specific MARCH Math SAT question!

Test Preparation
1

<p>If I remember correctly, the question asked</p>

<p>(x-y)^2 + (x+y)^2 < 25</p>

<p>Is this correct?</p>

<p>If so, or if not, I would like to see how it is done.</p>

2

<p>There are two inequalities,</p>

<p>0<=x<=y
(x+y)^2 - (x-y)^2 <= 25
The second inequality simplifies into 4xy<=25.</p>

<p>The question asks for the greatest possible value of y. Since y is greater than or equal to x, the greatest value of y occurs for these conditions:
x=y
4xy=25.</p>

<p>Therefore,
4y^2=25
y^2 = 25/4
y=5/2</p>

3

<p>maybe I'm not thinking this through clearly enough....but why does the greatest value of y occur for when x=y... for example, couldn't x=1/4 and y =25.... that would fit the inequality where x<y and 4(1/4)(25)=25...
did you mean that 0 <=y<=x?</p>

4

<p>I spent a good 5 minutes on this problem (it was the last grid-in) but never got it, although I understand how to do it now thanks to dualityim.</p>

<p>Maybe I remember wrong but...did the problem say that y had to be an integer? Everyone that I talked to after the test thought that the answer was 3 (smallest integer for the inequality to work).</p>

5

<p>It asked for the LEAST possible value of y, i think...</p>

6

<p>Oh right. Whoops. It asked for the LEAST possible value of y.</p>

7

<p>Did it ask for an integer or just a value?</p>

8

<p>Just a value. Didn't specify that it had to be an integer.</p>

9

<p>It was also greater than or equal to (and asked for the least possible value)</p>

<p>(x+y)^2 - (x-y)^2 >= 25</p>

<p>given that 0 <= x <= y</p>

<p>Set x = y, reduces to (2y)^2 >= 25</p>

<p>(2y) >= 5</p>

<p>y >= 2.5</p>

10

<p>yeah thats it</p>