Problem Solving

Hi there,

Could you give me your ELEGANT, QUICK, and EFFICIENT method to resolve (with these concepts and with finding the solution).


A list of measurements in increasing order is 4, 5, 6, 8, 10, and x. If the median of these measurements
is 6/7 times their arithmetic mean, what is the value of x ?

a)16
b)15
c)14
d)13
e)12

IMO A (16)

median is 7

arithmetic mean is median/(6/7)=7/(6/7)=7*(7/6)=49/6

(4+5+6+8+10+x)/6=49/6
(33+x)/6=49/6
33+x=49
x=16

many thks

OA is A

Nermal wrote:IMO A (16)

median is 7

arithmetic mean is median/(6/7)=7/(6/7)=7*(7/6)=49/6

(4+5+6+8+10+x)/6=49/6
(33+x)/6=49/6
33+x=49
x=16

Nermal how did u know that median was 7?

You have six numbers in increasing order and the median is always the middle number. If there is, as it is here, an even number of numbers you have to add the third and the fourth number and divide this sum by two:
(6+8)/2=7