If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n – 2 ? (A) 9 (B) 13 (C) 14 (D) 18 (E) 26 I'm confused how to set up the formulas here. Can any experts help?

ardz24 wrote:If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n – 2 ? (A) 9 (B) 13 (C) 14 (D) 18 (E) 26 I'm confused how to set up the formulas here. Can any experts help? The average (arithmetic mean) of 3, 6, 10, m and n = (3 + 6 + 10 + m + n)/5 = 9 => m + n = 26 The average of m + 4 and n – 2 = (m + 4 + n – 2)/2 = (m + n + 2)/2; replaing the value of m + n, we get (m + n +2)/2 = (26 + 2)/2 = 14 The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Jakarta | Nanjing | Berlin | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

ardz24 wrote:If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n – 2 ? (A) 9 (B) 13 (C) 14 (D) 18 (E) 26 The average (arithmetic mean) of 3, 6, 10, m and n is 9 So, (3 + 6 + 10 + m + n)/5 = 9 Multiply both sides by 5 to get: 3 + 6 + 10 + m + n = 45 Simplify: 19 + m + n = 45 Subtract 19 from both sides to get: m + n = 26 What is the average of m + 4 and n – 2 ? We get: average = [(m + 4) + (n - 2)]/2 Simplify: average = (m + n + 2)/2 Replace m + n to get: average = (26 + 2)/2 Simplify: average = (28)/2 = 14 Answer: C Cheers, Brent

Hello ardz24. Look, we have that the average of 3, 6, 10, m and n is equal to 9, that is to say: $$\frac{3+6+10+m+n}{5}=9\ \Leftrightarrow\ \ 19+m+n=45\ \Leftrightarrow\ \ m+n=26.$$ Now, we want to find the average of m+4 and n-2, that is to say $$\frac{m+4+n-2}{2}=\frac{m+n+2}{2}=\frac{26+2}{2}=\frac{28}{2}=14.$$ Therefore, the correct answer is the option C.

ardz24 wrote:If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n – 2 ? (A) 9 (B) 13 (C) 14 (D) 18 (E) 26 We can use the formula for the arithmetic mean to create the equation: (3 + 6 + 10 + m + n)/5 = 9 19 + m + n = 45 m + n = 26 We need to determine the average of m + 4 and n – 2; thus: (m + 4 + n - 2)/2 = (m + n + 4 - 2)/2 = (26 + 4 - 2)/2 = 28/2 = 14 Answer: C

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