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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards