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GMATSkilled
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 28 May 2018, 17:51
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

55% (02:59) correct 45% (03:04) wrong based on 240 sessions

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4 5 6 7

The figure given shows a seating plan of 7 people A, B, C, D, E, F & G during a presentation. Spot numbered 1 is to be taken either by A or B or C who are the board of directors. D & G do not want to sit adjacent to each other in the same row. How many different sitting arrangements can be made?

A. 144

B. 432

C. 576

D. 1584

E. 2160
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D
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chetan2u
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 28 May 2018, 18:52
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GMATSkilled
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4 5 6 7

The figure given shows a seating plan of 7 people A, B, C, D, E, F & G during a presentation. Spot numbered 1 is to be taken either by A or B or C who are the board of directors. D & G do not want to sit adjacent to each other in the same row. How many different sitting arrangements can be made?

A. 144

B. 432

C. 576

D. 1584

E. 2160
Show more

Let's find total ways..
Number 1 can be filled in 3 ways..(A,B,orC)
Rest all can be filled in 6*5*4*3*2*1
Total 3*6*5*4*3*2=2160

Actually choices give the answer straight way..
Answer will be <2160 but > 1/2 of 2160 since D can be with G in the same probability as it can be with E,F ...
Only 1584 fits in

Let's see which all ways D and G are together
D and G can be together at (2,3);(4,5);(5,6);(6,7)
So 4 ways and in these 4 ways they can be DG or GD so 2 ways.. total 4*2 ways

no 1 spot in 3 ways..
And the remaining seats, which are (7-3=4) in number, 4*3*2*1
Total 4*2*3*4*3*2=576

Our answer = 2160-576=1584

D
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 05 Jun 2018, 17:09
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chetan2u
GMATSkilled
1 2 3
4 5 6 7

The figure given shows a seating plan of 7 people A, B, C, D, E, F & G during a presentation. Spot numbered 1 is to be taken either by A or B or C who are the board of directors. D & G do not want to sit adjacent to each other in the same row. How many different sitting arrangements can be made?

A. 144

B. 432

C. 576

D. 1584

E. 2160

Let's find total ways..
Number 1 can be filled in 3 ways..(A,B,orC)
Rest all can be filled in 6*5*4*3*2*1
Total 3*6*5*4*3*2=2160

Actually choices give the answer straight way..
Answer will be <2160 but > 1/2 of 2160 since D can be with C in the same probability as it can be with E,F or G
Only 1584 fits in

Let's see which all ways D and C are together
D and C can be together at (2,3);(4,5);(5,6);(6,7)
So 4 ways and in these 4 ways they can be DC or CD so 2 ways.. total 4*2 ways

no 1 spot in 3 ways..
And the remaining seats, which are (7-3=4) in number, 4*3*2*1
Total 4*2*3*4*3*2=576

Our answer = 2160-576=1584

D
Show more

Hi chetan2u

Could you please help with the highlighted text please? Why have you considered D & C?
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 06 Jun 2018, 10:05
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chetan2u
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1 2 3
4 5 6 7

The figure given shows a seating plan of 7 people A, B, C, D, E, F & G during a presentation. Spot numbered 1 is to be taken either by A or B or C who are the board of directors. D & G do not want to sit adjacent to each other in the same row. How many different sitting arrangements can be made?

A. 144

B. 432

C. 576

D. 1584

E. 2160

Let's find total ways..
Number 1 can be filled in 3 ways..(A,B,orC)
Rest all can be filled in 6*5*4*3*2*1
Total 3*6*5*4*3*2=2160

Actually choices give the answer straight way..
Answer will be <2160 but > 1/2 of 2160 since D can be with C in the same probability as it can be with E,F or G
Only 1584 fits in

Let's see which all ways D and C are together
D and C can be together at (2,3);(4,5);(5,6);(6,7)
So 4 ways and in these 4 ways they can be DC or CD so 2 ways.. total 4*2 ways

no 1 spot in 3 ways..
And the remaining seats, which are (7-3=4) in number, 4*3*2*1
Total 4*2*3*4*3*2=576

Our answer = 2160-576=1584

D

Hi chetan2u

Could you please help with the highlighted text please? Why have you considered D & C?
Show more


Typing error..
Please read G for C...
Editing accordingly
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 03 Sep 2020, 15:42
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chetan2u
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1 2 3
4 5 6 7

The figure given shows a seating plan of 7 people A, B, C, D, E, F & G during a presentation. Spot numbered 1 is to be taken either by A or B or C who are the board of directors. D & G do not want to sit adjacent to each other in the same row. How many different sitting arrangements can be made?

A. 144

B. 432

C. 576

D. 1584

E. 2160

Let's find total ways..
Number 1 can be filled in 3 ways..(A,B,orC)
Rest all can be filled in 6*5*4*3*2*1
Total 3*6*5*4*3*2=2160

Actually choices give the answer straight way..
Answer will be <2160 but > 1/2 of 2160 since D can be with G in the same probability as it can be with E,F ...
Only 1584 fits in

Let's see which all ways D and G are together
D and G can be together at (2,3);(4,5);(5,6);(6,7)
So 4 ways and in these 4 ways they can be DG or GD so 2 ways.. total 4*2 ways

no 1 spot in 3 ways..
And the remaining seats, which are (7-3=4) in number, 4*3*2*1
Total 4*2*3*4*3*2=576

Our answer = 2160-576=1584

D
Show more


Can you please elaborate on this?
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 12 Oct 2021, 22:58
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GMATSkilled
1 2 3
4 5 6 7

The figure given shows a seating plan of 7 people A, B, C, D, E, F & G during a presentation. Spot numbered 1 is to be taken either by A or B or C who are the board of directors. D & G do not want to sit adjacent to each other in the same row. How many different sitting arrangements can be made?

A. 144

B. 432

C. 576

D. 1584

E. 2160
Show more

Total ways of arrangement = 3*6! = 2160

Total ways of arrangement D and G sit together = 3* 4*2 * 4! = 576

Therefore the required possibilities = 2160 - 576 = 1584

Therefore IMO D
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 13 Oct 2021, 00:55
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1st Arrangement- Position 1 can be filled in 3 ways.

1st row 2nd position is taken by D or G = 2 ways
1st row 3rd position is taken by other than (D or G)= 4 ways
2nd row can be filled in 4! ways.
So total ways= 3x2x4x24= 576 Ways

2nd Arrangement- Position 1 can be filled in 3 ways.

1st row 2nd position is taken by other than (D or G)= 4 ways
1st row 3rd position is taken by D or G= 2 ways
2nd row can be filled in 4! ways.
So total ways= 3x4x2x24= 576 Ways

3rd Arrangement- Position 1 can be filled in 3 ways.

1st row 2nd position is taken by other than (D or G)= 4 ways
1st row 3rd position is taken by other than (D or G)= 3 ways
2nd row can be filled in 4!- 3!2! (D & G are not together)= 12 Ways
So total ways= 3x4x3x12= 432 Ways

Total ways= Arrangement 1 + Arrangement 2 + Arrangement 3
= 576+576+432= 1584 Ways

Answer is D.
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The figure given shows a seating plan of 7 people A, B, C, D, E, F & G 24 Sep 2024, 12:07
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