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

 It is currently 18 Sep 2018, 10:38

### 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

# A number plate is in the format of XXYYYY where X can be any of the 26

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49206
A number plate is in the format of XXYYYY where X can be any of the 26  [#permalink]

### Show Tags

06 Oct 2017, 00:54
00:00

Difficulty:

55% (hard)

Question Stats:

46% (00:49) correct 54% (04:31) wrong based on 41 sessions

### HideShow timer Statistics

A number plate is in the format of XXYYYY where X can be any of the 26 letters and Y can be any number (0-9). How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?

A. 6,760,000
B. 260,000
C. 259,996
D. 259,974
E. 259,324

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6785
Re: A number plate is in the format of XXYYYY where X can be any of the 26  [#permalink]

### Show Tags

06 Oct 2017, 06:51
Bunuel wrote:
A number plate is in the format of XXYYYY where X can be any of the 26 letters and Y can be any number (0-9). How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?

A. 6,760,000
B. 260,000
C. 259,996
D. 259,974
E. 259,324

Hi...

I believe here that the two X and 4 Y themselves can be same or different digits that is it can be said as $$X_1X_2Y_1Y_2Y_3Y_4$$ or ABCDEF where AB are alphabets and CDEF are numbers..

so number is N _ _ _ _ _ ..
$$X_!$$ can be ONLY N so 1 way
$$X_2$$ can be any of 26 digits..
all ys can be any of 10 digits
so ways = 1*26*10*10*10*10= 260,000

But exception is where all Ys are 0, so ways that is possible = 1*26*1*1*1*1=26

ans = 260000-26=259,974
D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1213
Location: India
GPA: 3.82
Re: A number plate is in the format of XXYYYY where X can be any of the 26  [#permalink]

### Show Tags

06 Oct 2017, 06:58
Bunuel wrote:
A number plate is in the format of XXYYYY where X can be any of the 26 letters and Y can be any number (0-9). How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?

A. 6,760,000
B. 260,000
C. 259,996
D. 259,974
E. 259,324

XXYYYY

First X is N so only 1 way possible =1
Second X can be any of the 26 alphabets = 26
All the four Y's can take up any of the 10 digits. Hence no of ways = 10*10*10*10

So total no of ways in which a number plate in the XXYYYY format can be formed = 1*26*10*10*10*10= 260,000

But it is mentioned that the number plates contain atleast one non-zero digit. Hence we need to exclude all those number plates that are of the form
NX0000 = 1*26*1*1*1*1=26

Hence total no of plates possible = 260,000-26=259,974

Option D
Intern
Joined: 02 Feb 2016
Posts: 27
Location: United States
GMAT 1: 710 Q49 V38
GPA: 3.5
Re: A number plate is in the format of XXYYYY where X can be any of the 26  [#permalink]

### Show Tags

06 Oct 2017, 16:05
The plate is in the format: "N"XYYYY

There are 26 possible values for X, 10 each for Y.

Total possibilities = 26x10^4

However, all Y cannot be 0, so, illegal possibilities = 26 x 1

Possible valid plates = 260000 - 26 = 259974
Re: A number plate is in the format of XXYYYY where X can be any of the 26 &nbs [#permalink] 06 Oct 2017, 16:05
Display posts from previous: Sort by

# Events & Promotions

 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®.