If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?
(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.
(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.
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If 72 cupcakes must be divided equally among the students in
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BTGmoderatorDC
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Jay@ManhattanReview
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Say there are x number of students, thus, each would get 72/x cupcakes.BTGmoderatorDC wrote:If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?
(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.
(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.
Let's take each statement one by one.
(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.
=> The number of students, now = x - x/3 = 2x/3
Thus, each would get 72/(2x/3) = 108/x cupcakes
=> 108/x = 72/x + 3
=> x = 12 students. Sufficient.
(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.
=> (2*72)/x = 12
=> x = 12 students. Sufficient.
The correct answer: D
Hope this helps!
-Jay
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