Welcome back! Today, we’ll go over Tuesday’s Brain Twister problem.
x^n + x^n + x^n = x^(n + 1), where x cannot equal zero.
Which of the following must be true?
I. n = 2
II. x = 3
III. n^x < x^n
(A) I only
(B) II and III
(C) I and III
(D) II only
(E) None of the above
Answer and Explanation
There are a few ways to flub this question. One is to think that there is no way to know the value of ‘n’ or ‘x’ and then to blithely mark (E) as the answer. The reality is that one of the variables is a known, based on the relationship between the two sides of the equation.
Notice how there are three ‘x^n’ values on the left and on the right side of the equation we have x^(n + 1). Therefore, ‘x’ has to be ‘3’, since we are adding one more ‘x’ (remember the (n+1)).
Another way to miss this question is by forgetting the case for where x could equal n. So if we know that ‘x’ has to be three and we make n = 3, then Condition III is not true.
Therefore, the answer is (D).
See you again soon!