In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?
(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.
OA A
Source: Official Guide
In a certain office, 50 percent of the employees are college
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Let T = the total number of employees.BTGmoderatorDC wrote:In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?
(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.
Since 60% of the employees are over 40, we get:
Over 40 = 0.6T
30% of those over 40 -- in other words, 30% of the expression in blue -- have master's degrees.
Thus:
Over 40 with master's = 0.3(0.6T).
To calculate the value of the expression in red, we need to know the value of T.
Question stem, rephrased:
What is the value of T?
Statement 1:
Since the 100 college graduates constitute 50% of the total number of employees, T=200.
SUFFICIENT.
Statement 2:
Here, the information given by the prompt and the statement is constrained to PERCENTS.
Since no actual values are given, the value of T cannot be determined.
INSUFFICIENT.
The correct answer is A.
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This would be a perfect place for the "grid" (double matrix, table, you-name-it) ... but there is one more characteristic involved than expected, correct?BTGmoderatorDC wrote:In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?
(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.
Source: Official Guide
In this (rare) case our method suggests the following:
Put in the "grid" two of the three characteristics, the ones with "more info"... the third characteristic is dealt "in parallel"... see the grid below!
Now it´s really simple...
$$\left( 1 \right)\,\,5T = 100\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {3 \over {10}}\left( {6T} \right)\,\,\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$
(2) Insufficient: one possible VIABLE BIFURCATION (36 or 18, when T equals 20 or 10) is shown in blue and pink below:
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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