<p>Hey guys, if anyone has Chung's math or can answer this question, I'm confused on his Tip 3.</p>
<hr>
<p>Tip 3: Combined Range</p>
<p>If 5 ≤ A ≤ 10 and 2 ≤ B ≤ 5 , then</p>
<p>(1) 7 ≤ A + B ≤ 15
(2) 10 ≤ A x B ≤ 50
(3) 0 ≤ A - B ≤ 8
(4) 1 ≤ A/B ≤ 5</p>
<p>Smallest Value ≤ Combined Range ≤ Largest Value</p>
<hr>
<p>Are 3 and 4 perhaps typos? </p>
<p>(3) and (4) do not make sense! They don't seem to follow the rules for the first two. If someone could please explain to me how he arrived at (3) and (4) it would be greatly appreciated. </p>
<p>(3):
The lowest possible value is A: 5 - B: 5 = 0
Likewise, the highest possible value is: A: 10 - B: 2 = 8</p>
<p>You’re probably taking the lowest value of A and B. For subtraction, remember that the lowest possible difference is between the lowest value of the first value and the highest value of the second number.</p>
<p>Instead of memorizing these rules (which are confusing) I always teach to “try all the extremes.” There are 4 computations to do. For example, for (3) the extremes are 5 and 10 for A and 2 and 5 for B.</p>
<p>So the 4 computations are:</p>
<p>5-2=3, 5-5=0, 10-2=8, 10-5=5.</p>
<p>So the smallest value in the range is 0 and the largest is 8.</p>
<p>Note that we took each extreme value for A, and subtracted each extreme value for B.</p>
<p>You can also do most problems like this by picking numbers to eliminate answer choices.</p>
<p>Sometimes you have to be a bit more careful. For example, if -5 ≤ A ≤ 5, then what is the range for A^2?</p>