Hi Srav,

The best thing to do while solving questions of this type is to make use of the

Max/Min Concept of Inequalities.If we are given two ranges say

-11 < x < 9 and

-9 < y < 2 and the question asks us to find the max and min values of x * y then we can place the ranges one below the other and find the values for x * y for the 4 extreme values i.e. -11, 9, -9 and 2.

The four extreme values of x * y are

99, 18, -22 and -81. So

-81 < xy < 99.

To apply the max min concept we need to keep in mind that the inequalities of the two ranges are the same. If they are not then we manipulate the numbers or use the properties of inequalities to make them the same. This same procedure can also be used to find the extreme values of x + y and x - y.

So where do we use the max min concept?

Whenever we have been given two ranges, one for x and the other for y (with the same inequality sign) and the question asks us to find the value of x + y, x - y and x * y.Now coming to the question given

Is mn < 10?

(1) m < 5 and n < 2

(2) 1 < m < 3 and n^2 < 25Statement 1 : Clearly

insufficient as m can be 4 and n can be 1, which gives us a YES for mn < 10 or m can be -5 and n can be -2 which gives us a NO for mn < 10.

Statement 2 : 1 < m < 3 and n^2 < 25Now here we can apply the max min concept, since 1 < m < 3 and -5 < n < 5. Multiplying the extreme values we get -5, 5, 15 and -15. So the range here is

-15 < mn < 15.

Insufficient.

Combining statements 1 and 2 :

The range for m is 1 < m < 3 and the range for n is -5 < n < 2.Again applying the max min concept we get

-15 < mn < 6. Since mn here will always be less than 10.

Sufficient.

Hope this helps!

For some more strategies on Inequalities, you can download a free Inequality eBook from the link given below

http://gmat.crackverbal.com/free-resources/ebook-library/CrackVerbal Academics Team

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