From the beginning to the end of 2007, the price of a stock rose 20 pe

Let the initial stock price be x

X*120/100*75/100*120/100=x*54/50

x*54/50=1.08x

=108%.

Answer is option E

Let price of stock at beginning of 2007 be $100
At end of 2007 , price pf stock= 100*120/100=120
At end of 2008, price of stock=120*75/100=90
At end of 2009, price of stock=90*120/100=108
Therefore, reqd %=108/100*100=108%
Answer E

Here the choices are such that you do not require to carry out the calculations and can eliminate the wrong choices..
+20% and then -25% and then 20% would surely be more than the original...
only E left.. ofcourse the calculations are not lengthy and should be calculated if time permits

2 ways to solve this:

1. Algebraic method:

Let the value of the stock in starting of 2007 be P

By end of 2007 it became = 1.2P

in 2008 it became 25% less = 1.2P*0.75

Finally, in 2009, it increased by 20% = 1.2*0.75*1.2 P

Thus the required ratio = 1.2*0.75*1.2 P /P = 1.08 (in % terms = 108%)

E is the correct answer.

2. Assume a value at the beginning of 2007. As this is a % question, assume P=100.

At the end of 2007 it becmae = 1.2*100=120

At the end of 2008 it decreased by 25% = 120*.75 = 90

At the end of 2009 it increased by 20% = 90*1.2 = 108

Thus ratio = 108/100 = 1.08 (in % terms = 108%). Thus E is the correct answer.

at Beginning of 2007, Stock = s

at End of 2007, Stock = s+(20/100)s = 1.2*s [Rose by 20%]

at End of 2008, Stock = 1.2*s - (25/100)1.2*s = 0.75*1.2*s [Dropped by 25%]

at End of 2009, Stock = 0.75*1.2*s + (20/100)0.75*1.2*s = 1.2*0.75*1.2*s = 1.08*s [Rose by 20%]

i.e. Stock at the end of 2009 = (108/100) of Stock at the beginning of 2007 = 108% of Stock at the beginning of 2007


Answer: Option E

800score Official Solution:

This problem is most easily solved by picking a number for the price at the beginning of 2007, and then determining what the prices would be in 2008 and 2009, given that starting number.

Since we are dealing with percents, let’s start with $100 for the price at the beginning of 2007. By the end of 2007, the price had risen 20 percent, up to $120. In 2008, the price dropped 25 percent, but it dropped from $120, not from the original $100. So the price at the end of 2008 was:
$120 – 0.25 × ($120) = $120 – $30 = $90.

In 2009, the stock price rose by 20 percent, but it rose from $90, not from $100 or $120. So the price at the end of 2009 was:
$90 + 0.20 × ($90) = $90 + $18 = $108.

Now, since our starting value was $100, the question is really asking was percent $108 is of $100:
$108 is 108% of $100.

The correct answer is choice (E).

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