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
