If n is an integer such that 1/3 > 1/(1 - n) > 1/7, what is the

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Well, another inequality problem EZ, right? WRONG. Or well, you might be wrong, so be careful out there when solving such questions they have nasty traps sometimes, that are easy to miss.

Let's go, let's flip 'em all to make it easy, right? Not quite.

We must check first of all, that the given fraction of n is only positive or it may give negative values as well.

We see that possibility, (1-n) is negative when n>1 and positive when n<1.

So flipsy-doodle can be done only when that term is positive i.e. when n<1. But, upon paying close attention to the problem, we see that it is indirectly implied that n is indeed less than 1, because the given limits are both positive fractions.

\(\frac{1}{3} > \frac{1}{1 - n} > \frac{1}{7}\)

Flip the fraction and reverse the signs,

\(3 < 1- n < 7\)

\( -2 > n > -6\)

So, n can have -3, -4, -5 as its values. Since the values are in an AP, Mean = -4.­