Past Practice PSAT Math Question

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1

<p>This question is extremely easy. </p>

<p>Q#4 from 2010 PSAT/NMSQT practice test math section 2</p>

<p>Q. If (x-3)(x+3)=a, then (2x-6)(x+3) =</p>

<p>A) 2a
B) 3a
C) 4a
D) 6a
E) 9a</p>

<p>The answer is A. It is easy. However, it took me 45 seconds to do it. By this method:</p>

<p>(x-3)(x+3) = x^2+3x-3x-9 = x^2-9
(2x-6)(x+3) = 2x^2+6x-6x-18 = 2x^2-18</p>

<p>Which is 2a. </p>

<p>But what is the FASTEST method? Is their logic to be imposed in this question to make it answered in less then 30 seconds? What is it?</p>

2

<p>(x-3)(x+3)=a, then (2x-6)(x+3) =</p>

<p>Try
If (x-3)=a, what is (2x-6) = ?</p>

<p>Hint 2(x-3) = (2x-6)</p>

<p>=====================
In this case, KISS means NO multiplications. That IS the trap!</p>

3

<p>You should shave some time off by realizing that (x-3)(x+3) = x^2-9 immediately.</p>

<p>Xiggi’s method works too.</p>

4

<p>Haha I love these kinds of problems. I was about to di it the same way but realized that there is a much faster solution. The test really likes to trip you up.</p>

<p>(2x-6) can be written as 2(x-3).</p>

<p>so 2(x-3)(x+3), you can replace x-3 and x+3 with a</p>

<p>2a</p>

<p>I know what you thinkin. How did I not see that. Like I said they try to trip you up.</p>

5

<p>That’s the trap, IQ!</p>

<p>Look at it this way</p>

<p>(x-3)(x+3)
--------------- = a/?
(2x-6)(x+3)</p>

<p>(x-3)
------- = a/?
2(x-3)</p>

6

<p>I need to work on recognizing such shortcuts :o.</p>

<p>In any case, I’m usually not pressed for time in the math sections. It’s just the level 5 problems that occasionally trip me up. But more time to work on the level 5s may help …</p>

7

<p>It comes with practice. Betcha you will recognize it next time you see it! :)</p>

<p>By the way, you will find out how beneficial it is to do what you do now, namely answering the questions posed by others. It is one of the very best practices!</p>

8

<p>Yes, I won’t be diving straight into the math anymore, as tempting as it is ;).</p>

9

<p>I plugged in a random number for x and did it all in my head in about 8 seconds</p>

10

<p>I hope you did not plug a number in for (x+3) or used x = -3! :)</p>

11

<p>I plugged in 5 for x, so a=16
and (2x-6)(x+3)=32 so (2x-6)(x+3)=2a</p>

12

<p>My goodness. I could have spent 15 seconds on a question that took me 45 seconds.</p>

<p>I like both xiggi’s and easgles94. However:</p>

<p>I found xiggi’s to be the most fastest logically, however both have some relevance or similarity. </p>

<p>If I found out that (x-3) and (2x-6) are supposed to be related in some way, I could have solved it in 10 seconds. Since 2(x-3) = 2x-6 which is basically 2a. </p>

<p>But how could I not think of it :/</p>

<p>What am I supposed to do to perfect my skills in interpreting questions?</p>