If a+bm, what is the value of positive integer m?

Question

If a+b>m, what is the value of positive integer m?

(1) a and b are positive 
(2) (1/a +1/b)^(-1) < (1/a . 1/b)^(-1)

cyrwr1 · Answer

not sure whether i am writing stmt 2 correctly.

immarenbe · Answer

Bunuel   KarishmaB  could you share some thoughts on this? Thank you so much!

SaiPraneethPapire · Answer

B according to me. 
after simplifying statement 2 we get ab<0 or a+b>1 and since a+b is positive("positive integer m") a+b>1.

KarishmaB · Answer

The question isn't written in GMAT style. But I will attempt the question as per my understanding of what it is asking.

Given, a+b is greater than a positive integer. So a+b is greater than 1 (the smallest positive integer) at least. We need to find if it must be greater than some other positive integer.

Statement 2:

(1/a +1/b)^(-1) < (1/a . 1/b)^(-1)

\frac{ab}{(a+b)} - ab < 0

ab ( \frac{1}{(a+b)} - 1) < 0

Now, we know that (a+b) is a positive integer. So 1/(a+b) is less than 1 for sure. So 1/(a+b) - 1 is negative. 
Then, for the entire expression to be negative, ab must anyway be positive. Then a and b both must be positive (to ensure that a+b is positive too)

\frac{1}{(a+b)} - 1 < 0 
 a+b > 1

So m is 1.

Statement 2 alone is sufficient.

If a+b>m, what is the value of positive integer m?

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