If @(n) is defined as the product of the cube root of n and the positive square root of n, then for what number n does @(n) = 50 percent of n?

A. 16
B. 64
C. 100
D. 144
E. 729

(B) On test day, the @ symbol or any other symbol in a question usually represents a function. Though this question could be solved algebraically using fractional exponents, it is probably easiest to Backsolve from the answer choices.

Since choices (A), (C) and (D) don’t have integer cube roots, and because choice (E) is odd (so 50% of it is not an integer), let’s try choice (B) first.

The cube root of 64 is 4 and the positive square root of 64 is 8, so @(64) = 4 × 8 = 32, which is 50% of 64. The answer is (B)

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Can this question be arithmatically solved?

If you are not familiar with fractional exponents then you should solve by plugging in answer choices. However if you are then you can solve the given equation algebraically.

@(n) = 50 percent of n
can be rewritten as equation:


Since √n must be positive then n = 64