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Difficulty:
85%
(hard)
Question Stats:
41% (03:08) correct
59%
(03:14)
wrong
based on 27
sessions
History
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Yesterday, 3/4 of the students enrolled in a French course were born before the year 2000. Today, 44 people joined the French course, and now 4/5 of the students were born before the year 2000. Assuming that no students have dropped out of the course today, what is the median of the set of possible numbers of currently enrolled students born before the year 2000?
A. 64
B. 112
C. 120
D. 128
E. 140
A. 64
B. 112
C. 120
D. 128
E. 140
01 Sep 2026, 06:19
Kudos
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It's a bit long, but this was my approach. Would love to see shortcuts, if any.
Let number of students who studied French yesterday be represented by F
(3/4)*F must be an integer => F=4n
Yesterday
Total no. of students = F = 4n
No. of students born before 2000 = (3/4)F = 3n
Today
Total no. of students = F+44 = 4n+44
Now these additional 44 students could belong to the group which was born before 2000 or may be some part of them could belong to the group.
Let the additional students who were born before 2000 be represented by x
No. of students born before 2000 = 3n + x
We also know that today the ratio is 4/5
=> 4/5 = (3n+x) / (4n +44)
=> 16n + 176 = 15n + 5x
=> n = 5x - 176
The ratio is changing from 3/4 to 4/5. The ratio is increasing in value.
This means that we need to consider that more than 3/4 of the new 44 students i.e 33 were born before 2000.
With x = 34, 5x - 176 is negative => Invalid
With x = 35, 5x - 176 is negative => Invalid
With x = 36, 5x - 176 is POSITIVE => VALID
Therefore x can be 36, 37, 38, 39, 40, 41, 42, 43, 44
Median = 40
Remember, the question is asking for the no. of students today who were born before 2000 which are given by 3n +x
= 15x - 528 + x
= 16x - 528
= 16*40 - 528
= 112
Therefore, answer is B 112.
Let number of students who studied French yesterday be represented by F
(3/4)*F must be an integer => F=4n
Yesterday
Total no. of students = F = 4n
No. of students born before 2000 = (3/4)F = 3n
Today
Total no. of students = F+44 = 4n+44
Now these additional 44 students could belong to the group which was born before 2000 or may be some part of them could belong to the group.
Let the additional students who were born before 2000 be represented by x
No. of students born before 2000 = 3n + x
We also know that today the ratio is 4/5
=> 4/5 = (3n+x) / (4n +44)
=> 16n + 176 = 15n + 5x
=> n = 5x - 176
The ratio is changing from 3/4 to 4/5. The ratio is increasing in value.
This means that we need to consider that more than 3/4 of the new 44 students i.e 33 were born before 2000.
With x = 34, 5x - 176 is negative => Invalid
With x = 35, 5x - 176 is negative => Invalid
With x = 36, 5x - 176 is POSITIVE => VALID
Therefore x can be 36, 37, 38, 39, 40, 41, 42, 43, 44
Median = 40
Remember, the question is asking for the no. of students today who were born before 2000 which are given by 3n +x
= 15x - 528 + x
= 16x - 528
= 16*40 - 528
= 112
Therefore, answer is B 112.
01 Sep 2026, 07:06
Kudos
Bookmarks
More than 4/5 of the 44 newcomers must have been born before 2000. 4/5 *44 =176/5 =35.2
Thus of the newcomers , between 36 and 44 inclusive were born before 2000. The media of these possibilities is 40.
Thus of the newcomers , between 36 and 44 inclusive were born before 2000. The media of these possibilities is 40.
