Problem Solving

abhirup1711 wrote:Points A, B , C and D are evenly spaced on a line. If point A equals 2^17 and C equals 4^9, what is the value of point D?

A) 2^19
B) 2^17
C) 5(2^16)
D) 3(2^16)
D) 2^16

So, the numbers look like this: A....B....C....D

Here's one approach.

First, we can make things much easier on ourselves if we first recognize that:
A = 2^17 = (1)(2^17)

Next, notice that
C = 4^9 = (2^2)^9 = 2^18 = (2^1)(2^17) = (2)(2^17)

Why did I do that?
Well, now both of the two given values have like terms.
A = (1)(2^17)
and C = (2)(2^17)

If the numbers are equally spaced, then we get:
A = (1)(2^17)
B = (1.5)(2^17)
C = (2)(2^17)
D = (2.5)(2^17)

Now I check the answer choices, so see which one equals (2.5)(2^17). No matches.

I guess we'll need to simplify.
(2.5)(2^17) = (5/2)(2^17)
= (5)(2^17)/2
= (5)(2^16)
= C

Cheers,
Brent