Quote:
Suppose \(n\) is a two-digit positive integer with units digit 5, and tens digit u. Now, if \(E=\frac{(n^2-25)}{100}\), then express E in terms of u.
A. \(u+1\)
B. \(u^2+1\)
C. \(u^2-u\)
D. \(u^2+u\)
E. \(u^2+u+1\)
Anytime you have a problem with variables in the choices and the problem, consider plugging in your own easy value(s) as an alternative to an often needlessly complex textbook algebraic approach. Easy values are going to be numbers that conform to the conditions of the problem, but are not themselves in the answer choices. In this case, I might consider plugging in n = 35, which in turn means that u = 3.
Subsequently, E = (35^2 - 25) / 100 = 12.
Now, plug u = 3 into each of the choices, testing all individually, seeking a match to the found value E = 12.
A. 3 + 1 ≠ 12 | Eliminate
B. 9 + 1 ≠ 12 | Eliminate
C. 9 - 3 ≠ 12 | Eliminate
D. 9 + 3 = 12 | Hold
E. 9 + 3 + 1 ≠ 12 | Eliminate
Select Choice D as the only match to the sought value of 12.
_________________