Sixty cookies were equally distributed to x campers. Eight campers did

Question

Sixty cookies were equally distributed to x campers. Eight campers did not want cookies, so their share was redistributed to the other campers, who each received two more. What is the total number of campers?

A. 8
B. 10
C. 12
D. 16
E. 20

A. 8
B. 10
C. 12
D. 16
E. 20

GMATinsight · Answer

i.e. x is a factor of 60 as well as (x-8) is factors of 60 (i.e. two factors of 60 separated by 8)

Also,  \frac{60}{x} + 2 = \frac{60}{x-8}

Factors of 60 are {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}

Factors separated by 8 are  {4 and 12} doesn't satisfy above equation  and  {12 and 20} satisfies above equation

i.e. x = 20

Answer: Option E

GMATWhizTeam · Answer

Solution

• Each of the x campers should get  \frac{60}{x}  cookies.
• Since 8 campers didn't want cookies, so each (x -8) campers got  = \frac{60}{x -8} 
• Now,  \frac{60}{x-8} -\frac{60}{x} = 2 ⟹   = \frac{1}{30 }⟹\frac{8}{x(x-8)} = \frac{1}{30} ⟹\frac{1}{x(x-8)} = \frac{1}{240} =\frac{ 1}{x(x-8) }= \frac{1}{12*20} 
• Therefore, on comparing both sides we get,  x = 20  and  x-8 = 12  
Thus, the correct answer is  Option E.

poojakhanduja3017 · Answer

The answer is E

This question doesn't need full-fledged solving. I am presenting the solution for the community, but hit and trial can help solve this in 15 seconds.

Solution 1: 
Hit and Trial: 
Try with 12. 12 campers has 5 cookies each. Now, 8 of them didn't want, so 40 cookies were redistributed among the remaining 4. So, now each person is getting  5  more cookies. Hence, this is wrong. 
It also tells us that we should try with more. 
Option D can't be right since, 16 is not a factor of 60. 
Option E fits the above logic perfectly.

Solution 1:

STEP 1: Each of the x campers gets y cookies. =>  x*y = 60 
STEP 2: Since 8 campers didn't want their cookies, so remaining (x -8) campers each got :  60/(x−8) 
STEP 3: Solving,  60/(x−8)−60/x=2 
Step 4:  8/(x*(x−8))=1/30 ⟹ x=12

sambitspm · Answer

Follow the attachment

ScottTargetTestPrep · Answer

Solution:

First, let’s list the factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

We see that 2, 4, and 12 are 8 less than 10, 12, and 20, respectively. Let’s try 12 and 20 first.

Let’s say there are 20 campers. So each would have gotten 60/20 = 3 cookies. However, since 8 campers didn’t want cookies, the 60 cookies would then be distributed to 12 campers and each would get 60/12 = 5 cookies. Since this is exactly two cookies more than they would have gotten if everyone had wanted cookies, we see that there must be 20 campers.

Alternate Solution:

When 60 cookies are distributed to x campers, each camper gets 60/x cookies. Since 8 campers didn’t want any cookies, there were (60/x)*8 = 480/x cookies to be redistributed. Since these cookies were distributed to x - 8 campers, each camper got extra (480/x)/(x - 8) = 480/  cookies. We are told that this is equal to 2; hence:

480/  = 2

240/  = 1

x(x - 8) = 240

x^2 - 8x - 240 = 0

(x - 20)(x + 12) = 0

x = 20 or x = -12

Since the number of campers cannot be negative, we see that x must be 20. Thus, there are 20 campers.

Answer: E

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.

Sixty cookies were equally distributed to x campers. Eight campers did

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

Sixty cookies were equally distributed to x campers. Eight campers did

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