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01 Jul 2021, 05:00
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:37) correct
20%
(02:18)
wrong
based on 105
sessions
History
Date
Time
Result
Not Attempted Yet
A popular yoga studio that is always filled to capacity moves to a new location that is able to serve 45% more students. Unfortunately, 20% of the current students will no longer attend classes at the new location. If classes at the new location are also filled to capacity, what fraction of the students at the new location will be new students?
(A) \(\frac{25}{29}\)
(B) \(\frac{20}{29}\)
(C) \(\frac{16}{29}\)
(D) \(\frac{13}{29}\)
(E) \(\frac{9}{29}\)
(A) \(\frac{25}{29}\)
(B) \(\frac{20}{29}\)
(C) \(\frac{16}{29}\)
(D) \(\frac{13}{29}\)
(E) \(\frac{9}{29}\)
01 Jul 2021, 05:37
Kudos
Bookmarks
let the no of students at initial stage be 100
new classroom capacity will be 45% higher than current, therefore new capacity will be of 145 student
from initial capacity 20% don't attend new classes, therefore only 80 out of 100 attend new classes from initial classroom strength
since 145 new capacity is completely full, new student who joined will be = 145-80 = 65 (80 are one who still continues with new classroom)
therefore fraction of new students enrolled will be = 65/145 = 13/29
option D
new classroom capacity will be 45% higher than current, therefore new capacity will be of 145 student
from initial capacity 20% don't attend new classes, therefore only 80 out of 100 attend new classes from initial classroom strength
since 145 new capacity is completely full, new student who joined will be = 145-80 = 65 (80 are one who still continues with new classroom)
therefore fraction of new students enrolled will be = 65/145 = 13/29
option D
03 Jul 2021, 06:48
Kudos
Bookmarks
You have two methods to solve this problem 1) Algebric - Working with formulas to arrive to a fraction of new students /total students 2) Plug in smart numbers
I would suggest you to plug in smart numbers so let S0 be student before enlarging capacity and be equal to 1000 and let C0 be the original capacity and be 1000 (remember that in origin the location was full up to its capacity thus students=maximum capacity of studio in terms of student).
Then be S1 (students after reduction of 20%)= 1000* (80/100) = 800
Then C1 (capacity after 45% increase) = 1000 * (145/100) =1450
Given that the new studio will be full again we have to add a X number of new students so that the ratio of students to new capacity equals zero
Thus (800/1450) + (X/1450) =1 and so we need 650 new students.
650 new students to a total of 1450 students is 13/29 thus D
I would suggest you to plug in smart numbers so let S0 be student before enlarging capacity and be equal to 1000 and let C0 be the original capacity and be 1000 (remember that in origin the location was full up to its capacity thus students=maximum capacity of studio in terms of student).
Then be S1 (students after reduction of 20%)= 1000* (80/100) = 800
Then C1 (capacity after 45% increase) = 1000 * (145/100) =1450
Given that the new studio will be full again we have to add a X number of new students so that the ratio of students to new capacity equals zero
Thus (800/1450) + (X/1450) =1 and so we need 650 new students.
650 new students to a total of 1450 students is 13/29 thus D
