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Kaden’s salary last year was $125,000. If his salary is

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by M7MBA » Sat Mar 31, 2018 7:55 am
Kaden's salary last year was $125,000. If his salary is cut between x% and y%, then his new annual salary will be between:

(A) $125, 000(1 − x) and $125, 000(1 − y)
(B) $125, 000x and $125, 000y
(C) $125, 000 − x and $125, 000 − y
(D) $1, 250(1 − x) and $1, 250(1 − y)
(E) $1, 250(100 − x) and $1, 250(100 − y)

The OA is E.

I don't understand what should I do to get the answer here? Please, help!!!
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by swerve » Sat Mar 31, 2018 8:28 am
Hi M7MBA,

You can get the solution as follows,

Assume Kaden's salary ($125,000) is cut between x (10%) and y (20%)

We know that 10% of the salary is $12,500 and 20% is $25,000.

So, the new salary will be between $100,000 and $112,500.

From the answer options given,

$1,250(100 - x) or 1250(100 - 10) = 112500

and $1,250(100 - y) or 1250(100 - 20) = 100000

which is the option E gives us the same range for the new salary and is our correct answer.

Regards!
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by ErikaPrepScholar » Sat Mar 31, 2018 11:42 am
We can also solve by building equations.

If Kaden's salary is cut by x%, his remaining salary is 100-x%. To convert this into a decimal, we divide by 100. So Kaden's new salary will be:
$$125000\left(\frac{100-x}{100}\right)$$ or simplified $$1250\left(100-x\right)$$

If Kaden's salary is cut by y%, his remaining salary is 100-k%. Again converting into a decimal, Kaden's new salary will be
$$125000\left(\frac{100-y}{100}\right)=1250\left(100-y\right)$$

So Kaden's salary will be between those two values, or answer choice E.
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by Scott@TargetTestPrep » Mon May 27, 2019 4:23 am
M7MBA wrote:Kaden's salary last year was $125,000. If his salary is cut between x% and y%, then his new annual salary will be between:

(A) $125, 000(1 − x) and $125, 000(1 − y)
(B) $125, 000x and $125, 000y
(C) $125, 000 − x and $125, 000 − y
(D) $1, 250(1 − x) and $1, 250(1 − y)
(E) $1, 250(100 − x) and $1, 250(100 − y)
It is important to recall that x% can be expressed as x/100 and y% can be expressed as y/100.

If Kaden takes a x% cut, his salary is 125,000(1 - x/100) = 125,000(100 - x)/100 = 1,250(100 - x). If he takes a y% cut, his salary is 125,000(1 - y/100) = 125,000(100 - y)/100 = 1,250(100 - y). Therefore, his new salary is between 1,250(100 - x) and 1,250(100 - y).

Answer: E

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