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Set P consists of all the multiples of 4 from 12 to 52, incl

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Set P consists of all the multiples of 4 from 12 to 52, incl

by BTGmoderatorDC » Sun Dec 23, 2018 1:47 pm

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Set P consists of all the multiples of 4 from 12 to 52, inclusive. Set Q consists of 9 different integers drawn from set P. What is the average (arithmetic mean) of the integers in set Q?

(1) Set Q contains at most 4 consecutive multiples of 4.
(2) Set Q contains exactly 1 perfect square.

OA E

Source: Manhattan Prep
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by fskilnik@GMATH » Sun Dec 23, 2018 5:49 pm

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BTGmoderatorDC wrote:Set P consists of all the multiples of 4 from 12 to 52, inclusive. Set Q consists of 9 different integers drawn from set P. What is the average (arithmetic mean) of the integers in set Q?

(1) Set Q contains at most 4 consecutive multiples of 4.
(2) Set Q contains exactly 1 perfect square.
Source: Manhattan Prep
$$P = \left\{ {12,16,20,24, \ldots ,52} \right\}\,\,\,\,\,\,\left[ {16,36\,\,{\rm{perfect}}\,\,{\rm{squares}}} \right]$$
$$Q \subset P\,\,\,,\,\,\,\# Q = 9$$
$$? = {{\sum\nolimits_Q {} } \over 9}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,? = \sum\nolimits_Q {} $$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,{{\rm{Q}}_{\rm{1}}} = \left\{ {12,16,20,24} \right\} \cup \left\{ {32} \right\} \cup \left\{ {40,44,48,52} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = \sum\nolimits_{{Q_1}} {} \hfill \cr
\,{\rm{Take}}\,\,{{\rm{Q}}_{\rm{2}}} = \left\{ {12,16} \right\} \cup \left\{ {24,28,32} \right\} \cup \left\{ {40, 44,48,52} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = \sum\nolimits_{{Q_2}} \ne \sum\nolimits_{{Q_1}} {} \hfill \cr} \right.$$

The correct answer is therefore (E).


This solution follows 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
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