Challenge#2 (Numbers/Exponents)

Great question, Aneesh!
Multiple approaches (including one very fast approach) is the hallmark of a good GMAT math question.

Cheers,
Brent

aneesh.kg wrote:C#2:

If A, B, C and D are evenly spaced on the number line as shown below
A....B....C....D
and B = 3^13 and D = 3^15, then what is the value of A?

(A) 3^12
(B) 4(3^13)
(C) - 4(3^13)
(D) - 3^12
(E) - 3^14

Here's one approach.

First, we can make things much easier on ourselves if we first recognize that:
D = 3^15 = (3^2)(3^13) = 9(3^13)

Why did I do that?
Well, now both of the two given values have like terms.
B = 3^13 and D = 9(3^13)

At this point, we can “ignore” the 3^13 for a while. In fact, let’s say that x = 3^13
So, we have B = x and D = 9x
At this point, we can determine the value of C

If the numbers are evenly spaced, then it must be true that D-C = C-B
In other words, 9x – C = C – x
Rearrange to get: 10x = 2C
Solve to get: 5x = C

So, our numbers are: A=?, B=x, C=5x, D=9x
As you can see, we add 4x to each value to get the next value.
So….. A= -3x

At this point, we’ll replace x with 3^13 to see that A = -3(3^13)
Check the answer choices . . . not there. Looks like we need to rewrite it.

A = -3(3^13) = -1(3)(3^13) = -1(3^1)(3^13) = [spoiler]-1(3^14)[/spoiler] = E

Cheers,
Brent