Is rst 1? (1) rs + rt = 5 (2) r + st = 2

The question is testing you on the following concept:
If the sum of two non negative numbers is constant, their product is greatest when the numbers are equal. e.g. if a + b = 10, then ab is maximum when a = b = 5. Maximum value of ab = 5*5 = 25


Stmnt 1: Given rs + rt is constant, the maximum value of rs*rt will be when rs = rt = 5/2. Maximum value of \(r^2st= (5/2)*(5/2) = 25/4.\)
But we get no information about maximum value of rst so not sufficient.

Stmnt 2: Given r + st = 2, then maximum value of r*st will be when r = st = 1.
Maximum value of rst = 1 i.e. rst <= 1. Sufficient.

Answer (B).

Note here that though they haven't said that the numbers are non-negative, we can easily see that the product can be less than 1. We only need to worry about the product greater than 1. In that case, since the sum is positive and product we need is positive, we only need to worry about positive numbers.

Hello Bunnel,

In the second statement you have concluded that rst > = 0 which does not state that it has to be >=1. which the Q has asked to find... since it can have values from 0 to 1.
Please correct me if I am wrong..

Hi,

Let me answer that before Bunuel the Boss comes. If you see, What has been concluded is not \(rst >= 0\) but \((r-1)^2>=0\). Follow the procedure Bunuel has demonstrated. The statement has been manipulated, leading to mean that the question: Is \(rst< = 1\) is the same as Is \((r-1)^2 > =0\).

Hope its clear!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.