The average of m, n and p is q and the average of q and r is s. Which of the following is r, in terms of m, n, p and s?

A. (6s - m + n + p)/3

B. (6s - m - n - p)/3

C. (2s - m - n - p)/3

D. (s + m + n + p)/2

E. 2s - m + n + p
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

We are given that the average of m, n and p is q and the average of q and r is s. Thus:

q = (m + n + p)/3

AND

s = (q + r)/2

2s = q + r

r = 2s - q

We can substitute (m + n + p)/3 for q into the second equation and we have:

r = 2s - (m + n + p)/3 = 6s/3 - (m + n + p)/3 = (6s - m - n -p)/3

Answer: B
_________________

Another approach is the INPUT-OUTPUT approach.

First find some values of m, n, p, q, r and s that satisfy all of the given information.

For example, the following values satisfy all of the given information: m = 1, n = 1, p = 1, q = 1, r = 1 and s = 1
In other words, when m = 1, n = 1, p = 1, q = 1 and s = 1, the value of r is 1

QUESTION: Which of the following is r in terms of m, n, p and s?
Since r = 1, we're looking for an answer choice that yields an OUTPUT of 1, when we INPUT m = 1, n = 1, p = 1, q = 1 and s = 1

A. (6s - m + n + p)/3 = (6 - 1 + 1 + 1)/3 = 7/3. No good - we need an OUTPUT of 1. ELIMINATE A.

B. (6s - m - n - p)/3 = (6 - 1 - 1 - 1)/3 = 1. Perfect. KEEP B.

C. (2s - m - n - p)/3 = (2 - 1 - 1 - 1)/3 = -1/3. No good - we need an OUTPUT of 1. ELIMINATE C.

D. (s + m + n + p)/2 = (1 + 1 + 1 + 1)/2 = 2. No good - we need an OUTPUT of 1. ELIMINATE D.

E. 2s - m + n + p = 2 - 1 + 1 + 1 = 3. No good - we need an OUTPUT of 1. ELIMINATE E.

Answer: B

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com

Sign up for our free Question of the Day emails