If S denotes the sum and A the average of the consecutive positive int

Question

If S denotes the sum and A the average of the consecutive positive integers 1 through n, then which of the following must be true?

I. A = S/n
II. S = A/n
III. A – S = n

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

Source:   Nova GMAT  
Difficulty Level:   500

BillyZ · Answer

Average = \frac{Sum}{{#}}

Given: S=Sum, A=Average, #=n

A=\frac{S}{n}

Answer:  A

Skywalker18 · Answer

Average, A = Sum of consecutive numbers/number of consecutive numbers
A= S/n
Answer A - I

mohshu · Answer

average = total/ number

only i satisfies the condition,,,option A is the answer

JeffTargetTestPrep · Answer

Let’s analyze each Roman numeral.
 
I. A = S/n
 
This is true since average = sum/quantity.
 
II. S = A/n
 
This is not true since sum is not equal to average divided by quantity.
 
III. A - S = n
 
This is not true. For example, if n = 3, S = 1 + 2 + 3 = 6 and A = 6/3 = 2, but 2 - 6 does not equal 3.
 
Answer: A

If S denotes the sum and A the average of the consecutive positive int

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GMAT Problem Solving (PS) Questions

If S denotes the sum and A the average of the consecutive positive int

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