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?
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GMAT prep test 1 functions, fractions and sequence, range
Source: Beat The GMAT — Problem Solving |
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
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
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
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
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.
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.
