Inequalities guide 4th edition, chapter 12 q:1 page - 187

[tom.tharakan]

Chapter 12 : Inequalities advanced problem set : question 1
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This question is, if x > y, x < 6 and y > -3 what is the largest prime number that could be equal to x + y?

I was able to derive the inequality -3 < y < x < 6.

But I could not understand how the final answer 11 was obtained. There is no explanation in the guide as how 11 was obtained.
Could somebody explain?

Thanks..

[milanlee]

I found the answer explanation wasn't clear as well. Here's my approach to replicating the same answer of 11.

Firstly, the problem didn't state that x and y must be integers, the problem only asks for the largest prime number when maximizing x+y. So x and y can be non-integers. (This was the mistake I made at the beginning, assuming that x and y must be integers).

From the problem statement, it can be derived that -3 < y < x (just combine the two statements x>y and y>-3).

Next, since x<6, x can be any value such as 5.9, 5.0, -5.0, and so on. Since I wanted to maximize x+y, I tried 5.9 as a start.

To get y, think about the possible prime numbers greater than 6 are 7,11,13,....

Based on knowing what prime number to set the sum equal to, it is legitimate to set y=5.1 based on the condition -3 < y < x .

And 5.9 + 5.1 = 11 . This is the largest possible prime number I could get, given all the conditions listed in the problem.

Hope this makes sense :-)

[tom.tharakan]

Hi Milanlee,

Thanks for the explanation.

[Ben Ku]

Good explanation, Milanlee.