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
