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Asked: If 1 > 1 - ab > 0, which of the following must be true?
Minus 1: -
0> -ab > -1
Changing sign:-
0<ab<1
Since ab>0; a/b>0

I. a/b > 0
I. a/b < 1
III. ab < 1

IMO E
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Thanks for the solution. ab>0 means ab can be greater than 1 or smaller than 1 but greater than 0. How is it enough to say ab>0 without saying ab is less than 1. May be I am lacking some logic in my understanding in must be Q.

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Bunuel
If 1 > 1 - ab > 0, which of the following must be true?

I. a/b > 0
I. a/b < 1
III. ab < 1

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

Kudos for a correct solution.

1 > 1 - ab > 0
Multiply by -1.......1*(-1)<ab-1<0 => -1<ab-1<0
Add 1 to each part of inequality.....0<ab<1
This means a and b have the same sign, and at least one of the two is a fraction between 0 and |-1|.

Let us look at the options.
I. a/b > 0
This tells us that a and b have the same sign. We may not know the value of a and b, but surely they have the same sign and, therefore, a/b>0.

II. a/b < 1
Now, we do not know the value of a and b. we just know that at least of a and b is a fraction between 1 and -1.
Say a=1/3 and b=2.......\(\frac{a}{b}=\frac{\frac{1}{3}}{2}=\frac{1}{6}\)
Say b=1/3 and a=2.......\(\frac{a}{b}=\frac{2}{\frac{1}{3}}=\frac{2*3}{1}=6\)
Need not be true always.

III. ab < 1
We have already seen the inequality mean 0<ab<1.
True

I and III

E
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gayatri259
What does it mean in inequality DS when we say a/b>0 ==> ITS POSITIVE and the value of a/b does not matter, a/b could be 25/5 = 5 and 1-5 would be -4 which is not greater than zero. I am confused that what should I conclude from this?

You will have to elaborate further. What is 1-5?
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Hi Bunuel, The final equation I am getting out of this question is 0<ab<1

Now, as the question states MUST, how can E be the answer? According to me the answer should be A, as in 3rd option its written ab<1(must) now ab can be any value less than 1, it can also be -20. But if its -20 then it will make 0<ab<1 invalid. Please help me understand, where m I going wrong?
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