# Quickest way to solve a math problem of this nature?

<p>Ahh, I want to know the trick as well… This type of question always seems so confusing - -lll</p>

<p>I remember seeing a really interesting way of solving this on collegeboard.com under the “solutions/answers imagined” category, where they show you different ways to solve it. They animate the solution to the problem. I’m not sure how helpful that will be to you, but it’s worth looking at it.</p>

<p>For me personally, I’d just look at each answer and determine if, with the given information, it was possible for that answer to be true. If you start with the answers, it might be easier to figure out which one is not true.</p>

<p>I would draw a quick diagram that lets you visualize the relative heights</p>

<p>A D</p>

<hr>

<p>B</p>

<hr>

<p>C</p>

<p>then fill in how much they grew</p>

<p>A(2+) D(4+)</p>

<hr>

<pre><code> B(4+)
</code></pre>

<hr>

<pre><code> C (3+)
</code></pre>

<p>And use process of elimination + logic to reach answer choice (E). Since Dave was taller than Charles at the start and grew more, there is absolutely no way that Dave became shorter than Charles at the start of '07. The tricky part of this question is that you have to realize that a lot of stuff is possible, and that you can’t assume that Alan and Dave have the same height.</p>

<p>I don’t think this is the best method, but it works for me.</p>

<p>yeah i just logick it out.</p>

<p>I took a shot for fun. I am not sure it’s a good answer though.</p>

<p>2006:
A > B
D > B
B > C</p>

<p>2007:
A + 2 ? B +4
D + 4 > B + 4
B + 4 > C + 3</p>

<p>a) cannot be determined
b) cannot be determined
c) D is still > B
d) cannot be determined
e) correct: cannot be true because D > B and B > C</p>

<p>D
just write it down</p>

<p>A>B
D>B
B>C</p>

<p>A in relation to D is completely unknown no matter what they are…
A and D must be greater than C always at the start of 2006 whatever value they may be.
so:
A>C
D>C also
Afterward you have:
A+2
B+4
D+4
C+3</p>

<p>Notably if D increases more than C, which it does, it’s impossible for C to actually surpass D if D > C, so (E) is not possible.</p>

<p>The other standout error in this case was D+4, B+4, where B could never surpass D with an equal increment where D>B: this is not an answer choice given however.</p>

<p>collegeboard.com in the SAT section, click “Answers Imagined”</p>

<p>they explain this exact problem step by step</p>

<p>I’ve seen the “answers imagined” clip for this, and didn’t find it to be much of a help. For me, the easiest way to go about solving would be to just divide everything up into categories.</p>

<p>The answer is E, what i just did ( took 2 and a half minutes) partially because i went through every answer choice since E was the last one: </p>

<p>I wrote down the heights in 2006 from tallest to shortest, so A,D,B,C (keep in mind A is not necessarily taller than D or vice versa). Now go through every answer choice</p>

<p>A: Since Alan is taller than Boris in 2006 you can make him any height you wish, so Alan could of been 4 inches—> grow 2 become 6 inches while Boris started at 3—> grew 4 so he would be at 7. True</p>

<p>B: Alan could now be 3.1 inches, Boris would be 3, and Charles 2.9 inches. Alan becomes 5.1 and Charles becomes 5.9, once again TRUE</p>

<p>C: This ones easy, they both grew the same amount and Boris was shorter from the beginning</p>

<p>D: Plug in any numbers for this to work out since it does not specify which one was even taller in 2006. Make Alan 20 inches and Dave 10 inches. Alan becomes 22 and Dave becomes 14 (still shorter) so TRUE</p>

<p>E: If in 2006 Boris was taller than Charles and then he grew more than him how could Charles somehow become shorter. If this logic does not work lets apply some numbers. Boris is 3 inches. Charles is 2 inches. Boris grows 3 so he becomes 6 inches and Charles grows 2 to become 4 inches. Theres no way Boris can become shorter than Charles so that solution is false. </p>

<ul>
<li>Written out it seems complex, but thinking through in your head each option should take about 10-15 seconds. To go through all 5 should take a minute. Pre-planning, reading, and mapping out the question is another minute so 2 to 2 and half minutes total for the question and your in good shape imo</li>
</ul>

<p>My explanation in post #6: In 2007,</p>

<ol>
<li>We don’t know Alan was taller than Boris or Boris was taller than Alan: A ? B</li>
<li>Dave was taller than Boris: D > B</li>
<li>Boris was taller then Charles: B > C
Form (2) and (3) we can conclude that D > B > C, hence D > C</li>
</ol>

<p>Answer A is incorrect because of condition (1).</p>

<p>Answer B is incorrect because we cannot tell how tall A was in comparison with B and C.</p>

<p>Answer C is incorrect because Boris was shorter than Dave (condition (2)). This was TRUE.</p>

<p>Answer D is incorrect because we cannot tell how tall A was in comparison with D and B.</p>

<p>Answer E is correct because D > B > C. Charles was shorter than Dave. They ask for “what could NOT have been true”.</p>