Question

The earth is made up of four primary layers: the inner core, outer core, mantle, and crust. The distance between the Earth's center and the outer core is more than $800$ miles but less than $2,200$ miles . Determine which of the following inequalities represents all possible distances, $d$, in miles, from the Earth's center that are in the outer core.

• A. $|d+800|<2,200$
• B. $|d-800|<2,200$
• C. $|d+1,500|<700$
• D. $|d-1,500|<700$

Answer 1

Answer: (D)

$|d-1,500|<700$

Let the distance from earths center to outer core be $d$

Given that $800<d<2200$

$\Rightarrow 1500-700<d<1500+700$

$\Rightarrow |d-1500|<700$

Therefore option $D$ is correct