For part (a), we note that the greatest value of x + y is when x and y are as big as possibly (obviously). So the greatest possible value of x + y is 2 + 3, which equals 5.

For part (b), we look for possible positive and negative signs from x and y. If we can obtain a negative number, then the negative number with the greatest magnitude will become the smallest number. So the least possible value of xy is (-7) (3), which equals -21.

For part (c), we note that perfect squares have minimum of 0. For the greatest value of x2 - y2, we need the value of x2 to be as large as possible and y2 to be as small as possible. If y = 0 is available as an option, use it. So the greatest possible value of x2 - y2 is (-7)^2 - 0^2 = 49.

Part (d) and part (e) follow the same reasoning as part (b).

The trick is to find numbers 1 or -1 for the denominator. This is because a large positive number divided by 1 gives the greatest possible number, but put a negative sign in front of it and the number becomes the least possible number. So the smallest possible value of y/x is 3 divided by -1 which equals -3, while the smallest possible value of x/y is -7 divided by 1 which equals -7.

Hi thks for the detailed explanation. But for the below question:
Given -10< x <= -1; 1<=y<15

Find greatest 2x/y . We cannot just use 1 as denominator correct?..

Negative numbers cannot be avoided here as x is negative and y is positive, so we look for the negative number with the smallest magnitude.

Which is -1/14.

In this case 1 at the denominator does not work.

Hi Eric, Thks for the explanation. Look like there seem no fixed rules that we can apply for such questions right? To ensure we get the correct answer, seem like we have to consider all the possible negative n positive nod ...

Well more than that actually. For division questions, this is what I do.

1. Check to see if there are negative and positive numbers in x and y.

2. Suppose question asks for least number. If there is a negative number available, we pick it. A number is composed of two components - the signage and the magnitude. Look at -1 and -7, for example. 7 has a greater magnitude than 1 (obviously), but add the negative sign and -7 becomes smaller than -1.

To find the least number (especially negative ones), we look for combinations which give the biggest magnitude (without the - sign). 7 divided by 1 is 7, which is the largest possible number. Add a - to the front and the number becomes the smallest possible number.

3. From there, you can proceed to choose the respective numbers. For largest magnitude (ignoring signs), we take the largest value divided by the smallest value. Where possible, the denominator is 1 or -1.

Same idea applies for least negative number where the magnitude must be as small as possible. In this case, the numerator must be as small as possible (1 or -1) and the denominator must be as big as possible.

Hi Eric, thank you very much for such detailed explanation on how to solve such questions.