Jennifer Land explains how to solve for variables given limited data.
Data Sufficiency (DS) questions are perhaps the most dreaded on the Quantitative Reasoning section of the GMAT. Some people, however, get really good at them—and actually prefer them to Problem Solving questions because often you don’t have to solve them to answer the question. You only need to know whether a statement gives enough information to be able to get a solution.
For the rest of GMAT test-takers, Data Sufficiency remains a challenge. Fortunately, these tips will help ease the pain.
Follow linear equation rules for data sufficiency
The basic “n-variables, n-equations” rule of linear equations holds that you need n distinct (different) equations to solve for n variables; thus to solve for x and y, you need two distinct equations that include both x and y. Consider this Data Sufficiency problem:
What is the value of x?
- 3x + 2y = 6
- 4y = 12 – 6x
You see that you have two variables and you need to solve for one of them. Boom! Two variables, two equations—select “Together” and move on, right? Not so fast. This Data Sufficiency problem is designed to test whether you are cutting corners. If you fail to simplify or rearrange the equation in Statement 2, you will miss seeing that it is THE SAME EQUATION as the one in Statement 1, just multiplied by 2. Thus you only have one equation, even if you combine the statements. So, the correct answer is “Neither.” Don’t cut the corner and skip simplification.
Know when you don’t need to solve for all variables
Not all GMAT linear equation questions require you to solve for two variables. If a Data Sufficiency question asks for the value of an expression, such as 2a + 3b, you may not NEED to solve for both a and b. You may simply be able to solve for what you were asked to find: 2a + 3b. Here’s an example:
What is the value of 7x + 3y?
- 56x + 24y = 520
- 8x + 5y = 79 and 40x + 25y = 395
This question stem does not need to be simplified beyond identifying what we need for sufficiency: the ability to determine the value of the expression in the stem. If you notice that Statement 1 is divisible by 8, and that if you factor out 8 from the left side you are left with 7x + 3y, you already have enough information to answer the question. Statement 1 is indeed sufficient, and you do not need to divide 520 by 8 to confirm.
The tempting corner to cut comes with Statement 2. Again, two variables, two equations—done, right? You guessed it, these are the same equation presented two different ways. So, the answer is that Statement 1 alone is correct.
Remember the rules of taking square roots
Data Sufficiency statements often include quadratic equations. When the stem asks for the value of a variable or whether a variable is positive (or negative), you MUST remember the rules of solving quadratics. This includes recalling that there are TWO possible values for x when you know the value of x². Here’s an example:
What is the value of x ?
- x > 0
- 20 –x² = 4
Right away you see that Statement 1 is insufficient; knowing that x is positive does not give you a single value. Statement 2 requires a bit more work. Rearrange the equation to put x² on one side: x² = 16. That means x = 4 and 2 alone is the answer, right? Nope. Whenever you have a value for x², you have two possible values for x. In this example, x could be 4 but it could also be -4. That means Statement 2 alone is insufficient.
Remembering that same rule, however, means you can now consider the statements together; Statement 1 tells you x is positive, so taken together you know x = 4. Done.
(Bonus info: On the GMAT the radical symbol always gives you only the positive square root. So, although x² = 9 means x = 3 or x = -3, remember that √9 =3. Always.)
These are but a few tips for avoiding common pitfalls on the GMAT. I will discuss others in a later post. Next week, we switch gears to the Verbal section, so buckle up.
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