Math Questions

Test Preparation SAT Preparation
1

<p>In the triangle ABC above if a > b > c, which of the following must be true?</p>

<p>I. 60 < a < 180
II. 45 < b < 90
III. 0 < c < 60</p>

<p>A. I only
B. Ii only
C. I and III only
D. II and III only
E. I, II and III</p>

<p>C is correct answer</p>

<p>Paul has 24 pieces of candy, and Kate has 40 small pieces of candy. They have agreeded to make trades of 1 of Paul's large candies for 3 of Kate's small candies. After how many such trades will Paul and Kate each have an equal number of candies? </p>

<p>Correct answer is 4</p>

2

<p>a>b>c means ‘a’ is the biggest angle</p>

<p>Since ‘a’ is the biggest angle, a>60 (equilateral triangles are 60-60-60)</p>

<p>Thus I is true</p>

<p>If a>60, ‘c’ needs to smaller to compensate (angles have to add to 180)</p>

<p>Thus III is true</p>

<p>[C]</p>

<p>24 = 40
26 = 38 (First trade)
28 = 36
30 = 34
32 = 32</p>

<p>Four trades</p>

<p>One way to check this is that note the number of candies total is still 64.
34 = 34</p>

<p>5 Trades</p>

3

<p>

</p>

<p>What is the difference at the start? 40 - 24 = 16</p>

<p>What is the full impact of each trade? 4 (one loses two, the other gains two)</p>

<p>16/4 = 4.</p>

<p>Fwiw, this type of problem can be viewed as distance problems. For example, Paul lives in A and his girlfriend Kate lives in B. The cities are 16 miles apart. If Paul runs to Kate at 3 mph and Kate walks more slowly at 1mph in Paul’s direction. How long with their first kiss last? Oops, wrong question. Here is the real question: How long will it take before they meet? </p>

<p>Total D = 16
Combined rates = 3 + 1 = 4
Total time = 16/4 or 4 hours. </p>

<p>The key is to evaluate the combines rates correctly and not lose track of the directions. For instance, the same problem could state that while Paul walks in the direction of B, Kate actually runs away from him in the opposite direction. How long would it take for Paul to catch Kate?</p>

4

<p>Thanks both Greedisgood and Xiggi.</p>