=5

∴

\c=0

mean

={25^2+5^2+0^2}/3

\;\;\;\;\;\;\;\;\;\;\={625+25+0}/3

\;\;\;\;\;\;\;\;\;\;=650/3=216 2/3

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