?

[larhea]

The Product of a positive odd integer and the next consecutive odd integer is 195. What (is)(are) the possible solution(s)?

[RR]

Please post the entire question and the solution.

Any odd number can be represent in the form 2x + 1 where (-infinity < x < infinity)
Two successive odd numbers would be (2x + 1) and (2x + 3)

Your question now boils down to the equation
(2x + 1)(2x + 3) = 195
4x^2 + 8x + 3 = 195
4x^2 + 8x - 192 = 0
x^2 + 2x - 48 = 0
(x + 8)(x - 6) = 0
x = -8 or x = 6

Case I : x = -8
2x + 1 = -15
2x + 3 = -13
The two numbers are -15 and -13

Case II : x = 6
2x + 1 = 13
2x + 3 = 15
The two numbers are 13 and 15

[RonPurewal]

Please post the entire question and the solution.

Any odd number can be represent in the form 2x + 1 where (-infinity < x < infinity)
Two successive odd numbers would be (2x + 1) and (2x + 3)

Your question now boils down to the equation
(2x + 1)(2x + 3) = 195
4x^2 + 8x + 3 = 195
4x^2 + 8x - 192 = 0
x^2 + 2x - 48 = 0
(x + 8)(x - 6) = 0
x = -8 or x = 6

Case I : x = -8
2x + 1 = -15
2x + 3 = -13
The two numbers are -15 and -13

Case II : x = 6
2x + 1 = 13
2x + 3 = 15
The two numbers are 13 and 15

absolutely correct.

however, for 99% of students, PLUGGING IN odd numbers until you find the correct ones will be substantially faster and easier.
i.e., just try 2 consecutive integers. if your product is smaller than 195, then try again with bigger numbers, and vice versa.
it won't take too long to zero in on the correct numbers.

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also note that the wording of this problem is not up to gmat standards: you won't see "next" AND "consecutive" together.
it should say either "...and the next odd integer" or, more concisely, "the product of two consecutive odd integers".

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since this is clearly not a GMATPREP problem, i'm moving it to the general math folder where it belongs.