GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 07:42 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

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.  Call a number Guardian if it is composite but not divisible by 2, 3, o

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

Hide Tags

Senior Manager  Joined: 13 Jun 2013
Posts: 266
Call a number Guardian if it is composite but not divisible by 2, 3, o  [#permalink]

Show Tags

2
8 00:00

Difficulty:   95% (hard)

Question Stats: 29% (03:11) correct 71% (02:53) wrong based on 49 sessions

HideShow timer Statistics

Call a number Guardian if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many Guardian numbers are there less than 1000?
a) 100
b) 102
c) 104
d) 106
e) 108
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Call a number Guardian if it is composite but not divisible by 2, 3, o  [#permalink]

Show Tags

4
1
manpreetsingh86 wrote:
Call a number Guardian if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many Guardian numbers are there less than 1000?
a) 100
b) 102
c) 104
d) 106
e) 108

Dear manpreetsingh86,
I'm happy to respond. Here is my calculation:

Start with the numbers from 1 - 1000. We have 1000 numbers.

Subtract the primes:
1000 - 168 = 832

Now, subtract the even numbers, divisible by 2. There are 500 even numbers in the set, but the first, 2 itself, has already been subtracted with the primes. There are 499 non-prime even numbers in the set, including 1000 itself. (1000 itself really shouldn't be included, because are looking for numbers less than 1000, but it gets subtracted in this step anyway, so it doesn't matter.)
832 - 499 = 333

Now, numbers divisible by 3. There are 333 factors of three between 1 and 1000, but first of all, one of those is the prime number 3, already subtracted, so exclude that --- 332. Of those, half are even, already counted, so that leaves 332/2 = 166 non-prime odd multiples of 3.
333 - 166 = 167

Now, multiples of 5. There are 200 multiples of 5 up to 1000. Half are even, divisible by 10, so eliminate them --- 100 odd multiples of 5. Eliminate the prime number 5 itself, already counted --- 99 non-prime multiples of 5. Now, 1/3 of these are divisible by three, already counted, so we 2/3 of this number ==> 66. There are 66 non-prime multiples of 5 that are not divisible by 3.
167 - 66 = 101

The last number that needs to be subtracted --- not prime, not composite, not a multiple of 2 or 3 or 5, is 1 itself. This is not composite, so it is not a guardian.
101 - 1 = 100
That leaves 100 guardian numbers. OA = (A)

This is mathematically a very intriguing question, but I suspect that it's a notch too intricate and complicated to be something the GMAT would ask.

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
General Discussion
Senior Manager  Joined: 13 Jun 2013
Posts: 266
Re: Call a number Guardian if it is composite but not divisible by 2, 3, o  [#permalink]

Show Tags

1
S1 = total number of numbers divisible by 2 from 1-1000 = 500
S2 = total number of numbers divisible by 3 from 1-1000 = 333
S3 = total number of numbers divisible by 5 from 1-1000 = 200
S4 = total number of numbers divisible by 2 and 3 = 166
S5 = total number of numbers divisible by 2 and 5 = 100
S6= total number of numbers divisible by 3 and 5 =66
S7 = total number of numbers divisible by 2,3 and 5 = 33

thus total number of numbers divisible by 2,3 or 5 are = 500 +333+200-166-100-66+33 = 734

now since we have already included 2,3 and 5 while calculating their multiple in the above calculations, hence total number of prime numbers from 1-1000 becomes = 168-3 =165

also, since 1 is neither composite nor prime, hence we will subtract 1 from the final answer.

thus total number of guardian numbers are 1000-734-1-165 = 100
Non-Human User Joined: 09 Sep 2013
Posts: 13196
Re: Call a number Guardian if it is composite but not divisible by 2, 3, o  [#permalink]

Show Tags

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: Call a number Guardian if it is composite but not divisible by 2, 3, o   [#permalink] 21 Dec 2018, 09:50
Display posts from previous: Sort by

Call a number Guardian if it is composite but not divisible by 2, 3, o

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

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