List L: r, s, t, u, v

List M: w, x, y, z

Each number in each of lists L and M above is positive. The ratio of the average (arithmetic mean) of the numbers in list L to the average of the numbers in list M is 3 to 7. What is the ratio of the average of all the numbers in both lists L and M to the average of the numbers in list L ?

a) $$\frac{10}{7}$$

b) $$\frac{43}{27}$$

c) $$\frac{9}{5}$$

d) $$\frac{23}{12}$$

e) $$\frac{10}{3}$$

## Each number in each of lists L and M above is positive.

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$${{\,{\mu _L}\,} \over {\,{\mu _M}\,}} = {3 \over 7}\,\,\,\,\,\,;\,\,\,\,\,\,\,? = {{\,{\mu _{L \oplus M}}\,} \over {{\mu _L}}}$$DivyaD wrote:List L: r, s, t, u, v

List M: w, x, y, z

Each number in each of lists L and M above is positive. The ratio of the average (arithmetic mean) of the numbers in list L to the average of the numbers in list M is 3 to 7. What is the ratio of the average of all the numbers in both lists L and M to the average of the numbers in list L ?

$$a) \frac{10}{7}\,\,\,\,\,\,b) \frac{43}{27}\,\,\,\,\,\,c) \frac{9}{5}\,\,\,\,\,\,d) \frac{23}{12}\,\,\,\,\,\,e) \frac{10}{3}$$

$${\rm{Take}}\,\,\left\{ \matrix{

\,L = \left\{ {3,3,3,3,3} \right\} \hfill \cr

\,M = \left\{ {7,7,7,7} \right\} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,{\mu _{L \oplus M}} = \mu \left( {\left\{ {3,3,3,3,3,7,7,7,7} \right\}} \right) = {{43} \over 9}$$

$$?\,\, = \,\,{{\,\,{{43} \over 9}\,\,} \over 3}\,\, = \,\,{{43} \over {27}}$$

We follow the notations and rationale taught in the GMATH method.

Regards,

Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)

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Given that the ratio of the average (arithmetic mean) of the numbers in list L to the average of the numbers in list M is 3 to 7, let's take the average of list L = 3x and the average of list M = 7x.DivyaD wrote:List L: r, s, t, u, v

List M: w, x, y, z

Each number in each of lists L and M above is positive. The ratio of the average (arithmetic mean) of the numbers in list L to the average of the numbers in list M is 3 to 7. What is the ratio of the average of all the numbers in both lists L and M to the average of the numbers in list L ?

A. 10/7

B. 43/27

C. 9/5

D. 23/12

E. 10/3

Thus, the sum of 7 numbers in list (M + L) = 4*(7x) + 5*(3x) = 28x + 15x = 43x

Thus, average of 7 numbers in list (M + L) = 43x/9;

Thus, the ratio of the average of all the numbers in both lists L and M to the average of the numbers in list L = (43x/9) / (3x) = 43/27

The correct answer: B

Hope this helps!

-Jay

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