(10-w)(9-w) < 9 ... implies w > 6 ...how?
w(w-1) > 45 ..implies w>7...how?
I'm not able to derive the implication mathematically..Please help.
I think it would be given to you that w is an integer.
If this is a part of a GMAT question, rest assured you would not have to deal with it mathematically. There would be no time to do that.
As shown above, you will get w^2 -19w + 81 < 0 and the apprx roots as 6.5 ans 12.5 which will give (w - 6.5)(w - 12.5) < 0 which implies 6.5 < w < 12.5
(Check out this post if you have doubts in the last step: http://www.veritasprep.com/blog/2012/06 ... e-factors/
Instead, you only need to deal with it logically.
w(w-1) > 45
Think of the case where this is an equation: w(w-1) = 45
Two numbers which are close to each other give 45. We know 7^2 = 49 which is close to 45. If we put w = 7, we get 7*6 = 42 which is less than 45. So w must be greater than 7 for the product to be greater than 45.
Similarly, (10-w)(9-w) < 9
If the product of two numbers close to each other is 9, the number must be around 3. If w = 6, then the numbers are 4 and 3. But 4*3 = 12 which is greater than 9. Hence, w must be more than 6 to get the numbers smaller than 4 and 3 and hence the product less than 9.
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