What is the average (arithmetic mean) of A, B, and 4C?

This topic has expert replies
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 am
Thanked: 1 times
Followed by:5 members
What is the average (arithmetic mean) of A, B, and 4C?

(1) A + B = 17

(2) C^2 = 49

The OA is the option E.

Using both statements together is not sufficient to get an answer? Experts, can you show me what is the best way to solve this PS question?

Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Sat Mar 03, 2018 12:33 pm
$$mean\ of\ A,\ B\ and\ 4C\ is\ =\frac{A+B+4C}{3}$$
$$If\ c^2=49$$
$$then\ c=\sqrt{49}=\left(\frac{+}{-}7\right)$$
$$i.e\ c=+7\ and\ c=-7$$
[A+B=17], when c=+7
$$mean=\ \frac{17+4\left(7\right)}{3}=15$$
when c=-7
$$mean=\ \frac{17+4\left(-7\right)}{3}=\frac{11}{3}$$

Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

by Vincen » Tue Mar 06, 2018 3:45 am
Hello Gmat_mission.

We are asked for $$\frac{A+B+4C}{3}=?$$

(1) A+B=17.

This implies that $$\frac{A+B+4C}{3}=\frac{17+4C}{3}=?$$ Hence, we cannot determine the average.

$$\left(2\right)\ \ C^2=49.$$

This implies that C=7 or C=-7. Hence we get $$\frac{A+B+4C}{3}=\frac{A+B+4\left(\pm7\right)}{3}=\frac{A+B\pm28}{3}=?$$ Hence, we cannot determine the average.

Using both statements together we get $$\frac{A+B+4C}{3}=\frac{17\pm28}{3}.$$ We have two options $$\frac{A+B+4C}{3}=\frac{17+28}{3}=\frac{45}{3}=15$$ or $$\frac{A+B+4C}{3}=\frac{17-28}{3}=-\frac{11}{3}.$$ Since the options are different, hence this option is NOT sufficient.

Therefore, the correct answer is E.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Mar 07, 2018 9:09 pm
M7MBA wrote:What is the average (arithmetic mean) of A, B, and 4C?

(1) A + B = 17

(2) C^2 = 49

The OA is the option E.

Using both statements together is not sufficient to get an answer? Experts, can you show me what is the best way to solve this PS question?
You are supposed to calculate the value of (A + B + 4C)/3.

Certainly (1) and (2) alone are not sufficient. While (1) does not have the value of C, (2) does not have the value of A and B.

Even combining the two statements will not help as C^2 = 49 gives two values of C = 4 and -4. Thus, with each value of C, you get different values of (A + B + 4C)/3. In DS, we want a unique value, which is not the case here. Insufficient.

The correct answer: E

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.