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akash singhal: Master | Next Rank: 500 Posts; Posts: 152; Joined: Fri Apr 24, 2015 1:39 amFollowed by: 3 members; Location: Rourkela Odisha India; Thanked: 2 times; GMAT Score:650

by akash singhal » Thu May 14, 2015 11:56 pm

Before being simplified,the instruction for computing income tax in country R were to add 2% of one's annual income to the average(arithmatic 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 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

OE C

I am unable to understand the question???
Please explain...

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Source: Beat The GMAT — Problem Solving | Thu May 14, 2015 11:56 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu May 14, 2015 11:59 pm

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

Let I = 200 units of currency.
The tax is the SUM of two values: 2% of the income AND the average of 100 units of currency and 1% of the income.
2% of the income = .02(200) = 4.
The average of 100 units of currency and 1% of the income = (100 + .01(200)) / 2 = 102/2 = 51.
Tax = 4+51 = 55. This is our target.

Now plug I=200 into the answers to see which yield our target of 55.

Only answer choice C works:
50 + I/40 = 50 + 200/40 = 55.

The correct answer is C.

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Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Fri May 15, 2015 2:00 am

akash singhal wrote:Before being simplified,the instruction for computing income tax in country R were to add 2% of one's annual income to the average(arithmatic 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 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

OE C

I am unable to understand the question???
Please explain...

Hello akash singhal,

In this word problem translate each important phrase into algebra:-

Add 2% of I to the average of [100 units of currency + 1% of I]
= 2/100 X I +[(100+1I/100)/2]
=I/50+[(10000+I)/200]
=(5I+10000)/200
=I/40+50
=OptionC

800. Arjun's-Bird-Eye

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akash singhal: Master | Next Rank: 500 Posts; Posts: 152; Joined: Fri Apr 24, 2015 1:39 amFollowed by: 3 members; Location: Rourkela Odisha India; Thanked: 2 times; GMAT Score:650

by akash singhal » Fri May 15, 2015 3:10 am

GMATGuruNY wrote:
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
Let I = 200 units of currency.
The tax is the SUM of two values: 2% of the income AND the average of 100 units of currency and 1% of the income.
2% of the income = .02(200) = 4.
The average of 100 units of currency and 1% of the income = (100 + .01(200)) / 2 = 102/2 = 51.
Tax = 4+51 = 55. This is our target.

Now plug I=200 into the answers to see which yield our target of 55.

Only answer choice C works:
50 + I/40 = 50 + 200/40 = 55.

The correct answer is C.

Thanks Mitch i understood wrong...

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