5 of 5 Items .... Source: SAT

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Is there enough information to determine the least possible value of y?

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Can you find values for y that will make each answer true? Generalize the rules in effect here.

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This is from the end of a section of an SAT test, and is therefore a bitch to solve. At least, the results from the test seem to indicate so.  On a 5-choice multiple choice question, only 8% of respondents got this one right ... if they had covered their eyes, refused to read the question, and randomly guessed, they would have more than doubled their chances of getting it right. We can do better than that!

What numbers should I plug into the equations to test for correctness?

25. A watch loses x minutes every y hours. At this rate, how many hours will the watch lose in 1 week?

1. \(7xy\)


2. \(\dfrac{7x}{y}\)


3. \(\dfrac{x}{7y}\)


4. \(\dfrac{14y}{5x}\)


5. \(\dfrac{14x}{5y}\)

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Make similar questions ...

If \(x^2+y^2 = 196\) and \((x-y)^2 = 36\), what is the value of \(xy\)?

1. -116


2. -80


3. -8


4. 80


5. 160

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If you're a junior or senior, you've seen versions of this problem before, perhaps on the SAT (the source of this problem). As I've said before, the SAT is designed in a way that calculators are not necessary and each question must be solvable in less than a minute. Often, the student is expected to change the form of the question: text to algebra, or algebra to visual (graphical); or rearrange the terms, or work backwards from the known.