# GMAT DS: The Statements Cannot Contradict Each Other! A few good takeaways from this question:

-we can always rewrite integers as their factors, so we can say 9 = 3^2
-we can multiply across inequalities freely (without flipping the sign) when we know the variables are positive
-if a smaller integer is LARGER than a bigger integer and they both have unknown exponents, then the exponent of the smaller integer is obviously “making up” for the difference in value and must be larger than the bigger integer’s exponent

The flaw with the question: The statements are incompatible. It cannot be that x = 0 and y = 2, and Statement (2) is true. Because if we plug in x = 0 and y = 2, then Statement (2) reads:

1/16 > 16/9
1/16 is not larger than 16/9

So, while there’s good takeaways here, the fact that the statements contradict one another do not make this a great GMAT question. It is not an official GMAT problem for this exact reason.

Here’s a little more scratchwork, if you’re curious! # Distance and Rate Problems in Data Sufficiency This is a “Value” DS question. The Value we are looking for is the time it took Bob to finish. Let’s look at the specific wording:

How long did it take Bob to complete the race?

(1) If Bob were 2/3 faster, his time would have been 3 hours.
(2) Bob’s average speed was 30 miles per hour.

Given information: We know that Distance = Rate x Time, so if we knew Distance/Rate, then we could find the Time. We could think of this question as asking, what is the ratio between Bob’s Distance and Bob’s Rate?

Need: Distance/Rate

Statement (1):

We know D = R x T.
This says that (5/3)D = R x 3.

Let’s simplify:
(5/3)D = 3R
5D = 9R
D/R = 9/5

Sufficient! We found the ratio we were looking for!

Statement (2):

Average Speed = Total Distance / Total Time
30 = D/T

Unfortunately, we cannot find T. This is insufficient.