tonebeeze wrote:I got this problem correct using DS guessing theory. I still do not fully understand the algebra. Can someone flesh out statement 2 for me. Thanks!
Price increased by M% from 1991 to 1992 and by N% from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?
1. MN = 300
2. 100M + 100N + MN = 4300
OA is (B).
Plug in price = 100.
Increase from 1991 to 1992 = M/100 * 100 = M.
New price = 100+M.
Increase from 1992 to 1993 = N/100*(100+M) = N + MN/100
Total increase = increase from 1991 to 1992 + increase from 1992 to 1993 = M + N + MN/100
Since the initial price was 100, the total increase and the percent increase are the same. Thus, the question becomes:
What is the value of M + N + MN/100?
Statement 1: MN = 300.
Not sufficient to determine the value of M + N + MN/100.
Statement 2:
100M + 100N + MN = 4300
M + N + MN/100 = 43.
Sufficient.
The correct answer is
B.
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