Quantitative Comparison – Numberline, Absolute Value

p, q and r are three points on the real number line where q = $\frac{2pr}{p+r}$ .

Quantity A: $\left | \frac{1}{p} - \frac{1}{r}\right |$
Quantity B: $\left | \frac{1}{q} - \frac{1}{p}\right |$

Explanation:

q = $\frac{2pr}{p+r}$

qp + qr = 2pr

Divide both sides of the equation by pqr
(1/r) + (1/p) = (2/q)

[(1/r) + (1/p)]/2 = (1/q)< /div>

Thus we see that (1/q) is the arithmetic mean of (1/r) and (1/p).

Thus $\left | \frac{1}{p} - \frac{1}{r}\right |$ will be greater than $\left | \frac{1}{q} - \frac{1}{p}\right |$ .

Quantity A is greater.

%d bloggers like this:

Reader Interactions