Official GMAT Test Question - Arithmetic

Adding 5 numbers and dividing the sum by 5:
Case 1: If numbers are {1,2,3,4,5} then sum = 15 and result = 15/5 = 3
Case 2: If numbers are {2,4,4,10,15} then sum = 35 and result = 35/5 = 7

ST1: Multiplying the 5 numbers and then finding the 5 th root of the product.
Case 1: Product of 5 nos = 120 and 5th root is NOT EQUAL to 3 (Not TRUE)
Caes 2: Product of 5 nos = 2^6 * 3 * 5^2 and 5th root is NOT EQUAL to 7 (Not TRUE)
NOT TRUE

St2: Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
Case 1: Sum of 5 nos = 15, Mult by 2 = 30 and taking decimal 1 place to the left = 3 (True)
Case 2: Sum of 5 nos = 35, Mult by 2 = 70 and taking decimal 1 place to the left = 7 (True)
TRUE

ST3: Ordering the 5 numbers numerically and then selecting the middle number.
Case 1: Numerically ordering 5 nos = {1,2,3,4,5}, middle number = 3 (TRUE)
Case 2: Numerically ordering 5 nos = {2,4,4,10,15}, middle number = 4 (NOT TRUE)
Not True

Hence only statement 2 is always TRUE.
Ans C

Ans:
take any 5 numbers :
1,3,4,5,6
Adding them : 1+3+4+5+6 = 19
19/5 = 3.8
A)incorrect.
B)
sum = 19
19*2 = 38 shifting decimal to left gives 3.8 which is equal to 19/5 i.e. 3.8
C)incorrect as it gives 4 as middle term.

sparkles3144 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 5 th 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

I am really lost.
Can someone please help me?

Thanks!