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# How many people bought TVs at the Electronics Depot?

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
How many people bought TVs at the Electronics Depot?  [#permalink]

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28 Sep 2017, 00:59
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:10) correct 28% (01:18) wrong based on 138 sessions

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How many people bought TVs at the Electronics Depot?

(1) One out of every six Electronics Depot customers bought a TV.
(2) If four Electronics Depot customers are chosen at random there are 126 different groups of people that could be chosen.

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Joined: 15 Aug 2012
Posts: 42
Schools: AGSM '19
How many people bought TVs at the Electronics Depot?  [#permalink]

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28 Sep 2017, 22:13
1
Statement 1) 1 in 6 bought a TV. We don't know how many customers so NOT SUFFICIENT.

Statement 2) Picking 4 people for a group out of a certain number of people would result in 126 combinations. Let's say there are K customers. K!/4!*(K-1)!=126. Deducing this gives us K=9. So we know number of Customers but we do not know how many bought TV.

Statement 1) Gives ratio of number of people who bought TV to Customers and Statement 2) Gives the number of customers.

So C, Both required but neither alone sufficient.
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Joined: 22 Oct 2017
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Re: How many people bought TVs at the Electronics Depot?  [#permalink]

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01 Feb 2019, 03:37
1
[quote="rajudantuluri"]

Statement 2) Picking 4 people for a group out of a certain number of people would result in 126 combinations. Let's say there are K customers. K!/4!*(K-1)!=126. Deducing this gives us K=9. So we know number of Customers but we do not know how many bought TV.

Are you sure about the formula you used to solve Statement 2? shouldn't it be K!/4!*(K-4)!=126??
GMATH Teacher
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Re: How many people bought TVs at the Electronics Depot?  [#permalink]

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01 Feb 2019, 05:21
Bunuel wrote:
How many people bought TVs at the Electronics Depot?

(1) One out of every six Electronics Depot customers bought a TV.
(2) If four Electronics Depot customers are chosen at random there are 126 different groups of people that could be chosen.

$$? = P\,\,\,\,\left( {{\rm{\# }}\,\,{\rm{bought - TV - there}}\,\,{\rm{people}}} \right)$$

$$\left( 1 \right)\,\,P = {N \over 6}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,N = 6\,\,{\rm{customers}}\,\,\,\, \Rightarrow \,\,\,? = P = 1 \hfill \cr \,{\rm{Take}}\,\,N = 12\,\,{\rm{customers}}\,\,\,\, \Rightarrow \,\,\,? = P = 2 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\left( {N = \# \,\,{\rm{customers}}\,\,{\rm{there}}} \right)$$

$$\left( 2 \right)\,\,C\left( {N,4} \right) = 126\,\,\,\,\, \Rightarrow \,\,\,\,\,N\,\,{\rm{unique}}\,\,\,\left( {{\rm{and}}\,\,N > 4\,\,{\rm{for}}\,\,{\rm{sure}}} \right)\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,P = 1\,\,\,\, \Rightarrow \,\,\,? = 1 \hfill \cr \,{\rm{Take}}\,\,P = 2\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,{\rm{unique}}\,\,N\,\, = 6P\,\,\,\,\, \Rightarrow \,\,\,\,\,P\,\,{\rm{unique}}$$

The correct answer is therefore (C), indeed.

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

Regards,
Fabio.
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Re: How many people bought TVs at the Electronics Depot?   [#permalink] 01 Feb 2019, 05:21
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