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21 Aug 2019, 23:51
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:38) correct
30%
(02:50)
wrong
based on 47
sessions
History
Date
Time
Result
Not Attempted Yet
A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio of students per class?
A. 3
B. 4
C. 6
D. 8
E. 12
A. 3
B. 4
C. 6
D. 8
E. 12
22 Aug 2019, 05:24
Kudos
Bookmarks
Let x be the current ratio of students per class and c be the number of classes in the school.
From the question stem, we know that for an increase in the ratio by 1, there will be 10 fewer classes for 120 students.
So if x increases to x+1,then c=c-10,
So (x+1)(c-10)=120....... (1)
Additionally when the ratio is not increased it implies that xc=120......... (2)
Making c the subject of equation (1)
(x+1)(c-10)=120
xc-10x+c-10=120
c(x+1)=130+10x
c=(130+10x)/(x+1)
Putting c above into (2)
x((130+10x)/(x+1))=120
130x + 10x^2 = 120x + 120
x^2 + x - 12 =0
(x-3)(x+4)=0
x=3 or x=-4
Testing the values, when the ratio of students per class is 3, adding 1 to it makes the new ratio 4. A ratio of 3 results in 40 classes for 120 students, while 4 results in 30. We can clearly see that there are 10 less classes (40-30).
Meanwhile if the ratio was 4 originally, then the new ratio would be 5. 4 corresponds to 30 classes while 5 corresponds to 24 classes. Difference is 6,which is not 10, hence 4 cannot be the answer.
The answer is therefore A.
Posted from my mobile device
From the question stem, we know that for an increase in the ratio by 1, there will be 10 fewer classes for 120 students.
So if x increases to x+1,then c=c-10,
So (x+1)(c-10)=120....... (1)
Additionally when the ratio is not increased it implies that xc=120......... (2)
Making c the subject of equation (1)
(x+1)(c-10)=120
xc-10x+c-10=120
c(x+1)=130+10x
c=(130+10x)/(x+1)
Putting c above into (2)
x((130+10x)/(x+1))=120
130x + 10x^2 = 120x + 120
x^2 + x - 12 =0
(x-3)(x+4)=0
x=3 or x=-4
Testing the values, when the ratio of students per class is 3, adding 1 to it makes the new ratio 4. A ratio of 3 results in 40 classes for 120 students, while 4 results in 30. We can clearly see that there are 10 less classes (40-30).
Meanwhile if the ratio was 4 originally, then the new ratio would be 5. 4 corresponds to 30 classes while 5 corresponds to 24 classes. Difference is 6,which is not 10, hence 4 cannot be the answer.
The answer is therefore A.
Posted from my mobile device
22 Aug 2019, 05:41
Kudos
Bookmarks
A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio of students per class?
A. 3
B. 4
C. 6
D. 8
E. 12
Fastest would be to solve the problem using the answer choices.
There are total of 120 students (given in question).
Lets try option A - 3 students per class currently
Then the number of classes would be 120/3=40.
Now if 1 student per class is increase then the number of students per class would be 4 and the number of classes would be 120/4=30.
Thus there would be 10 classes less.
Voila! Option A is the correct answer
A. 3
B. 4
C. 6
D. 8
E. 12
Fastest would be to solve the problem using the answer choices.
There are total of 120 students (given in question).
Lets try option A - 3 students per class currently
Then the number of classes would be 120/3=40.
Now if 1 student per class is increase then the number of students per class would be 4 and the number of classes would be 120/4=30.
Thus there would be 10 classes less.
Voila! Option A is the correct answer
