Before being simplified, the instructions for computing

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Before being simplified, the instructions for computing

by BTGmoderatorLU » Fri Apr 20, 2018 2:15 pm

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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

The OA is C.

Please, can anyone assist me with this PS question? I don't know how can I solve it. Thanks!

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Source: Beat The GMAT — Problem Solving | Fri Apr 20, 2018 2:15 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Fri Apr 20, 2018 4:00 pm

Hi All,

We're told that 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 of 100 units of Country R's currency and 1 percent of one's annual income. We're asked 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. This question can be solved by TESTing VALUES.

To start, I'm going to use the variable "J" instead of an "I" (since that might be mistaken for the number 1)...

We're told to add "2% of one's income" to "the average of 100 and 1% of one's income"

Let's TEST J = 100

So we're adding 2% of 100 to (100 + 1% of 100)/2....

2 + 101/2 =
2 + 50.5 =
52.5

So we're looking for an answer that equals 52.5 when J = 100. There's only one answer that matches...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Sat Apr 21, 2018 8:31 am

I- income
0.02I - 2% of I ; 0.01I - 1% of I ; 100 units - i count as 100.

so

0.02I + (100+0.01I)/2 --> (0.04I+100+0.01I)/2

(100+0.05I)/2

50 + 0.05I/2 -- (0.05I/2 --> 5I/200 --> I/40)

50+I/40

Hence Answer is C.

Regards!

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Apr 26, 2018 3:04 pm

BTGmoderatorLU 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

We are given that 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. We need to determine the formula for computing the tax for a person who earns "I" annual income.

The expression is as follows:

0.02I + (100 + 0.01I)/2

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

2I/100 + 100/2 + I/200

2I/100 + 50+ I/200

50 + 4I/200 + I/200

50 + 5I/200

50 + I/40

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]