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 500,000 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:

The ratio of cupcakes to children at a particular birthday [#permalink]

Show Tags

09 Dec 2012, 08:54

1

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

65% (02:26) correct
35% (02:10) wrong based on 230 sessions

HideShow timer Statistics

The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each child at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday party do not eat anything. If the number of cupcakes that remain uneaten is less than the number of children at the birthday party, what must be true about the number of uneaten cupcakes?

I. It is a multiple of 2. II. It is a multiple of 3. III. It is a multiple of 7.

(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III

The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each child at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday party do not eat anything. If the number of cupcakes that remain uneaten is less than the number of children at the birthday party, what must be true about the number of uneaten cupcakes?

I. It is a multiple of 2. II. It is a multiple of 3. III. It is a multiple of 7.

(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III

Given that: The ratio of cupcakes to children is 104 to 7 --> \(\frac{cupcakes}{children}=\frac{104k}{7k}\);

Each child eats exactly x cupcakes --> the number of cupcakes eaten \(7kx\) and the number of cupcakes that remain uneaten is \(104k-7kx\);

The number of cupcakes that remain uneaten is less than the number of children --> \(104k-7kx<7k\) --> \(x>13\frac{6}{7}\) --> \(x=14\) (notice that x cannot be more than 14 since in this case 7kx>104k, which would mean that more cupcakes were eaten than there were).

Now, if \(x=14\), then the number of cupcakes that remain uneaten is \(104k-7k*14=6k\), thus the number of uneaten cupcakes must be a multiple of both 2 and 3.

The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each child at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday party do not eat anything. If the number of cupcakes that remain uneaten is less than the number of children at the birthday party, what must be true about the number of uneaten cupcakes?

I. It is a multiple of 2. II. It is a multiple of 3. III. It is a multiple of 7.

(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III

Assume there are 104 cupcakes and 7 children.

This line: "If the number of cupcakes that remain uneaten is less than the number of children at the birthday party,"

implies that 104 cupcakes are divided equally among 7 children till you get a remainder less than 7. 104/7 => Quotient is 14 (each child gets 14 cupcakes!) and remainder is 6. 6 is a multiple of 2 and 3.

What happens if there are 208 cupcakes and 14 children? (ratio is multiplied by 2) The quotient will still be 14 and the remainder will be 12 (the remainder will be multiplied by 2)

104a = 7a*14 + 6a

The remainder 6a will always be divisible by 2 and 3. Answer (D)
_________________

Assuming that each kid eats the exact same amount of cupcakes just pick any number. So any multiple of 7 can be taken away from 104, i took 14 (each kid eats 2). 90 is only divisible by 2 and 3 not by seven.

One additional condition is that number of leftover cupcakes must be less than the number of kids. So 90 leftover cupcakes is not correct. But even if we ignore this condition, note that 90 is divisible by 2 and 3 but not by 7 so we can say that 7 is certainly out. But can we say that in every case, the leftover cupcakes WILL BE divisible by 2 and 3? Not necessary!

Re: The ratio of cupcakes to children at a particular birthday [#permalink]

Show Tags

09 Sep 2013, 22:43

7 children eat 7x cupcakes.Let Z be the no. of cupcakes left, less than 7 7x+ z=104 7x=104-z. Now, 104-z must be more than 97 and must be divisible by 7, it can be only 98 7x=98+6 6 cupcakes left, so it is a multiplier of 2 and 3.

Re: The ratio of cupcakes to children at a particular birthday [#permalink]

Show Tags

13 Feb 2014, 21:31

What is being asked is what is the remainder and its factors.

Given that 104 is not a multiple of 7 AND given that the proportionality of the ratio will be kept (unless otherwise stated), no matter which (f) factor you apply: You can express the ratio as a division with remainder (it is stated in the problem that R(f)<7(f)) to account for all the cupcacakes:

The remainder is 6(f), so it must be a multiple of 2 and 3, no matter by which (f) the R (and the entire ratio) is multiplied. You can substitute the (f) for other numbers and 6 and (f) are, obviously, the factors of the remainder.

Re: The ratio of cupcakes to children at a particular birthday [#permalink]

Show Tags

10 Dec 2014, 07:38

Is it also correct to just do it like this:

Assuming that each kid eats the exact same amount of cupcakes just pick any number. So any multiple of 7 can be taken away from 104, i took 14 (each kid eats 2). 90 is only divisible by 2 and 3 not by seven.

Re: The ratio of cupcakes to children at a particular birthday [#permalink]

Show Tags

20 Sep 2016, 05:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...