Given that ab b, which of the following must be true?

Question

Given that  ab< 0  and  a > b , which of the following must be true?

I.  a>0

II.  b>0

III.  \frac{1}{a} > \frac{1}{b}

A. I only
B. II Only
C. I and III Only
D. II and III Only
E. I, II and III

Bunuel · Accepted Answer

ab< 0  means that a and b have different signs. Since also given that a > b, then a > 0 > b (a and b have different signs).

So, I is true and II is not.

Next, 1/a = 1/(positive) = (positive) and 1/b = 1/(negative) = (negative), thus 1/a > 1/b. III is true too.

Answer: C.

Hope it's clear.

Anurag06 · Answer

Hi Bunuel

I agree with the same answer but then I had a thought about the above highlighted 3rd option.
that suppose if we plugin values for a = 2 and b= -1; then 1/a= 1/2 will also be -2 if denominator and numerator shuffle and similarly RHS will become +ve too.

So how can we evidently say that 3rd statement MUST BE TRUE as well?

Bunuel · Answer

Not following you... If a = 2 and b= -1, then  (\frac{1}{a} =\frac{1}{2})> (\frac{1}{b}=-1) . Anyway, as it's eplxained in the solution: 1/a is positive, since a is positive, and 1/b is negative, since b is negative: positive>negative.

Anurag06 · Answer

Bunuel I mean to say that inverse of fraction would result in opposite signs in both LHS and RHS when values a and b are assumed 2 and -3. 
1/a = 1/2 and 1/b = 1/-3....if you reverse both sides it will be -2<3 instead of 1/2 > -1/3.. So it may not necessarily be MUST but CAN situation rather right?

Bunuel · Answer

Could you please show values of a and b for which III is not true? I still cannot understand what you mean.

GMATBusters · Answer

inverse of fraction: there is a swap in denominator and numerator. No change in sign.
if 1/a = 2, then a = 2 not -2.

Bunuel · Answer

Also, if you cross-multiply 1/2 > -1/3, you'll get -3 < 2 (flipping the sign because we multiplied by -3.)

bumpbot · Answer

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Given that ab< 0 and a > b, which of the following must be true?

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