Math Questions! ;/

Test Preparation SAT Preparation
1

<p>From the BB
1.) Two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT
1, 3, 4, radical 50, 10</p>

<p>is there some kind of rule/law/postulate, etc. that determines what the sides are?
the question states that two sides have lengths of 5, which means that is has to be an isosceles triangle, am I not correct?</p>

<p>2.) In the 30 day month of April, for every three days it rained, there were two days it did not rain. The number of days in April on which it rained was how much greater than the number of days on which it did not rain?</p>

<p>I drew a diagram for this one… (lol) did not even know how to approach it… I felt like I was over thinking the meaning of the problem because I thought it was contradicting if there were only two days it did not rain when it only rained every 3 days…?</p>

<p>3) A four digit integer WXYZ in which W, X, Y, and Z each represent a different digit, is formed according to the following rules</p>

<ol>
<li>X=W + Y + Z</li>
<li>W = Y+1</li>
<li>Z = W-5</li>
</ol>

<p>What is the four digit integer?</p>

<p>I tried using substitution for this one by plugging in e.g Y+1 in to W for the ‘x = w+y+z’ equation and so but i wasn’t able to find an actual value…</p>

2

<p>

</p>

<p>Yes. The third side of a triangle must fall between the sum of the other two sides and the difference of the other two sides. </p>

<p>In this case, the third side must lie between 10 and 0, non-inclusive. Therefore, the answer is 10.</p>

<p>

</p>

<p>So in each 5-day period in April, there were 3 rainy days and 2 no-rain days. </p>

<p>There are six 5-day periods in April, because 6 * 5 = 30. </p>

<p>Therefore, take the ratio 3:2 and multiply it by 6 to get 18:12 (rainy:no-rain). </p>

<p>18 - 12 = 6 (final answer).</p>

3

<br>

<br>

<ol>
<li>X=W + Y + Z</li>
<li>W = Y+1</li>
<li>Z = W-5</li>
</ol>

<p>What is the four digit integer?</p>

<p>I tried using substitution for this one by plugging in e.g Y+1 in to W for the ‘x = w+y+z’ equation and so but i wasn’t able to find an actual value… <<<<</p>

<p>W has to be 5 or larger. X cannot exceed 9.<br>
Try W = 5. That makes Y equal to 4. Z has to be 0.</p>

4

<p>^Thanks for stepping in xiggi. I was brain-dead on the last problem :.</p>

5

<p>There is an algebraic solution for the last problem that no one probably cares about…
WXYZ; put every digit in terms of Y
W = Y+1
X = W + Y + Z = Y + 1 + Y + Y - 4 = 3Y - 3
Y = Y
Z = Y - 4</p>

<p>Each digit must be greater or equal to 0 but less than or equal to 9
1) 0 ≤ Y+1 ≤ 9;
-1 ≤ Y ≤ 8</p>

<p>2) 0 ≤ 3Y-3 ≤ 9;
3 ≤ 3Y ≤ 12;
1 ≤ Y ≤ 4</p>

<p>3) 0 ≤ Y ≤ 9</p>

<p>4) 0 ≤ Y-4 ≤ 9;
4 ≤ Y ≤ 9</p>

<p>You can see that the only digit Y can be is 4. You can now plug in 4 for Y to find out the value of WXYZ or take the long way of algebra…</p>

<p>WXYZ = 1000W+100X+10Y+Z; put everything in terms of Y
1000(Y+1) + 100(3Y-3) + 10Y + (Y-4) = WXYZ
1000(5) + 100(9) + 10(4) + 0 = WXYZ
5940 = WXYZ</p>

<p>Honestly, I don’t see why anyone would take the algebraic solution. :)</p>

6

<p>@Jeffrey</p>

<p>Nobody would do this problem on the SAT algebraically, of course, but when preparing for the SAT I think it’s a good idea for strong students to practice solving problems like this algebraically. This will give a deeper understanding of the mathematics, increase mathematical maturity, and make you a better problem solver. Over time this can increase your potential SAT math score.</p>