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

It is currently 22 Nov 2019, 19:07

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

A 6-digit number comprises of only 2’s and 3’s. How many of

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

Hide Tags

Find Similar Topics 
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1096
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
A 6-digit number comprises of only 2’s and 3’s. How many of  [#permalink]

Show Tags

New post 23 Oct 2019, 03:22
1
5
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

44% (02:14) correct 56% (02:11) wrong based on 55 sessions

HideShow timer Statistics

A 6-digit number comprises of only 2’s and 3’s. How many of these are multiples of 12?

A. 0
B. 1
C. 6
D. 20
E. 21

Posted from my mobile device
Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8202
Re: A 6-digit number comprises of only 2’s and 3’s. How many of  [#permalink]

Show Tags

New post 23 Oct 2019, 03:39
2
3
Dillesh4096 wrote:
A 6-digit number comprises of only 2’s and 3’s. How many of these are multiples of 12?

A. 0
B. 1
C. 6
D. 20
E. 21

Posted from my mobile device


For it to be a multiple of 12, the number has to be multiple of 3 and 4..
1) Multiple of 4...
Last two digits have to be multiple of 4....Only combination is 32....ABCD32 .. 1 way
2) Multiple of 3..
Since we have used one 2 in 32, we will require to use 2 more 2s in first four digits..
So, ABCD can take two 2s and two 3s in 4!/2!2!=6way

Total 1*6=6

C
_________________
General Discussion
VP
VP
User avatar
D
Joined: 19 Oct 2018
Posts: 1083
Location: India
Premium Member CAT Tests
Re: A 6-digit number comprises of only 2’s and 3’s. How many of  [#permalink]

Show Tags

New post 23 Oct 2019, 03:40
1
Number must be a multiple of 4; hence, last 2 digits must me 32

Number must be a multiple of 3; hence there can be zero, three or six 2's in the number.

Case 1- numbers comprise of zero 2's and six 3's
Such number can't be a multiple of 4

Case 2- numbers comprise of three 2's and three 3's.
Last 2 digits are 32. We can arrange remaining two 2's and two 3's.

Total possible cases= \(\frac{4!}{2!2!}\)=6

Case 3- numbers comprise of six 2's.
such number can't be a multiple of 4

Total possible cases= 0+6+0=6





Dillesh4096 wrote:
A 6-digit number comprises of only 2’s and 3’s. How many of these are multiples of 12?

A. 0
B. 1
C. 6
D. 20
E. 21

Posted from my mobile device
Senior Manager
Senior Manager
User avatar
G
Joined: 21 Jun 2017
Posts: 307
Location: India
Concentration: Finance, Economics
Schools: IIM
GPA: 3
WE: Corporate Finance (Commercial Banking)
CAT Tests
Re: A 6-digit number comprises of only 2’s and 3’s. How many of  [#permalink]

Show Tags

New post 23 Oct 2019, 08:43
1
1
Last two digits should be 32. Rest 4 digits should be 2233 form ----> 4!/(2!*2!) = 6 = answer
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

GMAT 1 - 620 .... Disappointed for 6 months. Im back Im back. Bhai dera tera COMEBACK !!!


My explanation may not be clear to you, but my requirement of Kudo to survive in my struggle against GMAT is. So spread love , spread Kudo, look at my profile. I'm so benevolent
Intern
Intern
avatar
B
Joined: 19 May 2019
Posts: 29
Re: A 6-digit number comprises of only 2’s and 3’s. How many of  [#permalink]

Show Tags

New post 25 Oct 2019, 12:10
Hello,

I have a silly question, how do you guys know that the 4 first number must include two 2's and two 3's?

Thank you in advance
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8202
Re: A 6-digit number comprises of only 2’s and 3’s. How many of  [#permalink]

Show Tags

New post 25 Oct 2019, 19:17
azl wrote:
Hello,

I have a silly question, how do you guys know that the 4 first number must include two 2's and two 3's?

Thank you in advance



Hi,

We have 32 A’s last two digits.
The first 4 can be any of 3 and 2, but all 6 when added should give you a multiple of 3, a property for multiple of 3.
Now you can have as many 3s as they are multiple of 3, but when you have a 2, either you have a 1 with it as 2+1=3 but that is not possible. So you have to have three or six etc of 2. Here you can have three 2s and one 2 is already used in units digit abcd32. So ABCD can have two 2s and the remaining will be 3s

Posted from my mobile device
_________________
GMAT Club Bot
Re: A 6-digit number comprises of only 2’s and 3’s. How many of   [#permalink] 25 Oct 2019, 19:17
Display posts from previous: Sort by

A 6-digit number comprises of only 2’s and 3’s. How many of

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





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