<p>If 0 is less than or equal to x which is less than or equal to y and (x+y)^2 is greater than or equal to 25, what is the LEAST possible value of y? </p>
<p>Could someone please explain how to answer this question? Thanks.</p>
<p>Is the answer 3?</p>
<p>EssayTees is right. The answer is 3.
(x+y)^2 is greater than or equal to 25. Assuming it’s equal to 25, the possible combinations of x and y are 0 and 5, 1 and 4, and 2 and 3. We know x is greater than zero and less than y. If x is 0 and 5 is y, the equation works. But since it asks for the least possible value of y, we must take into consideration the closest combination. That leaves x as 2 and y as 3.</p>
<p>Wait! Actually it’s 2.5 (assuming you don’t have to use only whole numbers), since x and y can be equal. Sorry about that.</p>
<p>“0 less than or equal to x” means x > 0, or x = 0 .
“which is less than or equal to y” means x < y, or x = y</p>
<p>Finally (x + y) ^ 2 > 25 (or = 25)</p>
<p>What’s the smallest value of y for which this last inequality is true? We’ll want x to be as “large” as possible, and that happens when x = y, and the sum (x + y) ^ 2 = 25. Or y = 5/2.</p>
<p>I assume that there wasn’t a statement in the original problem that stated that x and y are integers.</p>
<p>2.5 is the answer</p>
<p>5/2 is the right answer…thanks everyone :)</p>