GMAT prep test 1 functions, fractions and sequence, range

[khurram]

No clue to solve this.

Khurram

[aatech]

D for me...

For K=1 to 10 the seq will look like

1/2, -1/4, 1/8, -1/16.......

Sum of first 2 terms is 1/4 and rest of the terms will only make the sum greater than 1/4..

OA?

[zacharyz]

I think the answer is D - between 1/4 and 1/2

As aatech points out

k eqn
---------
1 + 1/2
2 - 1/4
3 + 1/8
4 - 1/16
... and so on


So, for k = 1 and 2, you have 1/2 - 1/4 = 1/4. From here on out, you add some small value that will not get you back to the 1/2 benchmark and subtract a smaller value but it will always stay within the 1/4 to 1/2 range.



Note that the actual solution is below (from excel) for confirmation. But within the two minutes, you should have some sense of it.

k eqn sum
1 0.5 0.5
2 -0.25 0.25
3 0.125 0.375
4 -0.0625 0.3125
5 0.03125 0.34375
6 -0.015625 0.328125
7 0.0078125 0.3359375
8 -0.00390625 0.33203125
9 0.001953125 0.333984375
10 -0.000976563 0.333007813

[khurram]

yes, D is the answer

I got the workings but I usually time myself two minutes and move on.

So wanted to find the logic behind it

So yes, diff between first two is 1/4 and they add a bit but take out a bit less, so builds up very slowly. almost imagine walking like a turtle.

so ans will not go too far from 1/4

thanks
khurram

[zacharyz]

Yes. Technically, you are increasing a little after each pair, but you only have 1 through 10, so there is not much more movement.

At least, that is how far I would calculate and then take the range that I see.
If I thought you were dangerously close to overrunning back to the 1/2 again, you might spend another 20 seconds thinking about that and maybe you would have to guess between 1/4 to 1/2 and the range above 1/2. however, I think you can make an educated enough guess at this point.