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Math Expert V
Joined: 02 Sep 2009
Posts: 60625

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Difficulty:   55% (hard)

Question Stats: 70% (02:25) correct 30% (03:06) wrong based on 46 sessions

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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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Manager  G
Joined: 10 Dec 2017
Posts: 176
Location: India

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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

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:)
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5719
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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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
Yale Moderator G
Joined: 05 May 2019
Posts: 163
GPA: 3

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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 $$P+Q = 10$$ A teacher administers a test to two classes. She adds 15 points to eac   [#permalink] 06 Dec 2019, 02:19
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# A teacher administers a test to two classes. She adds 15 points to eac  