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.

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