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If 72 cupcakes must be divided equally among the students in

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If 72 cupcakes must be divided equally among the students in

by BTGmoderatorDC » Tue Jul 24, 2018 4:57 pm

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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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by Jay@ManhattanReview » Tue Jul 24, 2018 10:18 pm

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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.
Say there are x number of students, thus, each would get 72/x 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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