Problem Solving

Hi Everyone,

There was a question that i encountered while taking the powerpep.Please help me understand the problem statement.

Before being simplified,the instructions for computing income tax in country R were to add 2% of one's annual income to the arithmetic mean of 100 units of country R's currency and 1% of one's annual income.Which of the following represents the simplified formula for computing the income tax in R's currency for a person in that country whose annual income is I.
a)50 + I/200
b)50 + 3I/100
c)50 + I/40
d)100 + I/50
e)100 + 3I/100

Hi smriti16,

Wow - that's a fairly convoluted problem, so I definitely see where you're coming from! It's a fair question, though - like many GMAT problems, they're not testing your "pure math" abilities so much as they're testing your ability to take a unique situation and put structure on it (they do this a lot with number properties, algebraic equations, etc.). Here's how I'd look at this one:

1) "Add 2% of one's annual income to..." means 2% * I plus..., or 2I/100 +

2) "The arithmetic mean of 100 units of currency and 1% of one's annual income" means the sum of (100 + 1% * I) divided by 2: (100 + I/100)/2

3) The tax calculation is to combine these two terms: 2I/100 + (100 + I/100)/2

Now, the challenge becomes to simplify that algebra:

-Get a common denominator of 100 by multiplying the second term by 50/50: 2I/100 + 50(100 + I/100)/100

-Distribute the multiplication of 50: 2I/100 + (5000 + 50I)/100

-Simplify the right-hand term: 2I/100 + 5000/100 + (50I/100)/100

-Combine like terms and simplify: [2I + 1/2 (I)]/100 + 50

-Continue to simplify: [5/2 (I)]/100 + 50

-Reduce the fraction: I/40 + 50

Trying to go step-by-step above, I probably took more steps than you need to if you can combine steps. Ultimately, this problem is one of two phases:

1) Making sense of the algebra that the problem provides

2) Taking the convoluted algebra that they give you and working it to put it in the form of an answer choice

Both are important skills for the GMAT...best of luck as you continue to develop them!