Country R and its annual income

[Guest]

Q: Before being simplified, the instructions for computing income tax in country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax in country 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)

Answer: C

Your help is greatly appreciated! I have no clue.

[Quizzy]

Lets say Income is I

1% of income = I/100
2% of Income = 2I/100

Arithmetic Mean = (I/100 + 100C)/2 (Where C denotes the currency)

Therefore Total = 2I/100 + I/200 + 50
= 5I/200 + 50
Therefore C

[RonPurewal]

Lets say Income is I

1% of income = I/100
2% of Income = 2I/100

Arithmetic Mean = (I/100 + 100C)/2 (Where C denotes the currency)

Therefore Total = 2I/100 + I/200 + 50
= 5I/200 + 50
Therefore C

well done.

the principal challenge of this problem is the sheer length of the wording in the problem statement: there are just a ton of words crammed into a rather small amount of space.

when you parse something like this, you should try your best to break it down into smaller parts:
add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's annual income.
this is somewhat difficult to do on gmat problems, because you don't have a pre-printed piece of paper on which you can simply block things off and underline things; you'll have to write this stuff out on the yellow pad with which you're supplied at the exam.

[explorer31]

Hello Ron:

Why is it incorrect to compute the arithmetic mean as (100C+0.01I)/(100+1)? I am super confused!


Appreciate your help!

[RonPurewal]

"100 units of country R's currency" is a single amount of money. it's not 100 different amounts of money.
(like "100 dollars", or "100 euros", etc)

so, you are only averaging 2 different amounts of money. not 101 different amounts of money.

[JbhB682]

Hi Experts - wanted to laser focus on the word "Units" in the expression :100 units of Country R's currency

Lets say - Country R is France (we all know France's currency is the Euro)

Thus, 100 units of Country R's currency translates to 100 units of France's currency. This can be further translated into 100 units of Euro (as France's currency IS the Euro)

Isn't the word "Units" redundant in the expression 100 units of Euro ?

I dont see how 100 units of Euro can be thought of as the same as 100 Euro ?

[esledge]

Thus, 100 units of Country R's currency translates to 100 units of France's currency. This can be further translated into 100 units of Euro (as France's currency IS the Euro)

Isn't the word "Units" redundant in the expression 100 units of Euro ?

No, you are parsing the sentence in a way that separates the noun from its necessary modifier. I'll throw parentheses in to show what must stay together in your mind:

100 (units of France's currency) = 100 (Euros)

The "of" modifier is a necessary modifier, so that whole modified noun gets replaced by "euro."

[JbhB682]

Hi Emily - could you please expand on the above concept a bit more ? I am not allowed to parse essential modifiers ?

if you could provide some examples ...that would be great !

[esledge]

I am not allowed to parse essential modifiers ?

I would just suggest that this kind of close reading is not productive on a math problem. If you parse it the way you did, the question doesn't make sense. You have to think that the "math intent" was the more simple interpretation: our "unit of currency" is dollars, euro, yen, or whatever is familiar to you, and keep your focus on the math.