Question

Which of the following statements must be true whenever $n,a,b$ and $c$ are positive integers such that $n<a,c>a$ and $b>c$?

• A. $a<n$
• B. $b-n>a-n$
• C. $b<n$
• D. $n+b=a+c$
• E. $2n=a+b$

Answer 1

Answer: (B)

$b-n>a-n$

$c>a$ and $b>c$.

Therefore, $b>c>a$, or $b>a$

$b-\lambda >a-\lambda$ where $\lambda >0$ is a constant.

Replacing $\lambda$ by '$n^{\prime }$,

$b-n>a-n$