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

It is currently 08 Dec 2019, 01:27

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

How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2

  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: 59588
How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 08 Apr 2016, 02:48
1
4
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (02:16) correct 53% (02:28) wrong based on 79 sessions

HideShow timer Statistics

Manager
Manager
avatar
B
Joined: 01 Jul 2010
Posts: 56
Location: India
GMAT 1: 660 Q43 V38
GPA: 3.4
GMAT ToolKit User
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 08 Apr 2016, 03:08
Digit A can be filled in 9 ways (excluding 0)
Digit B can be filled in 10 ways
Digit C can be filled in 10 ways
Digit D can be filled in 2 ways (because of modulus A-D )

The answer will be 9*10*10*2 = 1800

Ans C
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8288
How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 08 Apr 2016, 04:53
raarun wrote:
Digit A can be filled in 9 ways (excluding 0)
Digit B can be filled in 10 ways
Digit C can be filled in 10 ways
Digit D can be filled in 2 ways (because of modulus A-D )

The answer will be 9*10*10*2 = 1800

Ans C



hi,
I donot think C should be the answer..
In highlighted portion you have taken following extra ways
1) A=0 and D-8
2) A and D as 1 and 9..so 3*100= 300 extra ways ans 1800-300 = 1500.


we are looking for |A-D|=2 so any of the two can be bigger..
these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..
another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..
so the ways A and D can be placed = 14+1=15 ways..
B and C can be placed in 10*10 ways..


Total = 15*10*10=1500
_________________
Intern
Intern
avatar
Joined: 07 Aug 2014
Posts: 1
Schools: ISB '16
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 22 Apr 2016, 00:58
Ans = 1600 (D)

(1,3)(2,4)...(7,9) = 7*2*10*10 = 1400
(2,0), (8,0) = 2*1*10*10 = 200

=> Ans = 1600
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1870
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 22 Apr 2016, 02:22
1
chetan2u wrote:

hi,
I donot think C should be the answer..
In highlighted portion you have taken following extra ways
1) A=0 and D-8
2) A and D as 1 and 9..so 3*100= 300 extra ways ans 1800-300 = 1500.


we are looking for |A-D|=2 so any of the two can be bigger..
these two can have values (1,2) ; (2,4) so on till (7,9) so total 7*2 = 15..
another arrangement could be A as 8 and D as 0... D as 8 and A as 0 is not possible as number will become 3 digits..
so the ways A and D can be placed = 14+1=15 ways..
B and C can be placed in 10*10 ways..


Total = 15*10*10=1500


Hi chetan2u,

A few observations, highlighted portion might be a typo.
It should read: (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14

Also, If A = 8 and D = 0, then |A-D| = 8 and not 2
Here D = 0, not 10
Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 90
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 23 Apr 2016, 07:50
rathan1488 wrote:
Ans = 1600 (D)

(1,3)(2,4)...(7,9) = 7*2*10*10 = 1400
(2,0), (8,0) = 2*1*10*10 = 200

=> Ans = 1600


i think 8 cannot be consider with 0 their mod diff is 8 not 2 hence 1500. Please correct if i calculated anything wrong
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4834
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 23 Apr 2016, 08:38
Bunuel wrote:
How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2?

A. 2,000
B. 1,900
C. 1,800
D. 1,600
E. 1,500


Good one...


ABCD is a four digit number , so A must be a non zero digit

Further |A – D| = 2

Lets draw a table
Attachment:
A - D Table.PNG
A - D Table.PNG [ 9.21 KiB | Viewed 2264 times ]


So we have A-D 15 possible arrangements

Now go for B & C Possible arrangements
Attachment:
B - C.PNG
B - C.PNG [ 1.52 KiB | Viewed 2259 times ]


For B = The digit can be any number from 0 - 9 ( 10 digits )

For C = The digit can be any number from 0 - 9 ( 10 digits )

So, The possible arrangements is 15 x 10 x 10 = 1500 :-D :lol: :P
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8288
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 23 Apr 2016, 10:53
OptimusPrepJanielle wrote:
chetan2u wrote:

hi,
I donot think C should be the answer..
In highlighted portion you have taken following extra ways
1) A=0 and D-8
2) A and D as 1 and 9..so 3*100= 300 extra ways ans 1800-300 = 1500.


we are looking for |A-D|=2 so any of the two can be bigger..
these two can have values (1,2) ; (2,4) so on till (7,9) so total 7*2 = 15..
another arrangement could be A as 8 and D as 0... D as 8 and A as 0 is not possible as number will become 3 digits..
so the ways A and D can be placed = 14+1=15 ways..
B and C can be placed in 10*10 ways..


Total = 15*10*10=1500


Hi chetan2u,

A few observations, highlighted portion might be a typo.
It should read: (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14

Also, If A = 8 and D = 0, then |A-D| = 8 and not 2
Here D = 0, not 10


Hi there were typos corrected.. Thank you
_________________
Director
Director
User avatar
P
Joined: 18 Dec 2017
Posts: 826
Location: United States (KS)
Premium Member CAT Tests
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2  [#permalink]

Show Tags

New post 29 Nov 2019, 09:28
Bunuel wrote:
How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2?

A. 2,000
B. 1,900
C. 1,800
D. 1,600
E. 1,500


Let's make the difference between A and D as 2.
First lets consider evens:
2 0
0 2
2 4
4 2
6 4
4 6
8 6
6 8

Odds:
1 3
3 1
3 5
5 3
7 5
5 7
9 7
7 9

All Except 0 2 don't work because that won't give us a 4 digit number.

Leaving 0,2 we have 15 choice. That's a straight E.

But to actually calculate, A and D at extremes can take 15 values, The middle two digits can take all 10 digits possible So we have
15*10*10

1500
Answer E
_________________
D-Day : 21st December 2019

The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
GMAT Club Bot
Re: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2   [#permalink] 29 Nov 2019, 09:28
Display posts from previous: Sort by

How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2? 2

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





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