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24 Aug 2022, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:39) correct
38%
(03:00)
wrong
based on 55
sessions
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The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74. The average marks of classes P and R is approximately
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5
Are You Up For the Challenge: 700 Level Questions
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5
Are You Up For the Challenge: 700 Level Questions
24 Aug 2022, 05:18
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Bunuel
The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74. The average marks of classes P and R is approximately
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5
The answer depends on the strength of the classes, and let rose be p, q and r respectively.
Logical
If short of time, I would use a bit of logic to get to the answer.
Average of P and Q is almost midway of the two averages, that is between 62 and 71.
So, p is slightly greater than q.
Average of R and Q is almost closer to 71.
So, q is greater than r.
The above two tell us that p>q>r: So, the average of P and R will be closer to p and between p and r.
Thus, A, D and E are eliminated.
Looking at the combined averages 66 and 74, 64.5 is too close to 62 as compared to distance from 79 to be correct.
C is correct option.
Weighted Average method
62–4–66–5–71, so p:q = 5:4
71–3–74–5–79, so q:r = 5:3
Thus, 5:4 and 5:3 can be combined by multiplying p:q by 5 and q:r by 4 => p:q:r = 5*5:4*5:4*3 = 25:20:12
Or, p:r = 25:12
The combined average of P and R = \(62+\frac{12}{12+25}*(79-62)=62+\frac{12}{37}*17=62+\frac{1}{3}*17=62+5.66=67.6\)
C
24 Aug 2022, 07:48
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Given: The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74.
Asked: The average marks of classes P and R is approximately
Let the number of students of classes P, Q & R be p, q & r respectively
The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively.
The average marks of classes P and Q is 66.
62p + 71q = 66(p+q)
5q = 4p
The average marks of classes Q and R is 74.
71q + 79r = 74(q+r)
3q = 5r
q = 5r/3 = 4p/5
p:q:r = 5/4: 1 : 3/5
The average marks of classes P and R = (62p + 79r)/(p+r) = (62*5/4 + 79*3/5)/(5/4+3/5) = (62*25+79*12)/(25+12) = 67.5
IMO C
Asked: The average marks of classes P and R is approximately
Let the number of students of classes P, Q & R be p, q & r respectively
The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively.
The average marks of classes P and Q is 66.
62p + 71q = 66(p+q)
5q = 4p
The average marks of classes Q and R is 74.
71q + 79r = 74(q+r)
3q = 5r
q = 5r/3 = 4p/5
p:q:r = 5/4: 1 : 3/5
The average marks of classes P and R = (62p + 79r)/(p+r) = (62*5/4 + 79*3/5)/(5/4+3/5) = (62*25+79*12)/(25+12) = 67.5
IMO C
