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# The 5 letters in the list G, H, I, J, K are to be rearranged so that G

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
The 5 letters in the list G, H, I, J, K are to be rearranged so that G  [#permalink]

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29 Jun 2018, 01:37
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:31) correct 32% (01:36) wrong based on 57 sessions

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The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are

A. 60
B. 36
C. 24
D. 12
E. 6

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Joined: 07 Dec 2017
Posts: 842
Re: The 5 letters in the list G, H, I, J, K are to be rearranged so that G  [#permalink]

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29 Jun 2018, 01:54
Bunuel wrote:
The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are

A. 60
B. 36
C. 24
D. 12
E. 6

As the calculation we're asked to do is relatively straightforward, we'll just do it.
This is a Precise approach.

We have 2 possible locations to place H (1st or 5th), 1 possible location to put G (3rd) and then need to divide the other 3 letters in the remaining 3 places.
This gives 2*1*3! = 2*6 = 12 possible options.

(D) is our answer.
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Joined: 14 Jun 2018
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Re: The 5 letters in the list G, H, I, J, K are to be rearranged so that G  [#permalink]

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29 Jun 2018, 01:59
1
Bunuel wrote:
The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are

A. 60
B. 36
C. 24
D. 12
E. 6
We have two case here...when h is at first place and when h is at second place
H at first place=6 ways
H at second place = 6 ways
Total= 12 ways
So...ans is D

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Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: The 5 letters in the list G, H, I, J, K are to be rearranged so that G  [#permalink]

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29 Jun 2018, 02:37
1
Bunuel wrote:
The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are

A. 60
B. 36
C. 24
D. 12
E. 6

Letters... _ _ G _ _
Total ways to fit in 4 ways = 4!
Let H and G be together...
1) let H be prior to G
_ H G _ _ - 3 places can be placed in 3! = 6 ways
2) Let H be after G
_ _ G H _ -- 3 places can be filled in 3! Ways
Total ways H and G are together = 6+6=12

Ans =24-12=12

D
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: The 5 letters in the list G, H, I, J, K are to be rearranged so that G &nbs [#permalink] 29 Jun 2018, 02:37
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# The 5 letters in the list G, H, I, J, K are to be rearranged so that G

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