Data Sufficiency Pack 2, Question 2) Is A > B?

Hi shyind,

Your logic, thinking and answer are all correct. However, you didn't technically prove the correct answer. When combining information in the two Facts, whatever examples/TESTs you come up with must 'fit' BOTH pieces of information (as well as any information that you might be given in the prompt). You provided individual TESTs for Fact 1 and a different pair of TESTs for Fact 2, but no 'overlapping' TESTs.

On this prompt, it worked out in your favor, but in other prompts, it might cost you the correct answer (and the points).

GMAT assassins aren't born, they're made,
Rich

Hi All,

As the other posters have noted, this question can be solved with a combination of Number Properties and TESTing VALUES. In these types of situations, it's important to remember that the variables COULD be NEGATIVE numbers...

We're asked if A > B. This is a YES/NO question.

(1) A/B > 1

With this Fact, we know that A and B are either BOTH positive OR BOTH negative.

IF....
A = 3
B = 1
Then the answer to the question is YES

IF....
A = -3
B = -2
Then the answer to the question is NO
Fact 1 is INSUFFICIENT

(2) A > 2B

In this Fact, we have a broader number of possibilities, including A or B equalling 0 and one positive/one negative combinations. However, many of the TESTs that you could have chosen for Fact 1 will also 'fit' Fact 2:

IF...
A = 3
B = 1
Then the answer to the question is YES

IF....
A = -3
B = -2
Then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know
A/B > 1
A > 2B

In the above examples, the same 'pairs' of values 'fit' both Facts and provide different answers to the given question (one YES and one NO).
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is A > B?

(1) A/B > 1
(2) A > 2B

There are 2 variables (A,B) and 2 equations are given from the conditions, making (C) our likely answer.
If we look at the conditions together,
the answer is 'yes' for A=3, B=1, but 'no' for A=-1.9, B=-1

From another solution, looking at the conditions together, if we multiply both sides by B^2, AB>B^2, (A-B)B>0, and we get A-B>0, and ultimately B>0? but since we cannot know the connotation of B, the answer is E.

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

(1) A/B > 1 insufic

a:…b:…a/b:……a>b?
3……1…3/1=3…yes
-3…-1…3………no

*note: a≠b, ab≠0, (a,b)=same.sign

(2) A > 2B insufic

a:…b:…a/b:……a>b?………a>2b
3……1…3/1=3…yes………3>2=y
-1…-1…1………no………-1>-2=y

(1 & 2) insufic
a:…b:…a/b:……a>b?………a>2b
3……1…3/1=3…yes………3>2=y
-0.5…-0.4…1.25…no………-0.5>-0.8=y

Ans (E)