The third question fro GMATprep

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BigFisch: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sat Feb 16, 2008 11:57 am; Thanked: 1 times

by BigFisch » Mon Mar 17, 2008 6:51 am

Hello everyone, i really appreciate that if anyone could tell me how to solve this question. Thank you so much guys.

(Question 3) 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

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Source: Beat The GMAT — Problem Solving | Mon Mar 17, 2008 6:51 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: The third question fro GMATprep

by Stuart@KaplanGMAT » Mon Mar 17, 2008 7:56 pm

BigFisch wrote:Hello everyone, i really appreciate that if anyone could tell me how to solve this question. Thank you so much guys.

(Question 3) 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

Algebraically:

2%(I) + (100 + 1%(I))/2

(2/100)I + 100/2 + ((1/100)I)/2

(2/100)I + (1/200)I + 50

(4/200)I + (1/200)I + 50

50 + (5/200)I

50 + (1/40)I

50 + I/40

choose (C)!!

For a quick guess, we know that the average formula is sum/# of terms. Since the number of terms in that part of the formula is 2, we know that the answer should include 100/2 = 50, so eliminate (d) and (e) quickly.

We also know that the other part is 2%(i) + something else, so eliminate (a). Worse case, you have a 50/50 shot.

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BigFisch: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sat Feb 16, 2008 11:57 am; Thanked: 1 times

by BigFisch » Thu Mar 20, 2008 3:48 pm

Thank you so much!!!!!!!!!!!

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gmat765: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Wed Apr 16, 2008 5:51 pm

by gmat765 » Fri Apr 18, 2008 5:54 pm

Stuart is something!

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leovonp: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Thu Jun 05, 2008 10:33 am; Thanked: 2 times; GMAT Score:710

by leovonp » Tue Jun 24, 2008 9:07 am

Sorry Stuart, one thing is unclear to me...

Since the number of terms in that part of the formula is 2, we know that the answer should include 100/2 = 50, so eliminate (d) and (e) quickly.

I had a lot of trouble understanding the wording of the question. How do you get from "the average (arithmetic mean) of 100 units of Country R’s currency" to a division by 2?

appreciate!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Tue Jun 24, 2008 1:45 pm

leovonp wrote:Sorry Stuart, one thing is unclear to me...

Since the number of terms in that part of the formula is 2, we know that the answer should include 100/2 = 50, so eliminate (d) and (e) quickly.
I had a lot of trouble understanding the wording of the question. How do you get from "the average (arithmetic mean) of 100 units of Country R’s currency" to a division by 2?

appreciate!

You need to read the entire sentence:

average (arithmetic mean) of 100 units of Country R’s currency and 1 percent of one’s annual income

It's not the average of 100 units of currency; it's the average of 100 units of currency AND 1% of annual income.

So, the two terms are:

(1) 100 units of currency; and
(2) 1% of annual income.

And since average = (sum of terms)/(# of terms), we know that the denominator is "2".

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Sun Feb 20, 2011 1:31 am

I don't believe GMATPRep could trick me with such a word-problem!! oh boy!!

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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 » Sun Feb 20, 2011 3:49 am

BigFisch wrote:Hello everyone, i really appreciate that if anyone could tell me how to solve this question. Thank you so much guys.

(Question 3) Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of oneï¿½s annual income to the average (arithmetic mean) of 100 units of Country Rï¿½s currency and 1 percent of oneï¿½s annual income. Which of the following represents the simplified formula for computing the income tax, in Country Rï¿½s 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

We also could plug in.

Let I = 400.
1% of income = 4.
Average of 100 + 1% of income = (100+4)/2 = 52.
2% of income = 8.
Total tax = 52+8 = 60. This is our target.

Now we plug I=400 into the answers to see which yields our target of 60.

Only answer choice C works:
50 + I/10 = 50 + 400/40 = 60.

The correct answer is C.

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