<p>Student Produced Response Question:
Triangle A has a base of length b and a height of length h. Triangle B is formed by tripling the base and halving the height of triangle A. How many times larger than the area of Triangle A is that of Triangle B?
The "real" answer was 1.5, but I say not, because the question is asking about how much LARGER the triangle is, shouldn't the answer be 0.5?</p>
<p>It asks how many times larger.</p>
<p>So can you explain to me how “larger” works, if 1.5 is the answer?</p>
<p>Let’s say Triangle A has a base of 6 and a height oh 10. We get an area of 30. (6 x 10/2)</p>
<p>Now we triple the base by 3 and half the height. So triangle B has a height of 18 and a height of 5. The area of triangle B is 45. (18 x 5/2)</p>
<p>45/30= 1.5</p>
<p>Exactly. How could the answer be otherwise?</p>
<p>I mean, for example, when you say 300 percent bigger, you mean 400 percent AS LARGE. For this one, shouldn’t 1.5 times as large actually be 0.5 times larger? Because 45 is only 50 percent larger than 30 is my reasoning.
Is there like, a concise definition for “larger than” questions?</p>
<p>You won’t see this type of wording in an SAT math question for the very reason that such wording can be open to interpretation. You will see questions asking how much greater one value is than another value but the meaning is clear (subtract the two).</p>
<p>Also, the use of the word “larger” normally would provide a hint to the answer (something the test makers would avoid), although in this case it seems to have primarily hindered you rather than helped :)</p>
<p>The question is reasonably SAT-like if the last sentence were phrased: “What is the ratio of the area of Triangle A to the area of Triangle B?”</p>
<p>^
I agree that that wording is more SAT like. </p>
<p>However, they DO sometimes test on the distinction between “x is k % of y” and “x is k % LARGER than y”. They word it precisely the way they want it so you just have to read carefully to see what the particular question is calling for.</p>
<p>I haven’t seen the word “larger” used with percents in an SAT question, at least not in the last few years. Please cite a reference. You <em>will</em> often see “percent decrease” and “percent increase” (or “decreased by N%” and “increased by N%”). The example you gave would instead read: “y is equal to x increased by k%”. I think there have been questions with sale prices referred to as “10% off the original price” but this isn’t common.</p>