The price of a radio decreased m percent between 2010 and 2011 and then increased n percent between 2011 and 2012. Was the price of the automobile lower in 2010 than in 2012?
1) m<n
2) mn<100(n-m)
Let the original price = 100.
Percent decrease between 2010 and 2011 = (m/100)100 = m.
New price = 100-m.
Percent increase between 2011 and 2012 = (n/100)(100-m) = n - mn/100
Thus, the total percent change = -m + n - mn/100 = n - m - mn/100.
For the price in 2012 to be lower than the price in 2010, the total percent change must be less than 0.
Question rephrased: Is n - m - mn/100 < 0?
Statement 1: m<n
If m=10 and n=20, then n - m - mn/100 = 20 - 10 - 200/100 = 8.
If m=90 and n=100, the n - m - mn/100 = 100 - 90 - 9000/100 = -80.
Since in the first case the total percent change is positive, and in the second case the total percent change is negative, INSUFFICIENT.
Statement 2: mn<100(n-m)
mn/100 < n-m
n - m - mn/100 > 0.
SUFFICIENT.
The correct answer is
B.
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