In the prior blog post, I hinted that there were (at least) 3 different approaches to solving the included OG Diagnostic question. Here they are:
 
1st Approach: Algebra
 
The explanations provided in the Official Guide often focus on the ‘math approach’ as that is that standard approach taken in most math books. However, that type of approach is often step-heavy and arguably takes the longest to complete.
 
For this prompt, we can create 3 variables:
 
N = revenue in November
D = revenue in December
J = revenue in January
 
With the information in the first half of the prompt, we can create two equations:
 
N = (2/5)(D)
J = (1/4)(N)
 
We’re then asked to calculate (D) / [(N+J)/2]
 
With the given equations, we can translate each variable ‘in terms of’ D and plug in… Again, this is tedious, step-heavy work, but you can view it in the Official Guide if you like.
 
2nd Approach: TESTing VALUES
 
Many questions in the Quant section can be solved with a Tactical approach (and part of your training should focus on learning those approaches and when certain Tactics are applicable). Here, we are given no actual values to work with, so we can choose our own.
 
Based on the fractions involved, the common denominator would be 20, so let’s start with D = 20…
 
IF….
D = 20 then
N = (2/5)(D) = 8
J = (1/4)(N) = 2
 
Now, we just have to place D = 20, N = 8 and J = 2 into the question….
 
(20) / [(8 + 2)/2] = (20) / (5) = 4
 
This is the answer to the question - and you’ll get that same result regardless of the values that you choose to TEST  (as long as your numbers ‘fit’ the given equations). This approach has the benefit of being fast and easy (consider the work involved - we’re really just adding and multiplying small numbers together). With fewer steps, you’re also less likely to make a little mistake along the way.
 
3rd Approach: Logic (and using the ‘spread’ of the answers to your advantage)
 
Certain questions in the Quant section are designed with really fast ‘concept shortcuts’ in mind. This is done on purpose to reward strong critical thinkers. Business Schools are looking for EXACTLY that type of critical-thinking applicant, but the GMAT has no way to give you extra points for ‘being clever’ – it can only provide you with potential shortcuts that will save you time and decrease whatever pacing-related anxiety that you might have. As a result of finding these shortcuts, your chances of scoring higher should increase, since you’ll have more time to answer the remaining questions than someone who is using lengthy math approaches and losing time as a result.
 
Here, consider how the given monthly revenues relate to one another….
 
1 - November’s revenue is 2/5 of December’s revenue. This means that the December revenue is MORE THAN DOUBLE November’s revenue.
 
2 – January’s revenue is ¼ of November’s revenue. Since January’s revenue is so much smaller than November’s revenue – and we already know that December’s revenue is MORE THAN DOUBLE November’s revenue, then this means that December’s revenue is a LOT greater (FAR MORE than double) than January’s revenue.
 
We’re asked to compare December’s revenue to the AVERAGE of November’s and January’s…. Averaging those two smaller numbers will lead to a result that is SMALLER than November's. By extension, December’s revenue will be far GREATER than double than average.  Looking at the answer choices, there’s only one answer that fits that description…. 4.
 
Now, consider how much actual work went into the 2nd and 3rd approaches to this prompt (especially relative to the work that went into the 1st approach). Assuming that you had an equal ability to tackle this question using all 3 approaches, which one would be fastest and easiest to implement? If you’re training to be a 760+ Assassin, then you know that it’s NOT the 1st approach.
 
GMAT Assassins aren’t born, they’re made,
Rich