Hi Daviesj,
The question here tests us on the concept of successive percentages. When dealing with successive percentage questions the following formula comes in very handy.
Overall %age = a + b + ab/100 where a and b is the percentage increase and decrease respectively. If a and b are percentage increases then we use a and b as positive. If a and b are percentage decreases then we use a and b as negative. If you are dealing with three percentages (a, b and c) then you find the overall percentage between the first two (a and b) and then use this overall percentage with the third (c).
The question here tells us that the price
decreased by m% and then
increased by n%. So the overall percentage will be
-m + n - mn/100Now let us break down the question. Here we are asked,
Was the price of the automobile lower in 2010 than in 2012?The price of the automobile will be lower in 2010 than in 2012 only if the overall percentage is negative. So the question can be rephrased as
Is -m + n - mn/100 < 0Evaluating the statements individually
Statement 1 : m < nThis does not give us any information whether -m + n - mn/100 < 0. If we consider m to be 10 and n to be 11 then we get a YES, but if we consider m to be 10 and n to be 20 then we get a NO.
Insufficient.Statement 2 : mn < 100n – 100mRearranging the terms we get
100n - 100m - mn > 0. Dividing throughout by 100 we get
n - m - mn/100 > 0This gives us a definite NO.
Sufficient.Hope this helps!
CrackVerbal Academics Team
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