Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If 72 cupcakes must be divided equally among the students in [#permalink]
19 Nov 2011, 13:07

1

This post received KUDOS

Let number of students be N. Each student will receive 72/N cupcakes.

(1) New number of students is 2N/3. Number of cupcakes per student is reduced by 3, which is 72/N-3. \(\frac{72}{2N/3} = 72/N -3\) This equation can be solved so (1) is SUFFICIENT.

(2) New number of cupcakes is 2*72=144. Each student gets 12. 144/N = 12. N=12. SUFFICIENT.

Re: If 72 cupcakes must be divided equally among the students in [#permalink]
17 Dec 2011, 20:58

D is the answer. Two approaches to solve this:

Approach 1: Simple Algebra Let 'n' be the number of students in the class. Let 'c' be the number of cupcakes each student receives. We are asked to find the value of 'n'. We know that n*c = 72.

Statement 1: Number of students is reduced by 1/3. Thus number of students becomes '2n/3'. Also, each student now receives 3 more cupcakes. Thus the number of cupcakes that each student receives = (c + 3). Again (2n/3)(c + 3) = 72. Using this equation with the one obtained previously, we have nc = (2n/3)(c + 3). Solving this we can get a value of 'c', which can further give us a value of 'n'. Thus SUFFICIENT.

Statement 2: Number of cupcakes is doubled. Thus number of cupcakes now = 72 * 2 = 144 Each student now receives 12 cupcakes. Thus c = 12. Substitute in the equation nc = 144 to find the value of 'n'. Thus SUFFICIENT.

Thus each statement is SUFFICIENT.

Approach 2: Factors 72 cupcakes must be divided equally among the students. Thus, if the number of students in the class is 'n', and the number of cupcakes that each student receives is 'c', then we know that 'n' and 'c' both are factors of 72. We can find out factor pairs of 72 as below: 1 * 72 2 * 36 3 * 24 4 * 18 6 * 12 8 * 9

So 'n' and 'c' both will have values from among the factors listed above. Statement 1: Each student now receives 3 more cupcakes. Thus, we can infer that even (c + 3) is a factor of 72. The numbers that satisfy the condition that both c and (c + 3) are factors of 72 are: c = 1, 3, 6, 9. By having a look at the corresponding pair of factors of the above numbers, we can find that the values of 'n' can be 72, 24, 12 and 8 respectively. That is, if c = 1, n = 72; if c = 3, n = 24 and so on.

Number of students is reduced by 1/3. Thus the new number of students (2n/3) is also a factors of 72. Now from our analysis above, we know that 8 cannot be the value of 'n' because if n = 8, then (2n/3) is not an integer. This is not possible as the number of students has to be an integer. If we take n = 12, then we find that 2n/3 = 8. Thus c = 9. This agrees with our analysis that initially n = 12; new n = 8; previously c = 6; new c = 9. Thus SUFFICIENT.

Statement 2: Number of cupcakes now = 144. Each student receives 2c. Thus 2c = 144. Thus, c = 12. Put this in the original equation to find a value of 'n'. Thus SUFFICIENT.

Thus both statements are SUFFICIENT.

Though the analysis for the second approach is a bit longer, it takes less than 30 seconds to solve using that method. The longer explanation need not imply longer time to think and analyze.

Last edited by siddharthmuzumdar on 04 Jan 2012, 07:05, edited 2 times in total.

The Importance of Financial Regulation : Before immersing in the technical details of valuing stocks, bonds, derivatives and companies, I always told my students that the financial system is...

One question I get a lot from prospective students is what to do in the summer before the MBA program. Like a lot of folks from non traditional backgrounds...