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

It is currently 16 Jul 2018, 02:08

Close

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

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

Close

Request Expert Reply

Confirm Cancel

What are the odds that a 3-digit number contains 3 distinct prime numb

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47012
What are the odds that a 3-digit number contains 3 distinct prime numb [#permalink]

Show Tags

New post 25 Dec 2017, 01:44
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

52% (01:06) correct 48% (01:02) wrong based on 23 sessions

HideShow timer Statistics

Expert Post
examPAL Representative
User avatar
S
Joined: 07 Dec 2017
Posts: 500
Re: What are the odds that a 3-digit number contains 3 distinct prime numb [#permalink]

Show Tags

New post 25 Dec 2017, 02:47
Bunuel wrote:
What are the odds that a 3-digit number contains 3 distinct prime numbers?

A. 3/125
B. 2/75
C. 24/899
D. 3/50
E. 1/15


The tricky part of this question is understanding the question...
We'll break it down, a Logical approach.

If a '3-digit number contains 3 distinct prime numbers' then each of its digits must be a different prime number.
So, we need to know how many single digit prime numbers there are.
These are 2,3,5, and 7.
Then there are 4*3*2 total ways to arrange 3 of these numbers.
Since we have a total of 9 options for the hundreds digit (it cannot be 0!) and 10 options for the tens and ones digits, there are a total of 9*10*10 3 digit numbers.
This gives odds of (4*3*2)/(9*10*10) = 24/900 = 12/450 = 6/225 = 2/75
(B) is our answer.
_________________

David
Senior tutor at examPAL
Signup for a free GMAT course
Image
We won some awards:
Image
Save up to $250 on examPAL packages (special for GMAT Club members)

Manager
Manager
avatar
B
Joined: 24 Nov 2016
Posts: 148
Re: What are the odds that a 3-digit number contains 3 distinct prime numb [#permalink]

Show Tags

New post 25 Dec 2017, 16:37
Bunuel wrote:
What are the odds that a 3-digit number contains 3 distinct prime numbers?

A. 3/125
B. 2/75
C. 24/899
D. 3/50
E. 1/15


One-digit distinct prime numbers are {2,3,5,7}.
From 999 to 100 their are \(999-100+1=900\) different 3-digit numbers.
Favorable outcomes starting from 200 is: {235,237,253,257,273,257} = 6, and the same result will also be for, 300, 500 and 700.
So, the favorable outcomes for all 3-digit number containing 3 distinct prime numbers is \(6*4=24\).

Thus, odds are: \(\frac{Favorable.Outcomes}{Total.Outcomes}=\frac{24}{900}=8/300=4/150=2/75\)

(B) is the answer.
Re: What are the odds that a 3-digit number contains 3 distinct prime numb   [#permalink] 25 Dec 2017, 16:37
Display posts from previous: Sort by

What are the odds that a 3-digit number contains 3 distinct prime numb

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.