This is a fascinating DS / weighted average question.
Many students who do not test examples or successfully complete the (complicated!) algebra will use theory to arrive at Choice E, because the difference between the
average salary of this task force and the average salary of managers and directors does not appear to be enough to deduce the
percentage of directors — which is in fact true for both conditions 1 and 2 individually (cross off A, D, and B).
However, when we combine the conditions in considering Choice C vs. Choice E, we realize that because both conditions are tied to the average salary of an employee, we in fact cannot change the ratio of managers to directors without changing the average salary, thus "breaking" the conditions. Hence,
Choice C is correct.
Keep in mind that if the question asked for the
number of directors, not the
percentage of directors, then Choice E would in fact be correct, because all we can deduce is the correct
ratio of managers to directors in the task force — not the actual number of directors (or managers, for that matter).
One final note: we cannot always infer a percentage from a ratio. We can only do so in cases where we know that the ratio includes all the elements in the set, which is why the question specifies that the task force consists of only managers and directors.
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My name is Brian McElroy, founder of McElroy Tutoring (https://www.mcelroytutoring.com). I'm a 42 year-old Providence, RI native, and I live with my wife, our three daughters, and our two dogs in beautiful Colorado Springs, Colorado. Since graduating from Harvard with honors in the spring of 2002, I’ve worked full-time as a private test-prep tutor, essay editor, author, and admissions consultant.
I’ve taken the real GMAT 6 times — including the GMAT online — and have scored in the 700s each time, with personal bests of 770/800 composite, Quant 50/51, Verbal 48/51, IR 8 (2 times), and AWA 6 (4 times), with 3 consecutive 99% scores on Verbal. More importantly, however, I’ve coached hundreds of aspiring MBA students to significantly better GMAT scores over the last two decades, including scores as high as 720 (94%), 740 (97%), 760 (99%), 770, 780, and even the elusive perfect 800, with an average score improvement of over 120 points.
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