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Picking Numbers

Mathematics: Standard Multiple Choice

Read the following SAT test question and then select your answer. 
Multiple-choices directions are really simple, aren't they? The questions on the test are longer, but they don't say much more than this. Remember that you are allowed to use your calculator, but that it can get you in trouble. I don't actually own one, and I use the one on my computer as little as possible. 
The weights of 10 bags of apples range from 2.75 pounds to 3.15 pounds. If w is the weight, in pounds, of one of these bags, which of the following must be true?
After reading carefully, the next step is to identify the bottom line. Here, the question asks "Which of the following must be true?" and that's extremely hard to put in mathematical shorthand, so the best choice here is to write weight=? at the top of your scratch work.
Next, assess your options. You could translate this problem into an inequality, but that could be complicated because the answers are all absolute value. Instead, pick numbers for w and see which inequality below works out. To make sure that the answer choice will always be true, try three different numbers. When picking numbers, always choose numbers that are easy to work with and that are distinct from one another. In this case, picking 3 and then picking 3 again won't tell you anything about the problem.   32.8, and 3.1 should work nicely. I picked 3 first because it is a whole number, and those are always easier to deal with. 2.8 and 3.1 are near the ends of the given range, so they will make sure you get the right answer. 
Take a look at the answer choices: 
(A) absolute value (w minus 2.75) less than or equal to 0.2
(B) absolute value (w minus 2.95) less than or equal to 0.2
(C) absolute value (w + 2.95) less than or equal to 0.2
(D) absolute value (w minus 0.2) less than or equal to 2.75
(E) absolute value (w minus 10) less than or equal to 2.95

You are probably accustomed to starting with A, but starting with E is a better habit. It will save you some time on this problem; you can eliminate E immediately. 3-10= -7, and 7 is too large an absolute value.

Look at D: 3-0.2= 2.8  D doesn't work either.

You can eliminate C right away because adding to the numbers you chose will not give a number with an absolute value less than 0.2--it would be closer to 6.

Now try B. 3-2.95= .05 That works with the inequality given in the answer choice. Plug in the other numbers you selected: 2.8-2.95= -.15 is also within the range. 3.1-2.95= .15  B fits the range given in the problem, so it is the right answer.



43% of those who attempted this question at sat.collegeboard.org got it right.

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