Equations, Inequalities DS Question - Pg 114

[SHREE_CS]

if ab = 8 , is a > b?

1 -3b >= -18
2 2b >= 8

Here, a and b need not be integers nor positive as its not explicitly specified. That being said, the official answer provided is B in the strategy guide but I am thinking it could be C.

1 returns b <= 6 and 2 returns b >= 4 so considering the fact a and b need not be integers nor positive, neither of them can be sufficient individually. Together, b's values are restricted to 4,5,6 which could make a to be 2,8/5,8/6 so, we have a N,N,N and hence IMO C is the right answer.

Please help me understand!

[jnelson0612]

[quote="SHREE_CS"]if ab = 8 , is a > b?

1 -3b >= -18
2 2b >= 8

Here, a and b need not be integers nor positive as its not explicitly specified. That being said, the official answer provided is B in the strategy guide but I am thinking it could be C.
Hi Shree,
Let's back up and walk through this very carefully. You are right that a and b do not have to be integers. Our only constraint is that a*b=8. Our question is do we have sufficient information to know whether a > b?

Let's start with statement 1:
1) -3b >=-18
Divide both sides by -3, and don't forget to flip the sign since we are dividing by a negative number. This transforms to b <=6.

If b is less than or equal to 6, then b could be 4 and a could be 2. In this case our answer to the question would be NO.

OR, b could be 2 and a could be 4. Then our answer becomes YES. Insufficient.

Statement 2:
2) 2b >=8
Divide both sides by 2. b>=4.

Let's think about this. We have two scenarios. If b is EQUAL to 4, then a would be 2, since a * b = 8. The answer to our question is NO.

If b is GREATER than 4, then a has to be smaller than 2. For example, if b is 8 then a is 1. If b is 16 then a is 1/2. Again, the answer to our question is NO. Statement 2 gives us a definitive answer of NO, so this statement is sufficient.

Please let us know if you need further explanation!