vipulgoyal wrote:In the number line, point A, B, C, D, and E are spaced equally. If point A represents 3^11 and point B represents 3^12, point E represents which of the following values?
(A) 3^11+3^12
(B) 3^13
(C) 3^12+3^13
(D) 3^14
(E) 3^15
B

Brent@GMATPrepNow wrote:

vipulgoyal wrote:In the number line, point A, B, C, D, and E are spaced equally. If point A represents 3^11 and point B represents 3^12, point E represents which of the following values?
(A) 3^11+3^12
(B) 3^13
(C) 3^12+3^13
(D) 3^14
(E) 3^15
B

Here's another approach:

First, let's examine some OTHER examples of equally-spaced values:
5, 15, 25, 35, 45
We can rewrite these 5 values as 1(5), 3(5), 5(5), 7(5), 9(5)
Notice that each value is rewritten as a product of 5.
Also notice that the coefficients (1, 3, 5 etc.) increase by 2 each time.

Here some more examples of equally spaced values:
4(2),7(2),10(2),13(2),17(2)
In this example, the coefficients (4, 7, 10 etc.) increase by 3 each time.

-3(11), 5(11), 13(11), 21(11), 29(11),
In this example, the coefficients (-3, 5, 13 etc.) increase by 8 each time.

So, if we can take equally-spaced values and rewrite them as products with like terms, the coefficients will increase (or decrease) the same amount.

Okay, now onto the question.
A = 3^11 = (1)(3^11)
B = 3^12 = (3^1)(3^11) = (3)(3^11)
So, the coefficients must increase by 2 each time, which means . . .
C = (5)(3^11)
D = (7)(3^11)
E = (9)(3^11) = (3^2)(3^11) = [spoiler]3^13 = B[/spoiler]

Cheers,
Brent