If the average (arithmetic mean) of 3, 8, w, x, and y is 14,

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Nov 01, 2018 5:21 am

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If the average (arithmetic mean) of 3, 8, w, x, and y is 14, then the average of w + 2, x - 3, and y + 8 is

A. 11
B. 13.2
C. 17
D. 19.4
E. 22

OA E

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Thu Nov 01, 2018 5:21 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Nov 01, 2018 5:42 am

BTGmoderatorDC wrote:If the average (arithmetic mean) of 3, 8, w, x, and y is 14, then the average of w + 2, x - 3, and y + 8 is

A. 11
B. 13.2
C. 17
D. 19.4
E. 22

Source: Magoosh

$$\left. \matrix{
? = \,\,{{\left( {w + 2} \right) + \left( {x - 3} \right) + \left( {y + 8} \right)} \over 3} = {{\left( {w + x + y} \right) + 7} \over 3}\,\,\, \hfill \cr
{{3 + 8 + w + x + y} \over 5} = 14\,\,\,\,\, \Rightarrow \,\,\,\,w + x + y = 70 - 11 \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {{70 - 11 + 7} \over 3} = {{66} \over 3} = 22$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8135; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Nov 02, 2018 4:04 pm

BTGmoderatorDC wrote:If the average (arithmetic mean) of 3, 8, w, x, and y is 14, then the average of w + 2, x - 3, and y + 8 is

A. 11
B. 13.2
C. 17
D. 19.4
E. 22

We can create the equation:

(3 + 8 + 14 + w + x + y)/6 = 14

25 + w + x + y = 84

w + x + y = 59

Thus, the average of w + 2, x - 3, and y + 8 is:

average = [(w + 2) + (x - 3) + (y + 8)] / 3 = (w + x + y + 2 - 3 + 8) / 3

= (59 + 2 - 3 + 8 ) / 3 = 66/3 = 22

Answer: E

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