Practice GMAT Problem Solving Question
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If (2439 + 18z)(81-18z)(2715 - 9z) = 1, what is the value of z?
Correct Answer: D
- Rewrite the terms on the left-side with common prime bases.
(2439 + 18z)(81-18z)(2715 – 9z)
= (35(9 + 18z))(34(-18z))(33(15 – 9z))
= (345 + 90z)(3-72z)(3(45 – 27z))
- Simplify by combining terms with like bases.
(345 + 90z)(3-72z)(3(45 – 27z))
= 345 + 45 + 90z – 72z – 27z
= 390 -9z
- As a result of this simplification, the equation is much easier to deal with.
390 -9z = 1
- At this point, the problem may appear unsolvable as different bases and exponents exist. However, remember that any number raised to the 0th power is 1. Consequently, 1 can be rewritten as 30. The equation now reads:
390 -9z = 1
390 -9z = 1 = 30
- Since the bases are the same, you can set the exponents equal to each other. The equation becomes:
90 – 9z = 0
90 = 9z
z = 10
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