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Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row

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Manager
Joined: 01 Sep 2016
Posts: 201
GMAT 1: 690 Q49 V35
Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row  [#permalink]

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20 Sep 2017, 14:13
2
00:00

Difficulty:

65% (hard)

Question Stats:

44% (02:16) correct 56% (01:38) wrong based on 27 sessions

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Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row containing chairs. How many seating arrangements are possible if Akash cannot sit next to Banny and Deol must sit next to Eren?

(A) 288
(B) 240
(C) 144
(D) 120
(E) 96

_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Manager
Joined: 01 Sep 2016
Posts: 201
GMAT 1: 690 Q49 V35
Re: Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row  [#permalink]

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20 Sep 2017, 14:19
2
The real test may give a question with one of these types of constraints, but it’s very unlikely that you’ll see a question with two such constraints. What’s the most efficient way to tackle this?

If Deol and Eren must sit next to each other, they can be treated as a single unit. The four separate people plus the single unit adds up to five “people” to place. There are 5! = 120 different ways in which five people can be placed in the chairs. Remember, though, that the unit has 2 possible orders in which it can be placed: D and then E or E and then D. As a result, multiply 120 by 2 to get the total number of ways to place six people, two of whom must be sitting next to each other (in either order): 240.

The maximum possible number of arrangements is 240. Eliminate answer (A). Further, at least one of those 240 arrangements will have Akash sitting next to Banny , so 240 itself is also too large. Eliminate answer (B).

Next, how many of these 240 arrangements also do NOT have Akash sitting next to Banny? That would actually be quite time consuming to calculate.

Luckily, there’s a shortcut! Calculate how many arrangements DO have Akash sitting next to Banny. Then subtract that number from 240.

Again, make Akash and Banny a single unit. Now, there are 2 separate people plus 2 units of two people each, adding up to 4 “people” to place, so there are 4! = 24 different ways to arrange these four “people.” But wait! Each of the two units can be arranged in two different orders: DE or ED and AB or BA. Multiply 24 by 2 and by 2 again to get 96.

240 – 96 = 144 arrangements in which Deol and Eren do sit next to each other but Akash and Banny do not.

_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Re: Akash, Banny, Carl, Deol, Eren, and Fuzzy are seated in a row &nbs [#permalink] 20 Sep 2017, 14:19
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