GMATPrep Data Sufficiency - new one!

[VivianKerr]

I hadn't seen this l'il guy posted and discussed before, so I wanted to share it with you all! I believe it is from GMATPrep 3, just reviewed it with a student. Sharpen your knives...

Of the numbers r+s, r-s, rs, and r/s, which is the greatest?

(1) r = s = 1
(2) r - s is the least

OA to follow!

[prachi18oct]

IMO A

(1) r = s = 1 => r+s = 2, r-s = 0, rs = 1, r/s = 1 r+s is greatest. SUFFICIENT
(2) r-s is least.

Since r-s is least , r+s > r-s => s>0
We have to check cases for r;
r > 0 , Let r = 3 s = 2
r+s = 5, r-s = 1 , rs = 6 , r/s = 3/2 => rs is greatest
Let r = 1/2 , s = 1/3
r+s = 5/6 , r-s = 1/6 , rs = 1/6, r/s = 3/2 => r+s is greatest here.
Different answers => NOT SUFFICIENT

Hence A

[Brent@GMATPrepNow]

Of the numbers r+s, r-s, rs, and r/s, which is the greatest?

(1) r = s = 1
(2) r - s is the least

Target question: Of the numbers r+s, r-s, rs, and r/s, which is the greatest?

Statement 1: r = s = 1
Beautiful, we're given the actual values of the only 2 variables.
r+s = 2, r-s = 0, rs = 1, and r/s = 1
r+s has the greatest value
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r - s is the least
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
Of course, we need to ensure that r-s has the smallest value.
One way to do this is to make r and s both positive AND make r < s. Doing so, will make r-s NEGATIVE, while the other three expressions will be positive. This ensures that r-s has the smallest value
Here are two possible cases that yield conflicting answers to the target question:
Case a: r = 1 and s = 2. Here, r+s = 3, r-s = -1, rs = 2, and r/s = 1/2. In this case r+s has the greatest value
Case b: r = 2 and s = 3. Here, r+s = 5, r-s = -1, rs = 6, and r/s = 2/3. In this case rs has the greatest value
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Answer = A

Cheers,
Brent

[VivianKerr]

Nice job, Prachi! Great question for picking numbers!

[nikhilgmat31]

Statement 2 is bit complex. Better to pick right numbers.

Answer is A