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Company ABC has decided to distribute to its clients several shares of

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Company ABC has decided to distribute to its clients several shares of  [#permalink]

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New post 28 Mar 2019, 07:19
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Difficulty:

  35% (medium)

Question Stats:

76% (02:51) correct 24% (03:04) wrong based on 29 sessions

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GMATH practice exercise (Quant Class 17)

Company ABC has decided to distribute to its clients several shares of stocks, 1000 stocks per share. Mr. Alicante (its minor client) received 1 share, Mrs. Jung (its second minor client) received 3 shares, Mrs. Thompson (its third minor client) received 5 shares, Mr. Kumbaktoob (its fourth minor client) received 7 shares, and so on. If exactly 1,089,000 stocks were distributed by Company ABC to its clients, how many clients received those shares of stocks?

(A) 32
(B) 33
(C) 37
(D) 38
(E) 39

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Re: Company ABC has decided to distribute to its clients several shares of  [#permalink]

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New post 28 Mar 2019, 07:47
1
The number of shares, to be distributed= 1089000/1000= 1089
The shares are distributed such that it forms an arithmetic progression, with first term 1, and the difference between 2 consecutive terms as 2 ( Since 1st person got 1 share,2nd got 3 shares, 3rd got 5 shares and so on).Let the shares be distributed to N people.
Now, Sum of an arithematic progression with N terms,having 1st term as A and difference between 2 terms as D is
Sum= (N/2)(2A+(N-1)D)

Here, substituting the values:
1089=(N/2)(2*1+(N-1)*2)
Gives N=33

Hence, Answer is B
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Re: Company ABC has decided to distribute to its clients several shares of  [#permalink]

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New post 28 Mar 2019, 12:14
fskilnik wrote:
GMATH practice exercise (Quant Class 17)

Company ABC has decided to distribute to its clients several shares of stocks, 1000 stocks per share. Mr. Alicante (its minor client) received 1 share, Mrs. Jung (its second minor client) received 3 shares, Mrs. Thompson (its third minor client) received 5 shares, Mr. Kumbaktoob (its fourth minor client) received 7 shares, and so on. If exactly 1,089,000 stocks were distributed by Company ABC to its clients, how many clients received those shares of stocks?

(A) 32
(B) 33
(C) 37
(D) 38
(E) 39

\(? = N\,\,\,\,\left( {\# \,{\rm{clients}}} \right)\)

\(\left[ {{\rm{shares}}} \right]\,\,\,\,\,{{1089000} \over {1000}} = 1089\,\,\, = \,\,1 + 3 + 5 + 7 + \ldots + \left( {2N - 1} \right)\,\,\,\,\,\,\left( * \right)\)

\(\left( * \right)\,\,::\,\,\,\,1 = 2 \cdot \boxed1 - 1\,\,,\,\,\,3 = 2 \cdot \boxed2 - 1\,\,,\,\,\,5 = 2 \cdot \boxed3 - 1\,\,,\,\,\, \ldots\)


\(1 + 3 + 5 + 7 + \ldots + \left( {2N - 1} \right)\,\,\,\mathop = \limits^{{\rm{Arith}}{\rm{.}}\,{\rm{Seq}}.} \,\,\,\,\left[ {{{1 + \left( {2N - 1} \right)} \over 2}} \right]\, \cdot N\,\,\, = \,\,\,{N^2}\)

\({N^2} = 1089 = {3^2} \cdot {11^2}\,\,\,\,\,\mathop \Rightarrow \limits^{N\, > \,0} \,\,\,\,? = N = 33\)


The correct answer is (B).


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

Regards,
Fabio.
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Re: Company ABC has decided to distribute to its clients several shares of  [#permalink]

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New post 05 Apr 2019, 14:06
fskilnik wrote:
GMATH practice exercise (Quant Class 17)

Company ABC has decided to distribute to its clients several shares of stocks, 1000 stocks per share. Mr. Alicante (its minor client) received 1 share, Mrs. Jung (its second minor client) received 3 shares, Mrs. Thompson (its third minor client) received 5 shares, Mr. Kumbaktoob (its fourth minor client) received 7 shares, and so on. If exactly 1,089,000 stocks were distributed by Company ABC to its clients, how many clients received those shares of stocks?

(A) 32
(B) 33
(C) 37
(D) 38
(E) 39


\(n^2 = 1089 = 3^2 * 11^2 <=> n= 3*11 = 33\)
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Re: Company ABC has decided to distribute to its clients several shares of   [#permalink] 05 Apr 2019, 14:06
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