theachiever wrote:During a 7-year period the profits of Midas, Inc. changed by what percent from the sixth year to the seventh year?
(1) The profits of Midas, Inc. during the seventh year were 50 percent greater than the profits during the third year.
(2) The increase in the profits of Midas, Inc. was the same for each year during the 7-year period.
To determine by what percent the profits changed from the 6th year to the 7th year, we need to know the RATIO of the two years:
6th year / 7th year.
Statements combined:
Case 1: 3rd-year profits = 8
Since the 7th-year profits are 50% greater, the 7th-year profits = 1.5(8) = 12.
Since there is a difference of 4 years between the 3rd year and the 7th year, the yearly increase = (12-8)/4 = 1.
Thus, the 6th-year profits = (7th-year profits) - (yearly increase) = 12-1 = 11.
The result:
6th year / 7th year = 11/12.
Case 2: 3rd-year profits = 24
Since the 7th-year profits are 50% greater, the 7th-year profits = 1.5(24) = 36.
Since there is a difference of 4 years between the 3rd year and the 7th year, the yearly increase = (36-24)/4 = 3.
Thus, the 6th-year profits = (7th-year profits) - (yearly increase) = 36-3 = 33.
The result:
6th year / 7th year = 33/36 = 11/12.
Since the ratio is the same in each case, the two statements combined are SUFFICIENT.
The correct answer is
C.
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