Brian@VeritasPrep wrote:Hey guys,
Great thread - and I love the explanation, kmittal!
Since we're talking strategy on this one, I wanted to point out that this question lends itself really well to a DS strategy that I think is really important and useful:
If both statements together make it particularly easy to solve the problem, you can probably do it with one statement alone and should work to see which one can do it.
Essentially, the GMAT has two ways to get you a wrong answer on the GMAT:
1) You think you have enough information but you actually don't
2) You think you don't have enough information but you actually do
The first is full of assumptions, forgetting to consider 0, etc.
The second is more subtle and can lend itself to higher difficulty problems like this one. Would most people have the patience to factor out Statement 1, or to play with the algebra for >5 steps to simplify? Probably not, particularly given the time pressure of this test. But when you look at both statements together, it's far too easy to pick 'C'. That should be your clue that it's worth putting in the extra time to work out the algebra in statement 1.
Whether you factor as kmittal did, or start to work through the equation by multiplying out the denominator, your guiding principle should be "both together are too easy, so it's worth the extra time to try to do it with this one alone". It's a great investment of your time at that point.
I worked through the algebra on this one:
3a/(a+b) = 7
3a = 7a + 7b
-4a = 7b
a = -7/4 b
Now that I know I can solve for a in terms of b, I can look at the initial question and see if that's enough (or if I need to do any additional work):
What is (2a + b)/(a+b)?
If I can express both the numerator and denominator in terms of b:
[2(-7/4 b) + b] / (-7/4 b + b)
Then I'll be able to get a b term on top and a b term on bottom, and then divide out the bs to get a number. Therefore, statement 1 alone is sufficient.
An excellent tip Brian, thanks
. Indeed I have also noticed, if combining option 1 and 2 leads to an answer quickly, more often than not you only need one equation equation.
Maybe this is a bit out of the scope of this discussion, but on a DS question, if option 1 and 2 are each enough to solve the problem, however they give different numerical answers, is this an indication you have done something wrong? For e.g., if the question asks you "Is x>0?" (1) x > 6 (2) x =3
Both (1) and (2) individually are enough to answer this, however they each give a different answer for x.
