Hi
Cryometer! Happy to help!
There are a couple of key things to keep in mind as someone with a math background who struggles with Data Sufficiency. The first of these is that the GMAT as a whole, is not a math test, in the same way it's not an english test. The GMAT, at its core, really is a critical thinking test - and if we can keep that in mind, it will help you better understand how to approach questions logically and push beyond just knowing and applying the mathematical knowledge into understanding why the testmaker has chosen to test you in this way (and with Data Sufficiency in particular - using this structure!)
With that in mind, there are a few major things to keep in mind when approaching Data Sufficiency questions that my students (even - and often especially those with math backgrounds) consistently struggle with.
-Understanding what the question is asking you in simplest terms
-Answering the question that's being asked
-Taking steps to ensure you've drawn the correct conclusion, rather than leaving the question with only 70-80% certainty
The first concerns taking the time on the front end of the question to understand what it's asking you in it's simplest terms. So, take an example like this one:
Quote:
Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?
(1) More of the people in the auditorium have their birthday in February than in March.
(2) Five of the people in the auditorium have their birthday in March.
Many students will rush too quickly through the question stem in an attempt to save time, but will end up quickly (and often confidently!) drawing the wrong conclusion that neither statement can be sufficient, as neither has to do with January. Or, they'll spend far too much time trying to map out all the possibilities for the distributions of these birthdays. But, if we take the time on the front-end of the question to understand that while there are many ways to answer this yes/no DS question yes - there is only one way to answer it no. In order to have zero birthdays in January, all other 11 months would need to be maxed out at 6 birthdays apiece, we can effectively rephrase the question to ask "are all other 11 months maxed out," and it becomes quick and clear how
each of our statements are sufficient.
So, being on the lookout, and taking the time at the front-end to understand what the question is asking you in simplest terms will allow you to more consistently understand how the testmaker is testing you, and what the most efficient path toward the answer looks like.
The second major theme I mentioned is answering the question that's being asked. This is a recurring theme throughout the GMAT, but can be exceptionally tricky in Data Sufficiency. Take an example like this one:
Quote:
If triangles ABC and CDE are each equilateral, what is the sum of the perimeters of the two triangles?
(1) Line segment AE measures 25 meters.
(2) Side BC is 2/3 as long as side DE.
In this case, many students will make the mistake of attempting to solve for each individual side length, then combining them to arrive at (C) - both statements together are sufficient. But, if we take the time to recognize that the question is just asking us for the sum of the perimeters, or 3(side 1) + 3(side 2), we can see that knowing the sum of the lengths of one side is actually all we need! So, when solving for some sort of combination (a sum, product, etc.) ensure you're looking to solve for the collective combination you're being asked for - not trying to solve for each individual element and putting them together. Often times, we can solve for what the question is asking us in DS without knowing absolutely everything about the situation/problem.
Finally, the third point you'll want to be on the lookout for is ensuring you're moving past questions confidently concluding you have drawn the correct conclusion, rather than "guesstimating" and moving on. So, for instance, on a question like this one:
Quote:
If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r.
(2) Every prime factor of s is also a prime factor of r.
You could spend quite a bit of time picking numbers for statement 1, without connecting to
why those numbers consistently answer the question "yes." Keep in mind, that we can never really "prove" sufficiency by picking numbers - so when we pick numbers, we should have the intention of trying to disprove sufficiency. If you find (as in statement 1) that you are unable to do so, there's a good chance that a bigger-picture takeaway exists in the statement. So, if the question is asking us if r/s is an integer - it's really asking us if "r is divisible by s," or if "s is a factor of r." If the question is asking us if "s is a factor of r" and statement 1 tells us "every factor of s is a factor of r," we know this is enough information because the largest factor of any number is itself, and if "s is a factor of s, it must also be a factor of r."
We may be inclined to apply the same logic to statement 2, but keep in mind that it's telling us something a little different than statement 1. If statement 2 tells us: "every prime factor of s is also a prime factor of r," we know they share the same prime numbers, but not necessarily to the same powers.
Thus, here we could pick some numbers to disprove sufficiency by answering the question yes, and answering it no. In this case, if we look a the values "12 - or 3*2*2" and "6 - or 3*2" - we know they share the same prime factors - 3 and 2, and thus could either plug:
r = 12, s = 6 -- to answer the question "yes" or
r = 6, s = 12 -- to answer the question "no" - thus disproving sufficiency
So, for many math-minded students, DS questions go wrong because students move through the questions without taking the proper steps to ensure they're confidently answering the question correctly, or take steps that don't add value to their analysis (picking numbers at random, etc.)
Keeping these three points in mind should aid you in "thinking like the testmaker," and beginning to more consistently and efficiently arrive at the correct answer.
To build on these skills, be sure to build the foundation using medium-level questions before trying to tackle the toughest questions the test has to offer. If you can build the foundation and really reflect on the DS questions you miss to understand not just why the correct approach is correct, but why the wrong answers are wrong and why the question was challenging for you (error logging to find the patterns in your "error types" for these questions can be extremely useful here!) - you should be able to begin to see regular improvement in your accuracy level in DS.
Let me know if you have any questions here! I hope these examples, and their overarching strategic takeaways, help!
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16 Apr 2019, 09:19
