In a class of P students, the average (arithmetic mean) of the test sc

Question

In a class of P students, the average (arithmetic mean) of the test scores is 70. In another class of N Students, the average of the scores for the same test is 92. When the scores of the two classes are combined, the average of the test scores is 86. What is the value of P/N?

A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 5/8

A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. ​5/8

RaghavKhanna · Answer

Using the concept of  weighted averages

86 = (70(P) + 92(N)) / (P + N)
=> 86P + 86N = 70P + 92N
=> 16 P = 6N
=>  P/N = 3/8

=>  Answer: C

satya2029 · Answer

70=X/P
92=Y/N
86=Combined Sum/ P+N
86P+86N=X+Y
86P+86N=70P+92N
16P=6N
P/N=6/16
=3/8
C:)

dhawalsachdeva · Answer

Ans (Higher average -combined average)/(Combined average - Lower average)

Therefore Required ratio = (92-86)/(86-70) = 6/16 = 3/8

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bM22 · Answer

Total Score of class P: 70P.
Total score of class N: 92N.
Combined average = (70P + 92N)/(P+N) = 86
=> 70P + 92N = 86P + 86N
=> 6N = 16P.
=> P/N = 6/16 = 3/8.

Answer C.

GMATWhizTeam · Answer

Solution 
 • In a class of P students,
 o Average test score  =\frac{ total \space marks \space obtained \space by \space P \space students }{P} = 70

o So, total marks obtained by P students  = 70P  
• In a class of N students,
 o Average test score   =\frac{ total \space marks \space obtained \space by \space N \space students }{N} = 92

o So, total marks obtained by N students  = 92N  
• When the two classes are combined,
 o Average test score  = \frac{ total \space marks \space obtained \space by \space P \space students \space + \space total \space marks \space obtained \space by \space N \space students }{P+N} = 86

⟹ \frac{70P + 92N}{P+N} = 86

⟹ \frac{35P + 46N}{P+N} = 43

⟹ 35P + 46N = 43P + 43N

⟹ 3N = 8P

⟹\frac{P}{N} = \frac{3}{8}

Thus, the correct answer is  Option C.

Sr1994 · Answer

Total marks of students P = 70P
Total marks of students N = 92N

Combined average = 86

(70P+92N)/(P+N) = 86

70P+92N = 86(P+N)
70P+92N = 86P + 86N

92N-86N = 86P-70P

6N = 16P

P/N = 6/16 = 3/8

Answer C

Archit3110 · Answer

given info
70p+92n = 86*(p+n)
16p= 6n
p/n = 3/8
option c

ScottTargetTestPrep · Answer

Solution:
 
We can create the following weighted average equation:

(70P + 92N)/(P + N) = 86

70P + 92N = 86P + 86N

6N = 16P

3N = 8P

3/8 = P/N

Answer: C

Kinshook · Answer

Given: 
1. In a class of P students, the average (arithmetic mean) of the test scores is 70.
2. In another class of N Students, the average of the scores for the same test is 92. 
3. When the scores of the two classes are combined, the average of the test scores is 86.

Asked: What is the value of P/N?

Average sores combined = (70P + 92N)/(P + N) = 86
70P + 92N = 86P + 86N
16P = 6N
P/N = 6/16 = 3/8

IMO C

Carlosfernando25 · Answer

P Students 
Mean= 70

N Students
Mean= 92

Combined average= 86

70P+92N / P+N = 86

70P+92N = 86P+86N

92N-86N = 86P-70P

6N = 16P

P/N = 6/16

P/N = 3/8 = C.

rounakkedia172 · Answer

A quicker approach would be:

70---------------86--------92
P---------------P+N-------N
|____________|______|
 16 units ...............6 units 
 away from the mean
So 86 is more closer to 92, so the weight will be:
P/N = 6/16 or 3/8.

AnirudhaS · Answer

70p+92n=86(p+n)
or,  \frac{p}{n}=\frac{3}{8}

In a class of P students, the average (arithmetic mean) of the test sc

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