Data sufficiency questions are typically not as straightforward as regular quantitative questions. Here are some strategies for eliminating definitively wrong answers:
Always start with the “easier” of the two options
Many times one statement will seem much more complicated than the other. Start with the simple one. This will present simple information that may or may not be sufficient without confusing you and will naturally “build-up” potentially relevant information. If this is not sufficient alone, see if the other serves as complement to provide enough information.
Look for contradictions
Since the questions are phrased in a yes/no format, we should focus on identifying potential contradictions to potential answers. Once you find a contradiction for each statement alone that is not resolved by the other statement, you know the answer is (E). If you don’t find one, chances are this will focus your attention in the right direction regardless.
If the numbers l and m are both greater than 0, is k/m an integer?
(1) k and m are both integers.
(2) k2 and m2 are both integers.
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 to answer the question asked, and additional data are needed.
If I were to pick numbers for Statement 1, say k = 6 and m = 2, then the answer is “yes”; k/m = 3, which is an integer. However, I can notice that picking k = 2 and m = 6 will yield a “no.” Same applies for Statement 2 in this particular question, so the answer is (E).
Know your logic
Statement 1 is sufficient: (B) and (C) and (E) are eliminated. Now focus on whether 2 alone is sufficient.
Statement 1 is NOT sufficient: (A) and (D) are eliminated.
- Check 2. Is this sufficient? If yes, (B). If no, move on.
- Can 1 be supplemented by more information? If yes, does Statement 2 do this? If yes, (C). If not, (E).
Statements 1 and 2 say the same thing: Many times both statements will be the same information put in different ways.
See the following example:
Mrs. K’s class has 10 students. If the average age of the students is 12, then how many of the students are 12 years of age?
(1) None of the students are younger than 12.
(2) None of the students are older than 12.
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 to answer the question asked, and additional data are needed.
Even if we don’t know the answer, we can see that if 1 is sufficient, then 2 must also be sufficient. Answer choices (A) and (B) are eliminated. Means always must be somewhere between the extremes, so if there are no values below 12, then ALL the values must equal 12. Choice (D) is the answer.
Watch for common assumptions
A common mistake is picking numbers, seeing they “work”, and claiming the information is sufficient. Especially with squared variables, we have to be careful that there is not a hidden solution. Let’s take a look:
What is the value of xy2?
(1) y = x – 2
(2) y = x2 – 2
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 to answer the question asked, and additional data are needed.
We can see pretty quickly that one of the two statements will not suffice. Namely, Statement 1 is a line and Statement 2 is a parabola, with infinite pairs of (x,y) coordinates. To check whether both together (C) is the answer, we’d set the equations equal.
x – 2 = x2 – 2
x = x2
Once here, some might see that x = 1, and others that x = 0. In fact, it’s both. (Think of the intersection of a line and parabola and how they hit in 2 spots.) x = 0 would yield xy2 = 0, but x = 1 yields xy2 = 1. Don’t forget about multiple solutions. Choice (E).
Look for superseded information
Especially when we are dealing with ranges, sometimes one statement will give you the same information and more. Depending on the situation, this tactic should eliminate some answer choices immediately. Look at this one:
If x is equal to one of the numbers 5/8, 3/4, or 1/2, what is the value of x?
(1) 1/4 < x < 3/4
(2) 1/3 < x < 2/3
My suggestion here is to draw out your ranges on a piece of paper. Note that the boundaries of Statement 2 are within both boundaries of Statement 1. Therefore, I’d start with Statement 2. Since that is not sufficient, surely Statement 1 will not be either, so choices (A) and (C) and (D) are out without even testing 1. The answer is (E).
Good luck! More GMAT math tips to come from Grockit!
