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

It is currently 17 Aug 2019, 08:18

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

Since 2001, the standard serial numbers on a New York state license pl

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57022
Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 30 Dec 2014, 07:38
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (00:56) correct 24% (01:05) wrong based on 132 sessions

HideShow timer Statistics

Tough and Tricky questions: Combinations.



Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?

A. 26 × 3 × 10 × 4
B. 26 × 25 × 24 × 10 × 9 × 8 × 7
C. 26³ × 9 × 9 × 9 × 9
D. 26 × 25 × 24 × 10 000
E. 26³ × 10 000

Kudos for a correct solution.

_________________
Manager
Manager
User avatar
Joined: 22 Oct 2014
Posts: 87
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45
GPA: 3.8
WE: General Management (Consulting)
Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 30 Dec 2014, 07:57
1
Answer E.

Since the 7 positions are completely independent from each other, we simply need to multiply the possibilities for each of the 7 positions. Each of the three letters allows 26 combinations (assuming 26 different letters) and the digits allow 10 different combinations for each position. We therefore get:

\(26 * 26 * 26 * 10 * 10 * 10 * 10 = 26^3 * 10 ^4 = 26 ^3 * 10,000\)
_________________
\(\sqrt{-1}\) \(2^3\) \(\Sigma\) \(\pi\) ... and it was delicious!


Please consider giving +1 Kudos if deserved!
Manager
Manager
User avatar
B
Joined: 20 Feb 2013
Posts: 74
Location: India
GMAT 1: 690 Q49 V34
WE: Information Technology (Computer Software)
Reviews Badge
Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 30 Dec 2014, 22:25
Solution:
3 repeated letters can be chosen as 26 * 26 * 26
4 repeated digits can be chosen as 10 * 10 * 10 * 10
Answer E
_________________
If my post is helpful/correct, consider giving Kudos..
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57022
Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 08 Jan 2015, 08:18
Bunuel wrote:

Tough and Tricky questions: Combinations.



Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?

A. 26 × 3 × 10 × 4
B. 26 × 25 × 24 × 10 × 9 × 8 × 7
C. 26³ × 9 × 9 × 9 × 9
D. 26 × 25 × 24 × 10 000
E. 26³ × 10 000

Kudos for a correct solution.


OFFICIAL SOLUTION:

(E) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 for the four digits. The number of different license plates is 26 × 26 × 26 × 10 × 10 × 10 × 10 = 26³ × 10 000.

The correct answer is choice (E).
_________________
Intern
Intern
avatar
Joined: 05 Jun 2018
Posts: 1
Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 30 Jun 2018, 04:52
Would the answer be A if the letters and numbers were not allowed to be repeated
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57022
Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 30 Jun 2018, 10:32
Intern
Intern
avatar
B
Joined: 27 Mar 2017
Posts: 49
Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

Show Tags

New post 09 Aug 2019, 22:42
Bunuel wrote:
Bunuel wrote:

Tough and Tricky questions: Combinations.



Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?

A. 26 × 3 × 10 × 4
B. 26 × 25 × 24 × 10 × 9 × 8 × 7
C. 26³ × 9 × 9 × 9 × 9
D. 26 × 25 × 24 × 10 000
E. 26³ × 10 000

Kudos for a correct solution.


OFFICIAL SOLUTION:

(E) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 for the four digits. The number of different license plates is 26 × 26 × 26 × 10 × 10 × 10 × 10 = 26³ × 10 000.

The correct answer is choice (E).


Hi,

I have a slight confusion about this problem.

Since all the answers are permutations, when we say 26 x 26 x 26 x 10 x 10 x 10 x 10 aren't we saying that order matters ?

What I mean to say is that there might very well be a number plate with CLL 1234 and as two Ls will be taken as different under this permutation based method the total count will include another CLL 1234, whereas hey should be counted as just 1 (2 number plates can not be the same).

Shouldn't we make an adjustment for this ?

Will appreciate a response on this please.
GMAT Club Bot
Re: Since 2001, the standard serial numbers on a New York state license pl   [#permalink] 09 Aug 2019, 22:42
Display posts from previous: Sort by

Since 2001, the standard serial numbers on a New York state license pl

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





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