A group of n college students bought three identical round cakes to sh

Question

A group of n college students bought three identical round cakes to share. They divided the first cake into equal-sized pieces, one piece for each of them. They did the same with the second cake. After 3 of the students decided they did not want any more cake, the remaining students divided the third cake into equal-sized pieces, one piece for each of them. If Silvia received 1 piece from each of the three cakes, then, in terms of n, the amount of cake that she received was the same as what fraction of 1 cake?

A. \(\frac{n+2}{n(n−3)}\)

B. \(\frac{2n−3}{n(n−3)}\)

C. \(\frac{3n−3}{n(n−3)}\)

D. \(\frac{3n−6}{n(n−3)}\)

E. \(\frac{3n−3}{2n(n−3)}\)

A.  \frac{n+2}{n(n−3)}

B.  \frac{2n−3}{n(n−3)}

C.  \frac{3n−3}{n(n−3)}

D.  \frac{3n−6}{n(n−3)}

E.  \frac{3n−3}{2n(n−3)}

amkathikar · Accepted Answer

(1/n + 1/n + 1/(n-3)) = 2/n + 1/(n-3) = 3n-6/n(n-3)

Archit3110 · Answer

I did the following way let n be 9 
so cake 1 ; 9 pieces
Cake 2 : 9 pieces
Cake 3 : 6 pieces

total pieces received by Silvia is 3

total cake pieces : 9+9+6= 24

1/9+1/9+1/6= 7/18

i.e. option D suffices this relation
  \frac{3n−6}{n(n−3)}

Tiburcio1987 · Answer

So what I would do here is basically to work with the numbers.
Let's sat that there are 10 students, so Silvia eats 
1/10 + 1/10 + 1/7 = 24/70

I would plug the numbers in and check for the correct answer. 
D

ScottTargetTestPrep · Answer

For the first and second cakes, Silva received 1/n + 1/n = 2/n of a piece of cake.

The 3rd cake was divided into 1/(n-3) pieces.

Thus, in total Silva had:

2/n + 1/(n - 3) = 2(n-3)/  + n/  = (2n-6)/  + n/  = (3n-6)/

Answer: D

KarishmaB · Answer

Put n = 6.

Sylvia received 1/6 + 1/6 + 1/3 = 2/3 of a cake.

Put n = 6 in options. Since den are same in 4 options, n = 6 gives 6*3 = 18 in the denominator. So we should get 12 in the numerator to get the fraction of 2/3.
When we put n = 6 in numerator of option (D), we get 12.

Answer (D)

varshas044 · Answer

Here is what I did, hope it helps

Total n students

1st cake for n students --------- 1/n part each

2nd cake for n students ----- 1/n part each

3rd cake for (n-3) students -------- 1/(n-3) part each

Sylvia got one of each ----------- she got total of 1/n + 1/n + 1/(n-3) 
Simplify this and you will get (3n -6 ) / n(n-3)

Fraction of the total cake -----  / 1 ===> (3n -6 ) / n(n-3)

Answer D

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A group of n college students bought three identical round cakes to sh

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