Question

If $x$ is a negative integer greater then $-1$, what is the ordering of $j=x^2-0.49$, $k=(x-0.49)2$, and $m=x^3-0.49$ from least to greatest?

• A. j $<$ k $<$ m
• B. j $<$ m $<$ k
• C. k $<$ j $<$ m
• D. m $<$ j $<$ k
• E. m $<$ k $<$ j

Answer 1

Answer: (E)

m $<$ k $<$ j

Since $x$ is a negative integer, $j$ must be positive as the least negative integer also gives $1$ on squaring, whereas $k$ is negative. $m$ will also be negative.

We know that $j$ has the largest value anyhow.

We can not compare $k$ and $m$ for all values of $x$. $k$ is larger than $m$ when $x=-1$ and $k$ is smaller than $m$ when $x<-1$