let us consider following problem:
Set $S$ and Set $T$ both contain x elements. The average of Set S is $40$. If the average of Set $S$ and Set $T$ combined is $50$, which of the following must be true?
I. The average of Set T is 60.
II. The range of Set T is greater than that of Set S.
III. x is an even number
(A) I only
(B) I & II
(C) II only
(D) I & III
(E) All of the above
answer of this questions says that,average of Set $T$ is $60$,i could not understand,when it says that set $S$ and $T$ contains both $x$ elements,does each one contain $x$ or total?if total let say that $s$ contain $2$ member,then sum of all number of set $s$ is $80$,if total average of $5$ member(let say $x=5$) is $50$,then total sum is $50*5=250$,which means that total sum of set $T$ is $250-80=170$,then average is $170/3= 56.666666666666666666666666666667$,why it should be $60$?please help me
Yes option 1 . It means each one contains x .
average = total strength / number of elements
total is set S = $ 40 *x $
total in set S and T = $ 50*2*x $ . (because total elements in set S and T together is $2x$
so total in set T = total in set S and T - total is set S = $ 60 * x $
so average is 60 in set T containing x elements