Know, Don’t Solve! Data Sufficiency in Disguise

Attempt the question; then read the explanation below.

GMAT Students, Look Familiar?

Many GRE students preparing to apply to business school have also considered taking the GMAT. There is significant conceptual and structural overlap between the two tests, but one area in which the two tests differ is in Quantitative question types. While both have multiple choice, select one problem solving questions, the GRE features Quantitative Comparison problems at the beginning of each Quant section while the GMAT intersperses Data Sufficiency problems throughout its Quantitative section.

These two question types, Data Sufficiency and Quantitative Comparison, are similar in one important respect: both test students’ abilities to ascertain whether sufficient information has been provided to determine a definite answer without performing excessive calculations. For these problems, students must eschew elaborate solutions and attempt to recognize when sufficient information has been provided to find the answer. If you do try to solve these problems exhaustively, you will likely run out of time!

Sometimes the GRE mixes in a Quant question that is nearly analogous to a GMAT Data Sufficiency problem. Consider the example above. Is it important to know exactly what y equals? No! You only have to determine whether each answer choice alone is sufficient to determine the value of y. You need not solve for y all the way.

The following is a solution:

• Start by Recording What You Know™ and getting your answer choices set up.
  • Good scratch work is essential!
• We know that x is a negative integer and that y = 7.2 ÷ 10^x.
• That second part is tricky. Let’s use our knowledge of exponents to rewrite the equation in a more useful format.
• Since we know x is a negative integer, we know that 10^x = 1 / (10^-x).
• From rules of fractions we also know that since we’re dividing by 1 / (10^-x) we are in fact multiplying by 10^-x!
• Consider the following example to illustrate:

• In other words, the problem has created a very convoluted process around a pretty straightforward exponent operation. Typical GRE!
• To simplify, we can treat the “divide by 10^x” operation like a “multiply by 10^-x” operation.
• Now let’s consider whether each answer choice provides sufficient information to solve for y.
• A does provide sufficient information since there is only one possible value of y that would fit within that range. In this case, x must equal -3. If x = -2, y would be 720. Too small. If x = -4, y would be 72,000. Too big. Thus, only one value works, and this answer choice is correct.
• B does NOT provide sufficient information. √x² < 4 leaves three possible values for x. -3 ≤ x ≤ -1. This answer choice by itself is insufficient to know the value of y. 
• C does provide sufficient information. y² = 5.184 ÷ (10^-7). Take one 10 out of 10^-7. Multiply that 10 into 5.184. Now we have y² = 51.84 ÷ (10^-6). Now let’s take the square root of both sides. y = 7.2 ÷ (10^-3). Thus we can determine the value of y. 
• Notice that answer choice C is an excellent example of a situation in which you need to recognize that sufficient information is provided without working through the actual calculations. For this answer choice, it’s a waste of time.
• How could you recognize sufficient information is provided? You could notice that there is an equation with only one variable and an arithmetic calculation. Thus, regardless of what the exact values of x and y are, you will only end up with one possible value of y. 
• A and C are the correct answers.