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?
$$A.\ \frac{6s-m+n+p}{3}$$
$$B.\ \frac{6s-m-n-p}{3}$$
$$C.\ \frac{2s-m-n-p}{3}$$
$$D.\ \frac{s+m+n+p}{2}$$
$$E.\ 2s-m+n+p$$
The OA is B.
I solved this PS question as follow,
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.
Is there a strategic approach to this question? Can any experts help, please? Thanks
The average of m, n, and p is q and the average q and r is s
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Your algebraic approach is perfect.AAPL wrote: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?
$$A.\ \frac{6s-m+n+p}{3}$$
$$B.\ \frac{6s-m-n-p}{3}$$
$$C.\ \frac{2s-m-n-p}{3}$$
$$D.\ \frac{s+m+n+p}{2}$$
$$E.\ 2s-m+n+p$$
The OA is B.
I solved this PS question as follow,
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.
Is there a strategic approach to this question? Can any experts help, please? Thanks
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
Cheers,
Brent
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We can create the equation:AAPL wrote: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?
$$A.\ \frac{6s-m+n+p}{3}$$
$$B.\ \frac{6s-m-n-p}{3}$$
$$C.\ \frac{2s-m-n-p}{3}$$
$$D.\ \frac{s+m+n+p}{2}$$
$$E.\ 2s-m+n+p$$
The OA is B.
(q + r)/2 = s
q + r = 2s
r = 2s - q
However, since q is (m + n + p)/3, we have:
r = 2s - (m + n + p)/3
r = 6s/3 - (m + n + p)/3
r = (6s - m - n - p)/3
Answer: B
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