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

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Thu Mar 01, 2018 6:52 am

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?

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Source: Beat The GMAT — Data Sufficiency | Thu Mar 01, 2018 6:52 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed 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
$$mean=\ \frac{17+4\left(-7\right)}{3}=\frac{11}{3}$$

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

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.

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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
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