MATH PLUG IN—A STRATEGY WHEN YOU NEED TO ‘SEE’ BETTER ON SAT for June 5
First, you need to know that if you look at the explanation on the collegeboard site, you may learn how to solve this particular kind of problem—and many others like it. It is worthwhile to look at the explanation on the www.collegeboard.com site, as that explanation displays how to work that problem.
Our strategy today is using this problem to ‘plug in’ your own figures and to make a mini-version of a problem that you do not know how to solve. This is a strategy to make your best educated guess when you do not know how to do the problem. This strategy, too, will work in many instances. Think of it as ‘plugging in’ a mini-version of the problem in much the same way that you solve fill in the blank language arts questions by filling in a simple word that does fit—and looking for that type of word in the choices.
Here on a math problem, you fill in a simple version, in ratio, if possible, and try out those features within the context of that mini-problem to see the answer to the maxi problem.
Rocketcat guessed at today’s answer by plugging in a ‘sample’ version of the question to see how the question looked. Remember Rocketcat is a visual learner. In fact, he is deaf, so every visual way of ‘seeing’ the answer is a strategy for Rocketcat. Jot this down, as you go.
Look at what he did to guess correctly. He created a mini-version of the problem and eliminated answers until he had a solid guess. He was correct, but his way of doing this problem is fraught with peril. So use this type of reasoning ONLY if you do not understand the clearest way to answer the problem already.
Now, look: Here is the Rocketcat strategy for a problem that he does not ‘see’ clearly. Draw a simplified version.
The original problem:
Mathematics>standard multiple choice.
Read the following SAT question, and then click on a button to select your answer:
A list of 100 integers has the property that the average (arithmetic mean), a, of the integers is greater than the median, m, of the integers. Which of the following must be true?
I.More of these integers are greater than a than are less than a.
II. More of these integers are greater than m than are less than m.
III. More of these integers are less than m than are greater than m.
(A) None.
(B) I only
(C) I and II
(D) I and III
Always, begin at the top left corner and read right to left, all the way through, visualizing the problem to put your mind into any ‘reminder’ areas available.
Rocket did this and this was hard to ‘see,’ so he plugged in some integers from 1 to 10, an exact ratio to the original problem with 100 integers. He is not told in the original problem the range or order of the integers. But look at what happens when he plugs in 1-10
1+2+3+4+5+6+7+8+9+10=55 Okay, now, which is “a” (the mean or average). Divide 55 by 10 (the total of the integers divided by the number of integers = the mean, or average=5.5 for our pretend problem.
Rocket looks at how this looks for this set of 10 integers. The average is 5.5 AND the median is 5.5. So a is 5.5 and m is 5.5.
He looks at I,II, and III in relation to this pretend problem with the same structure as the question
I.More of these integers are greater than a than are less than a.
More of these integers (1-10) are greater than a(5.5) than are less than a (5.5)?
NO. There are 5 integers greater than 5.5 and 5 less than 5.5.
6,7,8,9, 10 are greater and 1,2,3,4,5 are less than a (5.5)
II. More of these integers are greater than m than are less than m.
More of these integers are greater than m (5.5) than are less than m (5.5) NOPE. It’s the same amount as a, and we showed in I that 5 are less and 5 are more.
III. More of these integers are less than m than are greater than m.
More of these integers are less than m than are greater than m. NO. Same reason as before.
Rocketcat knows that his ‘plug-in’ problem may not be parallel in every way to the original problem because it is his version of the problem. But he has ‘solved’ his version. NONE of the statements fit his made up ‘plug-in’ problem. So he chooses A. NONE.
This is the correct answer.
Strategy: If you do not know how to solve a math problem, plug in your own numbers, in a correct ratio if possible. Make your version as simple as possible and label everything to see it visually.
Take the answer that works in your sample problem as the correct answer and mark it. At this point, you have narrowed the ‘guessing’ enough to offset any penalty for a n incorrect answer.
Today, the plug in and simplified visual version resulted in the correct answer for Rocketcat&judiethcarolc.May2010
