percent DS

[PGMAT]

The percent of an automobile 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 < 100n - 100m

Can some help me with statement 2? I went by plugging numbers, m=10,n=10.1 and m=10, n=16 and end up getting different answers. What am I doing wrong? OA is B

[Anurag@Gurome]

The percent of an automobile 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 < 100n - 100m

Say, the price was P units in 2010.
Hence, in 2011, the price was P*(1 - m/100)
Now, in 2012, the price is P*(1 - m/100)*(1 + n/100) = P*(1 - m/100 + n/100 - mn/10000) = P + P*(n/100 - m/100 - mn/10000)

Hence, we need to determine whether (n/100 - m/100 - mn/10000) is positive or negative.

Statement 1: We can conclude that (n/100 - m/100) is positive but we don't have any idea about mn/10000.

Not sufficient

Statement 2: As mn < 100n - 100m ---> mn/100 < n - m ---> mn/10000 < n/100 - m/100
Hence, (n/100 - m/100 - mn/10000) > 0

Sufficient

The correct answer is B.

[Anurag@Gurome]

Can some help me with statement 2? I went by plugging numbers, m=10,n=10.1 and m=10, n=16 and end up getting different answers. What am I doing wrong?

The red underlined set of values does not satisfy the condition given in the statement on the first place. So it is not a valid set of numbers.

m = 10 and n = 10.1 --> mn = 101
But, (100n - 100m) = (1010 - 1000) = 10 < 101 = mn

[GMATGuruNY]

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.