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# The image shows an office key holder where 8 different keys must be p

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 754
The image shows an office key holder where 8 different keys must be p  [#permalink]

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04 Feb 2019, 14:04
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:24) correct 26% (01:39) wrong based on 19 sessions

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GMATH practice question (Quant Class 18)

The image shows an office key holder where 8 different keys must be placed (one key per square).
If the two main keys must be placed in the blue squares, in how many ways can all the keys be placed in the key holder?

(A) 360
(B) 720
(C) 1440
(D) 2880
(E) 4320

Source: https://gmath.net

Attachment:

04-Feb19-12u.gif [ 2.68 KiB | Viewed 217 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Math Expert
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Posts: 7334
Re: The image shows an office key holder where 8 different keys must be p  [#permalink]

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04 Feb 2019, 18:29
fskilnik wrote:

GMATH practice question (Quant Class 18)

The image shows an office key holder where 8 different keys must be placed (one key per square).
If the two main keys must be placed in the blue squares, in how many ways can all the keys be placed in the key holder?

(A) 360
(B) 720
(C) 1440
(D) 2880
(E) 4320

Source: https://gmath.net

So the 8 keys are - 2 main and 6 others..
2main can be placed in 2! Ways
6 others can be placed in 6! ways

Total 2!*6!=2*720=1440

C
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Re: The image shows an office key holder where 8 different keys must be p  [#permalink]

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05 Feb 2019, 02:47
2 main keys can be placed in 2! ways and 6 keys in 6! ways
so total
6!*2! = 1440
IMO C

fskilnik wrote:

GMATH practice question (Quant Class 18)

The image shows an office key holder where 8 different keys must be placed (one key per square).
If the two main keys must be placed in the blue squares, in how many ways can all the keys be placed in the key holder?

(A) 360
(B) 720
(C) 1440
(D) 2880
(E) 4320

Source: https://gmath.net

Attachment:
04-Feb19-12u.gif

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 754
Re: The image shows an office key holder where 8 different keys must be p  [#permalink]

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05 Feb 2019, 05:30
fskilnik wrote:

GMATH practice question (Quant Class 18)

The image shows an office key holder where 8 different keys must be placed (one key per square).
If the two main keys must be placed in the blue squares, in how many ways can all the keys be placed in the key holder?

(A) 360
(B) 720
(C) 1440
(D) 2880
(E) 4320

Source: https://gmath.net

Our "official solution" is identical to the other two posted above. (Thank you for your contributions!)

Here is our wording:

$$?\,\,\,:\,\,\,\# \,\,{\rm{8 - keys}}\,\,{\rm{placing}}$$

$$?\,\,\, = \,\,\,\underbrace {\,{P_2}\,}_{{\rm{main}}\,\,{\rm{keys}}} \cdot \underbrace {\,{P_6}\,}_{{\rm{other}}\,\,{\rm{keys}}}\,\,\, = \,\,\,2!\,\, \cdot 6! = 2 \cdot 720 = 1440$$

The correct answer is therefore (C).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: The image shows an office key holder where 8 different keys must be p   [#permalink] 05 Feb 2019, 05:30
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