GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Jun 2020, 21:25

### GMAT Club Daily Prep

#### 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

# It is known that no more than 7 children will be attending a party. Wh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 02 May 2012
Posts: 10
It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

Updated on: 05 Feb 2019, 06:31
4
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:38) correct 42% (01:08) wrong based on 121 sessions

### HideShow timer Statistics

It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

A. 35
B. 105
C. 180
D. 210
E. 420

Spoiler: :: MY DOUBT
** Can someone please explain to me the intuition behind this answer? I figure it's a very straightforward answer, but what I don't understand is assuming the maximum number of children attend the party which is 7 and among the answers 35 looks to suffice as each child will receive 5 cookies, which makes it the smallest number among the answers. I'm a bit confused can someone point me to the right direction, Thanks. **

Spoiler: :: SOLUTION

Since the number of cookies must be divisible by 1, 2, 3, 4, 5, 6, and 7, let's find the least common multiple of the integers 1, 2, 3, 4, 5, 6, and 7. Every integer is divisible by 1. Let's find the prime factorizations of 2, 3, 4, 5, 6, and 7.

So we want to find the least common multiple of these integers, which we will write in a column.

The largest number of times the prime factor 2 appears in any of these integers is 2, in . The largest number of times the prime factor 3 appears in any of these integers is 1. Similarly, the largest number of times the prime factors 5 appears in any of these integers is 1, and the largest number of times the prime factors 7 appears in any of these integers is 1.

So the least common multiple of the first 7 positive integers must contain 2 prime factors of 2, 1 prime factor of 3, 1 prime factor of 5, and 1 prime factor of 7.

The least common multiple of the first 7 positive integers is 2 × 2 × 3 × 5 × 7 = 420.

The smallest number of cookies that must be brought to the party is 420, choice (E).

Originally posted by iNumbv on 11 Jun 2012, 12:53.
Last edited by Bunuel on 05 Feb 2019, 06:31, edited 3 times in total.
Edited the question and moved to PS forum.
##### Most Helpful Community Reply
Senior Manager
Joined: 28 Mar 2012
Posts: 286
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

11 Jun 2012, 19:27
5
Hi Unan,

The question states that there are no more than 7 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5, 6 or 7 children.

If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.

Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 7).

And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6, 7), i.e., 420.

Answer (E)

Regards,
##### General Discussion
Manager
Joined: 25 Jun 2012
Posts: 54
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

11 Jun 2012, 19:13
I'm reasonably certain that the problem here is that the question is just a little poorly-worded. My assumption is that they want you to give out all of the cookies, in which case the answer is as you posted. If it were not necessary to use all of the cookies, then the answer would actually just be 7, assuming that each child has to get at least 1 whole cookie.
Manager
Joined: 29 Mar 2010
Posts: 110
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

12 Jun 2012, 08:38
1
1
I just took a simpler route.

Because there are no more than 7 children # of cookies has to be divisible by 7.

Question does not tell us how many children are going to show up it has to be divisible by 6 as well. And 5....1.
So what I did was take 6*7=42 and the answer has to be divisible by 5, 4, 3 ,2 1 there is only one answer choice that satisfies these constraints which is 420

So
_________________
4/28 GMATPrep 42Q 36V 640
Intern
Joined: 04 Apr 2011
Posts: 8
Schools: Sloan '16
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

17 Jun 2012, 11:18
I also took the simpler route. Found the answer that was divisible by 1 thru 7.

Question: Why did you multiply 6*7? Did you look for an answer that was also divisible by 42?
Intern
Joined: 06 Mar 2012
Posts: 32
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

17 Jun 2012, 19:13
I agree with the last 2 responses in terms of how to attack the problem. Do not get caught up with the story of the problem. This type of problem is shown in the OG problem solving book with several variations. It all comes down to answering what number is divisible by the constraint (in this case the numbers 1 through 7).
Board of Directors
Status: Emory Goizueta Alum
Joined: 18 Jul 2015
Posts: 3590
It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

24 Jul 2016, 09:58
1
Bunuel wrote:
It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

A. 35
B. 105
C. 180
D. 210
E. 420

No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7.

We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers.

Hence , answer is E.
_________________
My LinkedIn abhimahna. | My GMAT Story: From V21 to V40 | My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
GMAT Club Inbuilt Error Log Functionality - View More | Best Reply Functionality on GMAT Club!
New Visa Forum - Ask all your Visa Related Questions - here | Have OPT questions? - Post them here.
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here. |
Manager
Joined: 21 Jul 2017
Posts: 182
Location: India
Concentration: Social Entrepreneurship, Leadership
GMAT 1: 660 Q47 V34
GPA: 4
WE: Project Management (Education)
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

22 Sep 2017, 19:06
1
1
The question states that there are no more than 7 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5, 6 or 7 children.
Cookies are to be equally divided among the children attending party.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 7).

And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6, 7), i.e., 420.

Answer (E)
--------------------------------------------------------------------------
Hit Kudos if this helped!
Non-Human User
Joined: 09 Sep 2013
Posts: 15060
Re: It is known that no more than 7 children will be attending a party. Wh  [#permalink]

### Show Tags

05 Feb 2019, 06:22
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.
_________________
Re: It is known that no more than 7 children will be attending a party. Wh   [#permalink] 05 Feb 2019, 06:22

# It is known that no more than 7 children will be attending a party. Wh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne