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A teacher administers a test to two classes. She adds 15 points to eac

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A teacher administers a test to two classes. She adds 15 points to eac  [#permalink]

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New post 03 Dec 2019, 01:22
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Question Stats:

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A teacher administers a test to two classes. She adds 15 points to each student’s score in the first class and 10 points to each student’s score in the second class, which increases the overall average of the two classes by 13.5 points. If the ratio of the number of students in the first class to the number of students in the second class is p:q where p and q are positive integers with no common factors, what is the value of p+q?

A. 8
B. 9
C. 10
D. 11
E. 13


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Re: A teacher administers a test to two classes. She adds 15 points to eac  [#permalink]

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New post 03 Dec 2019, 02:33
Bunuel wrote:
A teacher administers a test to two classes. She adds 15 points to each student’s score in the first class and 10 points to each student’s score in the second class, which increases the overall average of the two classes by 13.5 points. If the ratio of the number of students in the first class to the number of students in the second class is p:q where p and q are positive integers with no common factors, what is the value of p+q?

A. 8
B. 9
C. 10
D. 11
E. 13


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10........13.5........15
-3.5 +1.5
Wq/Wp=Q/P=1.5/3.5
P/Q=3.5/1.5
Since P and Q are integers and have no common factors
P/Q=7/3
P+Q=10
C:)
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Re: A teacher administers a test to two classes. She adds 15 points to eac  [#permalink]

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New post 03 Dec 2019, 03:08
total avg ; 13.5
class A = 15 points is 1.5 away and class B = 10 points is 3.5 away
ratio ; 1.5:3.5 ; 3:7
p+q = 10
IMO C

Bunuel wrote:
A teacher administers a test to two classes. She adds 15 points to each student’s score in the first class and 10 points to each student’s score in the second class, which increases the overall average of the two classes by 13.5 points. If the ratio of the number of students in the first class to the number of students in the second class is p:q where p and q are positive integers with no common factors, what is the value of p+q?

A. 8
B. 9
C. 10
D. 11
E. 13


Are You Up For the Challenge: 700 Level Questions
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Joined: 05 May 2019
Posts: 163
GPA: 3
A teacher administers a test to two classes. She adds 15 points to eac  [#permalink]

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New post 06 Dec 2019, 02:19
The Answer is C
Algebraic Method

For Class 1 - Sum of Scores = S1, and P(or multiple of P) Students. Either way, P works.
For Class 2 - Sum of Scores = S2, and Q(similar to P) Students.

The average of the two classes increases by 13.5 marks.
Equate this to get \(\frac{(S1+15P)+(S2+10Q)}{P+Q} = \frac{S1+S2}{P+Q}+13.5\)

Simplify and get \(\frac{P}{Q}=\frac{3.5}{1.5}\)

convert to integer form and simplify further to get \(\frac{P}{Q}=\frac{7}{3}\)

This is the reduced form (no common factors). Add and get \(P+Q = 10\)
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A teacher administers a test to two classes. She adds 15 points to eac   [#permalink] 06 Dec 2019, 02:19
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