Math Problem

Test Preparation SAT Preparation
1

<p>In this problem they use a circle with a line through it. I will use (|) to represent this. I got this from Gruber’s Complete SAT Guide 2013.</p>

<p>a (|) b = a - b -ab</p>

<p>If a (|) 3 = 6, a = </p>

<p>a) 9/2
b) 9/4
c) -9/4
d) -4/9
e) -9/2</p>

<p>Choice E is correct. a (|) b = a - b - ab
a (|) 3 = 6</p>

<p>Substitute a for a, 3 for b:
a (|) 3 = a - 3 - a(3) = 6
= a - 3 - 3a = 6
= -2a - 3 = 6
2a = -9
a = -9/2</p>

<p>My question is back at “= -2a - 3 = 6”.</p>

<p>How do they know to rearrange the order? -3a was on the right, but now it has moved to the left. I understand -3a + a would yield -2a, but why isn’t it “-3 -2a” instead? Is it just arbitrary?</p>

2

<p>Addition is commutative which means it doesn’t matter what order it’s in</p>

3

<p>“Is it just arbitrary?”</p>

<p>Pretty much, but it’s conventional to put the constant at the end.</p>

4

<p>You have some equal signs in the wrong places. The solution should look like this:</p>

<p>a - 3 - a(3) = 6
a - 3 - 3a = 6
-2a - 3 = 6
2a = -9
a = -9/2</p>

<p>I probably would have solved it like this:</p>

<p>a - 3 - a(3) = 6
a - 3 - 3a = 6
-2a - 3 = 6
-2a = 9
a = -9/2</p>

<p>The following is also okay:</p>

<p>a - 3 - a(3) = 6
a - 3 - 3a = 6
-3 - 2a = 6
-2a = 9
a = -9/2</p>

<p>Hope that helps.</p>