Explanation
You can first identify the multiples of 2, which are 8, 12, 18, and 36, and then among the
multiples of 2 identify the multiples of 3, which are 12, 18, and 36. Alternatively, if
you realize
that every number that is a multiple of 2 and 3 is also a multiple of 6, you can identify the
choices that are multiples of 6.
The correct answer consists of Choices C (12), D (18), and F
(36)
.
3. Each employee of a certain company is in either Department X or Department Y, and there are
more than twice as many employees in Department X as in Department Y. The average
(arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the
employees in Department Y. Which of the following amounts could be the average salary for all
of the employees of the company?
Indicate all such amounts.
A. $26,000
B. $28,000
C. $29,000
D. $30,000
E. $31,000
F. $32,000
G. $34,000
Explanation
One strategy for answering this kind of question is to find the least and/or greatest possible
value. Clearly the average salary is between $25,000 and $35,000, and
all of the answer choices
are in this interval. Since you are told that there are more employees with the lower average
salary, the average salary of all employees must be less than the average of $25,000 and
$35,000, which is $30,000. If there were exactly twice as many employees in
Department X as in
Department Y, then the average salary for all employees would be, to
the nearest dollar, the
following weighted mean,
dollars
where the weight for $25,000 is 2 and the weight for $35,000 is 1. Since there are more than
twice as many employees in Department X as
in Department Y, the actual average salary must
be even closer to $25,000 because the weight for $25,000 is greater than 2. This means that
$28,333 is the greatest possible average. Among the choices given, the possible values of the
average are therefore $26,000 and $28,000.
Dostları ilə paylaş: 
