reciprocal of inequality

[acethegmat]

Can the instructors please help to solve this methodically. Thanks.

This is what I did:
n^2 < 1/100
Therefore:

-1/100 < n^2 < 1/100
-1/10 < n < 1/10
Taking the right side and cross multiplying, I get:
10 < 1/n

Taking the left side
-1/10 < n
1/10 > -n (multiplying both sides by -1)
1/n > -10 (cross multiplying)

Hence I get answer E

[RonPurewal]

your mistake is in the last step here:

Taking the left side
-1/10 < n
1/10 > -n (multiplying both sides by -1)
1/n > -10 (cross multiplying)

Hence I get answer E

first of all, that's not what "cross multiplying" does; there's no way that "cross multiplying" would move n from the numerator (where it's located in the next-to-last step) into the denominator (where it's located at the end).
"cross multiplying" always eliminates all denominators.

second, and much more importantly, you can't perform "cross multiplication" on inequalities, anyway.
"cross multiplication" actually involves multiplication by the denominators of the fractions that are present -- so it won't work if one of those denominators happens to be negative. (your use of "cross multiplication" ignores the very important issue of whether you have to turn around the ">"/"<" sign.)

--

to get from your next-to-last to your last step, you have to perform two operations:

1/10 > -n (starting inequality)

MULTIPLY BY 10 --> this doesn't change the ">" sign
gives
1 > -10n

DIVIDE BY N --> in this instance, n is negative, so you have to turn the inequality sign around!
gives
1/n < -10

there you go.

by the way, you don't have to consider positive values of n at all, since the information in the problem's stem guarantees that n is negative.

[sergiosammartano]

Tough one to follow. I feel like my mind just got off a roller coaster after that one.

"If n denotes a number to the left of 0 on the number line" = n is negative

the square of n is less than 1/100. so what must the square of n look like? 1/101, 1/1000 2/3000 etc...

what kind of negative numbers squared will give us that result? n could be -1/11, -1/100 etc

n is negative so n < -1/10...i think

reciprocal of n = 1/n therefore 1/n < -10

Phew...my mind is still in loops.

You may want to wait for a MGMAT instructor to take this one, before you run with my explanation. I got the correct answer, but feel a little unsure

Ok, but let me get this straight. Do you agree that n=-1/2 is < -1/10? but in that case n^2=1/4 which is not < 1/100....if this is right the condition n< -1/10 does not work.

[MAJIDYOUSAF111]

it is great post.[spam deleted]

[tim]

keep your spam off our boards!

[tim]

Ok, but let me get this straight. Do you agree that n=-1/2 is < -1/10? but in that case n^2=1/4 which is not < 1/100....if this is right the condition n< -1/10 does not work.

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