zonda12 wrote:Just a little concern: how in the hell is an average person supposed to come up with that approach in under minutes? I mean, my math is decent, but no way near the level of thinking of that on the spot. I don't wish to belittle your answer, because you are indeed a genuius; I'm merely curious.
Is this a normal (easy/mid) question for gmat, or is this considered at a hard one (750+ score) one?
That's a valid point. Sometimes when explaining a solution to a problem it's easy to make it sound like one just steps up and . . . voila . . . everything just falls into place. The actual process is much more complex, and seldom so straightforward.
Here's another way to tackle the question:
First, I'd love to know the sum of 1/31 + 1/32 + 1/33
without actually doing all of the calculations.
One option would be to conclude that, since 1/32 falls between the other two fractions, then 1/31 + 1/32 + 1/33 should be approximately equal to 1/32 + 1/32 + 1/32 = 3/32
At this point I ask how 3/32 compares with 1/n and 1/(n+1)
I know that 3/32 is a little
less than 1/10 since 3.2/32 would be equal to 1/10
I also know that 3/32 is
greater than 1/11 since 3/33 = 1/11
So, from here, I could conclude that 1/11
< 1/31 + 1/32 + 1/33
< 1/10
The original question features the inequality 1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n
So, we can see that 1/11 = 1/(n+1) . . . which means n=10
I'm finding it hard to predict the degree of difficulty on this one. I'm going to go out on a limb and say it falls somewhere around 650 (even though I should be predicting an approximate raw score
)
