study wrote:
Yes, the negative sign vanished, cuz negative * negative = positive. So a negative 1/n * negative 1/10 = + 1/10n
And that is exactly the part I don't understand. Why would you retain a negative after multiplying a negative number by another negative number? Would you please explain
To illustrate
-2 * -5 = 10. Not -10
so why would -1/n * -1/10 = -1/10n?
If you multiply, say, -1 by x, the result is -x. It makes no difference if x is positive or negative. If x is negative, then -x is a *positive* number, even if it might look negative because of the negative sign in front. There is a second negative sign 'hidden' inside of 'x'.
That's the issue with the step you took in your edited post. When you multiply 1/n by -1/10, the result is *always* equal to -1/10n. It makes no difference at all if n is positive or negative. If n is negative, then -1/10n is a positive number, because you have two negatives in the fraction, one in the numerator and one in the denominator (since n is negative).
I'd strongly suggest you review this part of algebra, because it's fundamental in many GMAT questions.
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