In the sequence of positive number x1, x2, x3,. . . what is

[pushkalk]

My approach (I am using x1 instead of x sub1)

From statement 1 we have x2=x1/2. This means each term is 1/2 the previous term for all terms after 1(i>1).

Therefore:
x3=x1/4
x4=x1/8...................(eq-1)
x5=x1/16.................(eq-2)

thus the first 5 terms of the sequence are :
x1+(x1/2)+(x1/4)+(x1/8)+(x1/16)

Not putting values of x4 and x5 obtained above, in the statement 2 gives us a linear equation in 1 varianble.

hence C.

[tim]

looks good to me..

[rustom.hakimiyan]

I tried to do this by plugging in numbers and after 3+ minutes, I chose "Neither Suff" b/c I wasn't seeing any trends.

A and B are both insufficient because we don't have a starting point. When I combined, I still didn't see a starting point and went through the calculations only to realize that I STILL didn't have a starting point.

In retrospect, if I was to plug in numbers, what would be the better approach? Should I pick a number for say X5 and work backwards on both A and B or does picking numbers in this problem fail? It seemed to me that I could get MULTIPLE values since I could assign ANY value to X5 etc.?

[RonPurewal]

First off"”"”Please be sure to refer to the statements as (1) and (2). (A and B are answer choices; not quite the same.)

A and B are both insufficient because we don't have a starting point.

Basically yes.

More specifically:
In (1), you have a relationship, but no specific numerical values.
In (1), if you have ANY value in the sequence, you'll be able to find EVERY value in the sequence"”"”just divide by 2 to move forward, or multiply by 2 to move backward.
But you don't have any such value yet.

In (2), you have a relationship between the fourth and fifth values, but no information whatsoever about any of the others. You also can't generalize this relationship, because these are specifically the fourth and fifth values, not the "n - 1" and "n" values.

[RonPurewal]

When I combined, I still didn't see a starting point and went through the calculations only to realize that I STILL didn't have a starting point.

This, you should re-visit.

Statement (2) gives a relationship between the fourth and fifth values.
Statement (1) gives another relationship between the fourth and fifth values (namely, the fifth value is half the fourth one).

You can combine these relationships algebraically. Try it. Once you have a number, statement (1) will give you every other number in the whole sequence.

In retrospect, if I was to plug in numbers, what would be the better approach? Should I pick a number for say X5 and work backwards on both A and B or does picking numbers in this problem fail? It seemed to me that I could get MULTIPLE values since I could assign ANY value to X5 etc.?

You can't pick numbers for the combined statements, because ...
... there's no clear way to pick values that satisfy both of them at the same time,
... any values you pick will be wrong, except the one pair of values that actually satisfies both statements. (If there's actually a correct value for something, you can't pick random values for it.)

[RonPurewal]

Final thought: Maybe the problem is that you didn't make this realization (boldface):

In (1), if you have ANY value in the sequence, you'll be able to find EVERY value in the sequence"”"”just divide by 2 to move forward, or multiply by 2 to move backward.

You want to make sure that you understand what the whole "n - 1"/"n" index notation means.
You should think of these as, respectively, "previous value" and "current value", or else as "current value" and "next value". This relationship allows you to move forward a step or to move back a step in the sequence.

E.g., let's say that a certain job involves a 3% pay raise every year.
Then you can write "X sub n = 1.03(X sub n-1)", and that expresses the relationship for all years.