1963 TMTA High School Algebra I Contest Problem 30

Problem

If $x$ is positive, which of the following is always less than one?

$\text{(A)} \quad 1/x \quad \text{(B)} \quad x^2 \quad \text{(C)} \quad \frac{x}{x+1} \quad \text{(D)} \quad \frac{1+x}{x} \quad \text{(E)} \frac{1-x}{x}$

Solution

Most of the answer choices can be eliminated by selecting a number $x$ such that $0<x<1.$ This gets rid of $1/x$ and $\frac{1-x}{x}.$

If you select a very large value for $x,$ then $x^2$ will be bigger than $1.$

$x$ is positive, so $\frac{1+x}{x}>\frac{x}{x}$ and will always be bigger than $1.$

So, the answer is $\boxed{\text{(C)} \quad \frac{x}{x+1}}.$

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 29	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 31

Page

Toolbox

Search

1963 TMTA High School Algebra I Contest Problem 30

Problem

Solution

See Also