If a / b > 2, is 3a + 2b < 18?

Could anyone else please provide alternative ways of solving this problem?

Thank you.

First thing is always to note that if a/b > 2, then a & b are same sign.

Now manipulate the given formula from a/b>2 --> a > 2b

Data 1: a - b < 2
Manipulate this formula in terms of a: so a < b + 2
Now we know that "a" > 2b and a < b + 2.
The only way for the above to be true is if b < 2.
Now for a, if we know b's limit is 2, than we know a - 2 < 2, so a < 4.
If we look at 3a + 2b and plug in our greatest limits of b =2 and a = 4 we get 3(4) + 2(2) = 16 which is less than 18.
Therefore, A is sufficient.

Data 2: b - a 2
Similar manipulation to part A reveals that a > b - 2 and a > 2b, this does not give us any limitations on the values.
Therefore insufficient.

Therefore answer is A.

please leave kudos, first time posting!

I looked at the first two lines of your response and found a flagrant error (marked in red above) that made me disregard the rest of your explanation.

You say that: a/b > 2 --> a > 2b

If a = -3 and b = -1 ---> -3/-1 = 3 > 2. From this does not follow that: a > 2b ---> -3/-1 * -1 = -3 > 2*-1 = -2

Can anyone else please explain in detail the answer to this problem and also what is the fastest way to solve it?

Thank you.

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