An SAT Question on Functions
Date: 08/23/98 at 12:13:01 From: rachel Subject: SAT Question I was taking an SAT prep test on the computer from a program that I have. I ran across a question that I was completely unable to answer: Let the "tricate" of a number x be defined as one-third of the smallest multiple of 3 greater then x. If the tricate of z is 3, which of the following could be the value of z? A) 2 B) 5 C) 7 D) 9 E) 11 The question comes with an explanation of how to get the answer but I am still confused. What is a tricate? The explanation does not help at all: Read carefully. If the tricate of z is 3, that means that one-third of the smallest multiple of 3 greater than z will be 9 only if 6 < z < 9. Answer choice (C) is the only number in their range so it must be correct. Now here is my problem. I can see how they reached 7, because it is greater then 6, and less then 9, but how did they come up with 6, how did they come up with 9, and how does this relate to x? Again, what is a tricate? I think if I first off knew what a tricate was, then I would be able to solve this problem.
Date: 08/24/98 at 12:38:51 From: Doctor Peterson Subject: Re: SAT Question Hi, Rachel. I think you may be confused by the word "tricate". The fact is, they have told you what it is, and you know better than I did coming in to this problem what it means. That's because what they are doing is defining a made-up term for you (one that no one in the history of math has ever used, as far as I know), and asking you to apply it. Mathematicians are used to defining new words, sometimes just for use in one article, but that idea may be new to you. Maybe you will be a little more comfortable with calling it a function: t(x) = 1/3 of the smallest multiple of 3 greater than x What in the world does that mean? Let's try to sketch a graph of this function. For x = 0, t(x) is 1, since the smallest multiple of 3 greater than 0 is 3, and 1/3 of that is 1. In fact, until x reaches 3, t(x) will remain the same. Do you see why? Then for any x from 3 to 6 (excluding 6 itself), t(x) will be 2, which is 1/3 of 6, the next multiple of 3. So the graph will look like this: | 4+ * | 3+ *--------o | 2+ *--------o | 1*--------o | 0+--+--+--+--+--+--+--+--+--+-- 0 1 2 3 4 5 6 7 8 9 So the numbers z for which t(z) = 3 are those for which: 6 <= z < 9 Does that help? - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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