GMATPrep QBank-1 #QPS00573

[shailendra.sharma]

The question:

If K is the sum of the reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following ?

A) 1/12

B) 1/10

C) 1/8

D) 1/6

E) 1/4

My difficulty with the solution

1) I could quickly identify

a) K < 6 * (1/42) ==> K < 1/7
b) K > 6 * (1/48) ==> K > 1/8

2) So 1/7 < K < 1/8, hence I could choose official answer C, that is 1/8

3) But when I looked at the solution explanation by GMAC, I was surprised to see their solution even went to the extent of proving K is more closer to 1/8 than 1/6

a) I am not sure if problems on GMAT requires that last leg of the proof.

b) Obviously, with lack of time one would avoid the last leg of proof - but the first part I got in 40 seconds, so I might have time to do that too. But do I really need it on GMAT ?

c) They explained with series of non-intuitive algebra that K - 1/8 is smaller than 1/6 - K.

Code: Select All Code

Their explanation on the last leg
K < 1/7
==> K - 1/8 < 1/7 - 1/8
==> K - 1/8 < 1/56 < 1/42 = 1/6 - 1/7,
so K - 1/8 < 1/6 - 1/7

Since K < 1/7
==> -1/7 > -K
==> 1/6 - 1/7 < 1/6 - K

Thus K - 1/8 < 1/6 - K

d) I am looking for certain insights, from experts, for a better approach on that last leg.

[RonPurewal]

On this problem, your best bet is to ignore everything past your realization that the target value is between 6/42 and 6/48. That's the only thing the problem is designed to test.

When you look at GMAC's answer keys, you'll find that some of them engage in this sort of misdirection (and that they almost never show non-"classroom" solutions to problems, even when those are by far the most efficient solutions). That's partly because they don't want to do too much to help you beat their own test, of course, but also partly because the people who write the solutions aren't the same people who write the problems.

In any case, you should know that official problems will NEVER demand long or obscure proofs.
I'd even argue that spending too much time on the superfluous explanation will have a negative impact on your gmat prowess, by turning your attention away from what's actually necessary and toward what isn't.

(Not to mention that there's at least one mistake in the quoted algebra. If we know that k < 1/7, then it's most certainly false that -1/7 > -k. I sort of stopped reading after that.)

[shailendra.sharma]

Thanks Ron. That's what I wanted to hear. I am in last few weeks of preparation, so I got highly confused seeing those type of proofs -- I never saw such things in MGMAT Guide, your explanations in Thursday sessions, or forums / blogs. I am saved :) !

[jnelson0612]

Thanks Ron. That's what I wanted to hear. I am in last few weeks of preparation, so I got highly confused seeing those type of proofs -- I never saw such things in MGMAT Guide, your explanations in Thursday sessions, or forums / blogs. I am saved :) !

Great to hear!