For today’s GMAT tip, our friends at Manhattan Review work through a data sufficiency problem, to show a strategic way to tackle such questions efficiently:
It is true that Data Sufficiency is, in its own way, a unique form of testing question, and most likely quite different from anything you’ve ever seen before.
The concepts being tested here are not only purely mathematical, but logical. The crux of answering a data sufficiency question correctly is being to test for CERTAINTY and differentiate between CERTAINTY and mere POSSIBILITY.
Let’s test this idea with a real GMAT Data Sufficiency question:
If 2x(5n) = t, what is the value of t?
(1) x = n + 3
(2) 2x = 32
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) together are NOT sufficient.
Let’s start by defining this troublesome word, “Sufficient.” Sufficient, in the context of a Data Sufficiency, means that an unequivocal, CERTAIN answer can be found to the initial question. Must you determine that answer? NO. All you need to determine is the efficacy of the statement’s clue.
Also, let it be said that the two statements need not have anything to do with one another. That is why you must test each one individually first. It’s usually easier to test the simpler-looking statement first.
For the sake of this question, let’s look at Statement 2 first:
(2) 2x = 32
Well, it is easy to determine that x = 16, but we are concerned with the value of t. Let’s replace 2x with 32 into our equation:
32(5n) = t
Can t’s identity be determined with CERTAINTY? No, it cannot. Therefore, we can say with confidence that Statement (2) is NOT sufficient. Go to your answer choices right away, and eliminate the choices that give independent sufficiency to Statement (2): B, D. Remaining: A, C, E.
Now, we wipe our memories of Statement 2 and examine Statement 1:
(1) x = n + 3
Once again, we are provided with a value for x. Let’s replace x in our original equation with n + 3:
2(n + 3)(5n) = t
While this simplifies our equation by eliminating one of the variables, we are still no closer to identifying the CERTAIN identity of t. Statement (1) is NOT sufficient. Now, eliminate the choices that give independent sufficiency to Statement (1): A. Remaining: C, E.
Note to the short-cutters: you’ve already got a 50-50 chance of answering this question correctly!
Now, how does one test Statement (1) and Statement (2) together? First, see how you can combine the information into a single, comprehensive statement. What do we know? We know that x = n + 3, and we know that 2x = 32. Since we were able to determine that x = 16 according to Statement (2), we can substitute this CERTAIN value into Statement (1):
16 = n + 3
This is a very easy equation! n = 13. Now we have CERTAIN values for 2 of our variables. Let’s substitute these values into our original equation:
2(16)(5(13)) = t
Stop right here! Do NOT proceed to do your multiplication, which, without a calculator, will take a good few minutes. You KNOW that a CERTAIN value for t is going to be found. That’s all you need to do: C is your answer — when taken TOGETHER, Statement (1) and Statement (2) are sufficient.
Spare yourself the endless numerical testing, number-picking, and operations in Data Sufficiency. It just isn’t necessary, and eats up your precious time. There’s only one word you need to remember, and that’s CERTAINTY!
