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At a certain company, employees who earn $20.00 per hour will be given

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At a certain company, employees who earn $20.00 per hour will be given  [#permalink]

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New post 10 Dec 2019, 01:07
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At a certain company, employees who earn $20.00 per hour will be given an increase of $1.00 per hour. For each of the other employees, either the employee will be given an increase of $1.00 per hour or the employee will be given a percent increase equal to the percent increase that will be given to the employees who earn $20.00 per hour, whichever results in a larger increase for that employee. Which of the following statements are true?

I. An employee who earns less than $20.00 per hour will be given a percent increase that is greater than the percent increase that will be given to the employees who earn $20.00 per hour.
II. An employee who earns $22.00 per hour will be given an increase of $1.10 per hour.
III. An employee who earns $24.00 per hour will earn $25.20 per hour after the increase.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

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Re: At a certain company, employees who earn $20.00 per hour will be given  [#permalink]

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New post 10 Dec 2019, 02:59
Bunuel wrote:
At a certain company, employees who earn $20.00 per hour will be given an increase of $1.00 per hour. For each of the other employees, either the employee will be given an increase of $1.00 per hour or the employee will be given a percent increase equal to the percent increase that will be given to the employees who earn $20.00 per hour, whichever results in a larger increase for that employee. Which of the following statements are true?

I. An employee who earns less than $20.00 per hour will be given a percent increase that is greater than the percent increase that will be given to the employees who earn $20.00 per hour.
II. An employee who earns $22.00 per hour will be given an increase of $1.10 per hour.
III. An employee who earns $24.00 per hour will earn $25.20 per hour after the increase.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

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This tells us three things
(a) that <20.00$ will lead to an increase of $1.00
(b) that >$20.00 will lead to a percent increase equal to 100*1/20 or 5%
(c) that =20.00$ will lead to an increase of $1.00

Now we are looking at MUST be true question

I. An employee who earns less than $20.00 per hour will be given a percent increase that is greater than the percent increase that will be given to the employees who earn $20.00 per hour.
1 will be a greater percentage of <20.00 that for 20.00.
On an amount of 20, 1 gives 5%, but for an amount 10, it will be 100*1/10=10%, so on amounts less than 20, it will always be >5%.
True

II. An employee who earns $22.00 per hour will be given an increase of $1.10 per hour.
The employee will get a 5% increase, so increase =22*5/100=1.1$
True

III. An employee who earns $24.00 per hour will earn $25.20 per hour after the increase.
The employee will get a 5% increase, so amount=24+24*5/100=24+1.2$=25.20$
True

All three true

E
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Re: At a certain company, employees who earn $20.00 per hour will be given  [#permalink]

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New post 16 Dec 2019, 23:18
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The hidden clue in this question is the percentage increase in salary given to the persons earning $20/hr. If you are someone who earns $20/hr and you receive a $1/hr raise, you received a 5% increase, right?

You will now see that interpreting the second statement of the question becomes very simple. But before that, let’s break up the persons into three categories:

Category 1 – People who earn $20/hr. These people receive a $1/hr (or a 5% raise).

Category 2 – People who earn <$20/hr. 5% of a number less than 20 is less than $1. Therefore, these people receive a $1/hr increase which represents more than 5% of their salary.

Category 3 – People who earn >$20/hr. 5% of a number more than 20 is more than $1. Therefore, these people receive an amount equal to 5% of their salary since this will be more than $1.

Now that this is clear, let’s evaluate the statements one by one.

Statement I says that people in category 2 earn a higher percentage increase than people in category 1. From the above discussion, we know that this is true. Statement I has to be a part of the answer, so answer options B and C can be eliminated.

Statement II and III talk about two individuals who are in category 3. It’s clear that these individuals will receive a 5% increase on their respective salaries.
5% of 22 is 1.10 and 5% of 24 is 1.20. Clearly, statement II is true. When 1.20 is added to 24, the result is 25.20. Statement III is also true. Answer options A and D can be eliminated.

The correct answer option is E.

Hope that helps!
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Re: At a certain company, employees who earn $20.00 per hour will be given  [#permalink]

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New post 03 Mar 2020, 08:02
Bunuel wrote:
At a certain company, employees who earn $20.00 per hour will be given an increase of $1.00 per hour. For each of the other employees, either the employee will be given an increase of $1.00 per hour or the employee will be given a percent increase equal to the percent increase that will be given to the employees who earn $20.00 per hour, whichever results in a larger increase for that employee. Which of the following statements are true?

I. An employee who earns less than $20.00 per hour will be given a percent increase that is greater than the percent increase that will be given to the employees who earn $20.00 per hour.
II. An employee who earns $22.00 per hour will be given an increase of $1.10 per hour.
III. An employee who earns $24.00 per hour will earn $25.20 per hour after the increase.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III



So, the $20 people will have a raise of h*1 dollars (h is the number of hours they worked)
% increase for the $20: h/20%

I. People who earns less than 20 (say, x<20) will either choose to have a raise of h/20% or get $1/hour. If they take the dollar amount, their percent increase will be h/s% > h/20% (since x<20). TRUE. And furthermore, it's better for them to take the $1/hr raise.
II. Similarly, people who earn more than 20/hr will be better off taking the % increase. Their hourly raise will be h/20%*22 = 1.1h dollars. So they have $1.1 raise per hour in wage. TRUE.
III. Same as (II).

IMO E
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Re: At a certain company, employees who earn $20.00 per hour will be given  [#permalink]

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New post 03 Mar 2020, 11:36
$20 to $21 is a 2% increase
22/2 = 11 -> $1.10 > $1 so they will get a $1.10 increase
24/2 = 12 -> $1.20 > $1 so they will get a $1.20 increase

all three true
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Re: At a certain company, employees who earn $20.00 per hour will be given   [#permalink] 03 Mar 2020, 11:36

At a certain company, employees who earn $20.00 per hour will be given

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