[email protected] wrote: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
C
Easiest way to do this is going to be picking numbers. Since the question is asking us which of the following IS ALWAYS equivalen, we want to pick numbers to show that the roman numerals can give a different result, so we can eliminate that roman numeral.
On most roman numeral questions we start with the statement that appears most frequently in the choices, so let's start with (I).
Let's choose {1, 2, 3, 4, 5}
If we add them then divide by 5, we get 15/5 = 3
If we mutiply then take the 5th root, we get the 5th root of 120 which is certainly NOT = 3.
So, (I) is out: eliminate (b) and (e).
(II) and (III) are equally represented, so start with the one that seems simpler.
III. Ordering the 5 numbers numerically and then selecting the middle number.
Let's choose {1, 2, 3, 4, 6} (Remember, we're trying to choose numbers that DO NOT work out the same for both rules!)
If we take the middle number (statement III), we get 3.
If we add and divide by 5, we get 3.2
So, (III) is out: eliminate (D).
Sadly, it could still be (a) or (c), so we need to check (II).
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
Let's choose {1, 2, 3, 4, 6} again.
If we add, double and move the decimal, we get 3.2
If we add and divide by 5, we get 3.2
hmm.. let's think about this for a sec..
Moving the decimal to the left is the same as dividing by 10.
Doubling and dividing by 10 is the same as dividing by 5.
So, "Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left" is actually the same as "adding 5 given numbers and then dividing the sum by 5".
Choose (C) II only.
