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Suppose that n is an integer such that n/3 is 12 greater than n/2 . Which of the following is the value of n ?

User Swap L
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You said that n/3 = n/2 + 12 .

There's only one number that 'n' can be.
It may or may not be an integer. We'll have to see.

Subtract n/2 from each side: n/3 - n/2 = 12

Multiply each side by 12 : 4n - 6n = 144

Do the subtraction on the left: - 2n = 144

Divide each side by -2 : n = - 72

Yep. It turns out that 'n' is an integer.
It didn't have to be, just because you said so.
For example, if you said that n/3 is only
11 greater than n/2 , we could figure out
what number 'n' must be, and it wouldn't
be an integer.
User Tedsuo
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