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

 It is currently 15 Dec 2018, 08:08

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• \$450 Tuition Credit & Official CAT Packs FREE

December 15, 2018

December 15, 2018

10:00 PM PST

11:00 PM PST

Get the complete Official GMAT Exam Pack collection worth \$100 with the 3 Month Pack (\$299)
• FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

In how many ways can the letters D, I, G, I, T be arranged so that the

Author Message
TAGS:

Hide Tags

Intern
Joined: 02 Nov 2009
Posts: 17
In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

Updated on: 06 Oct 2017, 05:34
2
12
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:22) correct 53% (01:27) wrong based on 284 sessions

HideShow timer Statistics

In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-letters- ... 20320.html

Originally posted by sudai on 21 Apr 2010, 00:20.
Last edited by Bunuel on 06 Oct 2017, 05:34, edited 2 times in total.
Manager
Joined: 13 Dec 2009
Posts: 113
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

21 Apr 2010, 02:55
2
1
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

36

total number of ways to arrange all the letters = 5!/2!
this includes when both I's are together and not together.
now consider both I's are combined together and arranged, then total number = 4!
these are the arrangements when both the I's are together.

so number of ways when both I's are not together = 5!/2! - 4! = 60-24 = 36
Retired Moderator
Joined: 29 Apr 2015
Posts: 843
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

05 Aug 2015, 11:49
3
1
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

OA:

First, find the number of total choices: the number of ways to arrange 5 letters of which 2 are identical equals the number of arrangements for 5 different letters divided by the number of internal arrangements of the 2 identical letters (which we don't want to count, since they do not yield distinct arrangements):

Next, find the number of Forbidden choices (in which the 2 I's are next to each other) - treat the 2 I's as one, so you have to arrange only 4 terms (3 different digits plus one "big" digit of two Is): that's 4! options.

Note: since the two I's are identical, you need NOT multiply that by the number of internal arrangements of the I's (2!)

Finally, find the number of Good choices:

60 - 4! = 60-24 = 36
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

05 Aug 2015, 13:14
1
1
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

1 D
2 I
1 G
1 T

Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60

Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGT = 4! = 24

Total allowed cases = 60-24 =36

Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 377
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

07 Dec 2016, 19:19
We only care about the two I's, so we can do the following:

5C3 = 10 --> total number of combinations we can have with the two I's

*take 4 away from this number because those are all of the combinations that have the two i's next to each other

Next, when the two i's are in a combination, we have 3x2x1 = 6 ways to arrange the other 3 letters --> thus for each of the 6 combinations for the two i's, we have 6 ways to arrange the other letters --> 6x6 = 36

A.
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

12 May 2017, 21:03
1
Top Contributor
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

13 May 2017, 00:09
BrushMyQuant wrote:
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

_________________
Done. Thank you.
_________________
Manager
Joined: 08 Jun 2017
Posts: 59
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

01 Aug 2017, 05:37
Engr2012 wrote:
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

1 D
2 I
1 G
1 T

Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60

Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGT = 4! = 24

Total allowed cases = 60-24 =36

But cant we consider 4! * 2 as the two Is considered can be arranged in two ways?

mike Bunuel can you guys help me?
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: In how many ways can the letters D, I, G, I, T be arranged so that the  [#permalink]

Show Tags

06 Oct 2017, 05:34
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-letters- ... 20320.html
_________________
Re: In how many ways can the letters D, I, G, I, T be arranged so that the &nbs [#permalink] 06 Oct 2017, 05:34
Display posts from previous: Sort by