MBT- Equiv. of add 5 numbers / 5

[kanha81]

Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5?
I. Multiplying the 5 numbers and then finding the 5th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
III. Ordering the 5 numbers numerically and then selecting the middle number.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

How to solve such questions faster and effectively?

[raleigh]

The procedure given is the procedure to calculate the arithmetic mean (average).

I. This one just seems way off. If you think this could somehow be close to the mean, put together a very quick example. Take the numbers 1,2,3,4,5. The mean clearly 3. The product is 120. Does the is 3^5 = 120? Nope. This does not work.

II. The thing here is translating moving the decimal one place to the left as dividing by 10. This should translate to 2(x1 + x2 + x3 + x4 + x5)/10 = (x1 + x2 + x3 + x4 + x5)/5. This is the mean. So this works.

III. That is the procedure for finding the median. We should know that the mean does not always equal the median.

So the answer is C.