VJesus12 wrote:The price of a consumer good increased by p% during 2012 and decreased by 12% during 2013. If no other change took place in the price of the good and the price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012, what was the value of p?
A. −2%
B. 2%
C. 22%
D. 25%
E. Cannot be determined
[spoiler]OA=D[/spoiler]
Source: e-GMAT
We let the 2012 price = n and thus, the price at the end of 2013 will be:
(1 + p/100)(0.88)(n)
Since the price at the end of 2013 was 10% higher than at the beginning of 2012, we can create the equation:
1.1n = (1 + p/100)(0.88)(n)
1 = (1 + p/100)(0.8)
1 = 0.8 + 0.8p/100
Multiplying by 100, we have:
100 = 80 + 0.8p
20 = 0.8p
25 = p
Alternate Solution:
Let's let the price at the beginning of 2012 be 100. Since the price at the end of 2013 was 10% higher, the price at the end of 2013 is 1.1 x 100 = 110. We know the price decreased by 12% and became 110; therefore, before decreasing by 12%, the price was 110/0.88 = 125. Now, the price of 100 increases by p percent and becomes 125; therefore the value of p is [(125 - 100)/100] x 100 = 25.
Answer: D
