<p>If 3 less than x less than 7 and 4 less than y less than 7, which of the following best describes the range of values of x minus y?</p>
<p>How can the answer be -4 < x-y < 3</p>
<p>How can a possible value be -3??</p>
<p>3<x<7
4<y<7</p>
<p>To find the lowest possible value of x-y, you want the LOWEST X and the HIGHEST y (because you are subtracting it; if you subtract a large number you get a small number):</p>
<p>(lower bound of x) - (upper bound of y) = 3 - 7 = -4</p>
<p>To find the highest possible value of x-y, you want the HIGHEST X to be subtracted by the LOWEST y:</p>
<p>(upper bound of x) - (lower bound of y) = 7 - 4 = 3</p>
<p>-4 < x-y < 3</p>
<p>x-y could be -3 if x = 3.5 and y = 6.5</p>
<p>you have to think logically. if you have somewhere between 3 and 7 quarters, and someone takes away between 4 and 7 quarters, how poor can you be? You’d need to start low (3) and lose a lot (7)</p>
<p>That answer above is WRONG! </p>
<p>I know that its the one given by the SAT, but the symbol < signifies “up to that number, but not including it”. By that I mean 3<x<7 means x can have values of 4, 5 and 6 (but not 3 and 7). There is a separate < symbol which has a line underneath it, which then signifies including 3 and 7 in the value set of x.</p>
<p>This is a big error on SAT’s part, unless of course this is how its taught in the US.</p>
<p>It’s not unlikely that the sign in the book is “greater than or equal to” and he just couldn’t type it.</p>
<p>3<x<7 also includes 3.00000001 and 6.99999998, not just integers. There is no flaw in this problem. For example, x-y could be 3.00001 - 6.99999, which is still approximately -4, but it can never be -4. hence the answer is also in an open interval. Since x and y both are in open intervals, x-y also is in an open interval.</p>
<p>Shawking:</p>
<p>There’s nothing wrong with that answer. </p>
<p>Jollybolly:</p>
<p>“How can x - y = -3?”</p>
<p>3 < x < 7
Therefore x can be 3.5</p>
<p>4 < y < 7
Therefore y can be 6.5</p>
<p>x - y = 3.5 - 6.5 = -3</p>