If $a > b > c > 0,$ which of the following is always positive ?
(A) $(a-c)÷b$
(B) $b+c-a$
(C) $(c-b)×(a-b)$
(D) $(c-b) × (b-a)$
(E) $(a×b) - (a ×c)$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (D), (E) only
$a > b > c > 0$ [given]
$⇒a-b>0;b-c>0;a-c>0$
(A) $(a-c)÷b$ will always be positive as both $(a-c)$ and $b$ is positive.
(D) $(c-b)<0, (b-a)<0$
$∴(c-b)(b-a)>0$ $[-1×-2=2]$ → Ex.
(E) $(a×b) - (a ×c)=a×(b-c)$
as both (A) and $(b-c)$ is positive the product will be also a positive.