Company ABC has decided to distribute to its clients several

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Mar 28, 2019 6:21 am

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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

Answer: [spoiler]______(B)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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Source: Beat The GMAT — Problem Solving | Thu Mar 28, 2019 6:21 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Mar 28, 2019 11:17 am

fskilnik@GMATH 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.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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