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Q: Best represents the product of two consecutive integers?
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Which set best represents the positive integers?

The set of positive integers, of course!


The sum of squares of two positive consecutive even numbers is 52 What is the smaller number?

This is best solved by trial-and-error. If one set of consecutive even integers doesn't work, try a different set. Hint: The integers involved are fairly small.


Which set best represents the integers?

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What are two consecutive odd integers that multiply up to 225?

13 x 15 = 195 . . . too small15 x 17 = 255 . . . too bigThere are none.The best we can do for you is: (14 x 16) = 224 .===================================For the advanced student:If you work it from the generic form of two consecutive odd numbers,then you would say(2x - 1) (2x + 1) = 225Whence . . . (4x2 - 1) = 225 . . . 4x2=226 . . . x2=56.5 . . . x=sqrt(56.5)The two numbers are 14.0333 and 16.0333 . (rounded)A truly revolting development. Although their product is nice and close to 225,there's no way you could pass them off as odd integers.


What is the greatest possible product that can be formed by two integers whose sum is negative 256?

16,384 is my best guess. -256/2 = -128 -128 + -128 = -256 -128 * -128 = 16384.


What solution set best describes the set of integers less than or equal to -1?

The set of negative integers.


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