This English Teacher Got Today’s SAT Math Question Correct that Only 56% Solved; and She Has Advice to Make It Easier for You: Answer the Right Question!
Note: If you are taking the SAT this week (March 13), there will be ratio questions. You could pick up a point or two by practicing some from the Princeton Review and/or the College Board site on the types of questions that allow several different ratio questions. They can be like riddles, almost fun.
Over one hundred thousand people answered today’s Question for the Day and only 56%, .56, 56/100 or 28/50 or 14/25 got it right. I got it right, and I understand it. That feels good. Even so, I did not do it the way the College Board explains it. I like their explanation, though. It gives insight to answer more complex questions.
It also gives me the chance to emphasize one more time. If you are not knowledgeable enough right now to do a diagram recognizing triangles like they suggest, 1) You may be able to get the correct answer another way. I did. 2) If it is unfamiliar after you attempt it, mark the answer sheet with a dot in the circle of your best guess and MOVE ON. You can keep on studying and learning; but don't panic about any one test. It's just a test. It's a tool, hopefully for use as much as anyone's.
March 7 Math Question http://www.collegeboard.com/
I absolutely forced myself to make sure I was answering the correct question. This is my key strategy in the mathematics section if my answer is fast, as it was here. My second key strategy is to move on after marking my most educated guesses if I am taking too long. This solution was fast, so I moved to the ‘check the question’ part of my strategy and, sure enough, I was wavering on which question.
It was like: Oh, I know, I know!!!
Then, I stopped—and I realized: I know which answer would be the height of the shadow of the post, as a ratio to the height of the man and his shadow.
I also knew which answer would be the height of the fence post, as a ratio to the height of the man and his shadow. Uh-oh. I almost answered the wrong question.
The question says: The man’s shadow is 60 centimeters long, and the fence post’s shadow is t centimeters long. The man is 180 centimeters tall, so his shadow is 1/3 his height.
(You don’t even have to know what a centimeter is to answer this, but study your terms anyway!)
His shadow is 1/3 his height. MORE IMPORTANTLY FOR THE QUESTION, HIS HEIGHT, therefore, IS 3 TIMES HIS SHADOW’S LENGTH.
So we have the ratio for the fence post and the fence post shadow. We just have to make sure we answer with which is 1/3 and which is 3 times ….
L=1/3H and H=3L (L=length of shadow and H=height of man)
Guess what? The College Board test designers had the answers for both questions—the one I thought it was asking at first and the one it was REALLY asking. Even so, it’s easy to figure.
The College Board solution has a great graphic with some information that will help on many other types of similar problems. But you don’t have to do all of this with this one. The ratio is really easy to see on this one.
The question asks, in terms of t (already given as the length of the SHADOW of the post), what is the height of the fence post?
Okay, the man is an upright vertical line and so is the fence post. He casts a shadow that is 1/3 his height.
Therefore, by the same ratio, the fence post casts a shadow that is t (the label of the length of the shadow). So the height of the fence post is 3 times that length of the shadow which is t --or 3t.
Either way, though, I did not work it out as shown in the College Board solution. You should look at their solution because that recognition of the triangles and the hypotenuse and right angles is classic algebra and geometry that will give you even more answers in other problems.
Learn the metric system terms. Keep them in front of you while doing practice. Never avoid trying a problem because you do not know the terms. You do not have to know what a centimeter is to do this problem. Cent is the root word for hundred. Meter means measurement. The metric system is based on tens. It is an international system. Keep learning it, but do not let the terminology stop you from doing the problems.
