Quantitative Section Format

Following the AWA is the Quantitative section, during which you will be asked to answer 37 questions in 75 minutes (on average, about 2 minutes per problem). The quantitative questions will come in two different formats, Problem Solving and Data Sufficiency, and the two question types can be presented in any order. Test-takers are generally offered between 20 and 22 Problem Solving questions and between 15 and 17 Data Sufficiency questions.

Both question types can vary from quite easy to extremely difficult, but every problem has a solution method that will take two minutes or less, though not everyone will discover or be capable of executing that method in that timeqframe. In general, as questions become more difficult, two things will separate those who get the question right from those who get it wrong: knowledge of the quantitative content being tested and knowledge of the optimal solution method. Timing strategies will be discussed in more detail later in this document.

Problem Solving

Problem Solving questions require you to set up and complete any necessary calculations in order to find a specific numeric or algebraic answer, which will be located among five answer choices provided with the problem. An ex- ample of a Problem Solving question and solution appears below.

Problem:

   1727 has a units digit of:

  1. 1
  2. 2
  3. 3
  4. 7
  5. 9

Solution:

When raising a number to a power, the final units digit is influenced only by the units digit of that starting number. For example 142 ends in a 6 because 4 2 also ends in a 6.

1727 will therefore end in the same units digit as 727. The units digit of consecutive powers of 7 follows a distinct pattern; your task is to find that pattern:

Power of 7 Units digit
71 7
72 9
73 3
74 1
75 7 (repeat!)

The pattern repeats after 4 powers, so every multiple power of 4 will end in the same units digit. For example, the units digit of 78 is 1, and the units digit of 712 is also 1. Find the largest power of 4 that is still smaller than your desired exponent, 27. The largest power of 4 that is still smaller than 27 is 24, so 724 has a units digit of 1. Count out the pattern on the chart (ignoring the fifth row, which is a repeat of the pattern): 725 has a units digit of 7, 726 has a units digit of 9, and 727 has a units digit of 3. The correct answer choice is (C).

Data Sufficiency

Data Sufficiency questions require you to understand (a) how to set up a problem and (b) whether the problem can be solved with the given information. You do not actually need to solve the problem as you would with a Problem Solving question. In fact, you should not spend time completing the necessary calculations for these questions as you will then be unable to finish the test in the given amount of time. For example, if the question asks how old Sue is and provides the information that (1) Joe is 12 and (2) Jim is 18, then you cannot solve for the unknown value: Sue’s age. If the information, however, tells you that (1) Joe is 12 and (2) Joe is 4 years younger than Sue, then you can solve for Sue’s age, but you shouldn’t spend time doing so. Sue’s age will not actually appear in any of the answer choices; rather, the correct answer choice will indicate that you need both data points (1) and (2) in order to solve the problem.

Data Sufficiency problems can be worded in one of two main ways: as value questions or as yes/no questions.

Type Description Example
Value:
How old is Sue?
Sufficient data will allow you to calculate one unique value for the unknown in question Sufficient: Joe is 12 and Joe is 4 years younger than Sue
Insufficient data will allow you to calculate either zero values or more than one value for the unknown in question Not sufficient: Joe is 12 and Jim is 18
Yes/No:
Is Sue 16 years old?
Sufficient data will allow you to determine that the answer is either always yes or always no Sufficient: Sue is between 20 and 25 years of age
Insufficient data will allow you to determine that the answer is maybe: sometimes yes and sometimes no Not Sufficient: Sue is between 15 and 20 years of age

A full example of a value Data Sufficiency problem and solution is below.

Problem:

What is the greatest common factor of positive integers a and b?
      (1) a = b + 4
      (2) is an integer

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.

Solution:

First, it’s important to be aware that the five answer choices shown above are exactly the same on every data sufficiency problem. The text is identical and the order of the answers is always the same — for example, answer choice (A) always says that statement 1 is sufficient alone but statement 2 is not. You can, and should, memorize the answer choices before you go into the exam.

Factors are integers that divide evenly into other integers. For example, 4 is a factor of 8 because = 2, an integer with no remainder. 3 is a factor of 9 because = 3, an integer with no remainder.

The greatest common factor of two numbers is the largest factor that is common to both numbers. For instance, the greatest common factor of 4 and 8 is 4, because 4 is the largest factor that divides evenly into both numbers. The greatest common factor of 8 and 12 is also four, because 4 is the largest factor that divides evenly into both numbers.Examine statement (1) alone first. If you try some numbers, you can see the fact that a = b + 4 leaves you with multiple possible answers to the question. For instance, if b is 4 and a is 8, then the greatest common factor is 4. If, however, b is 5 and a is 9, then the greatest common factor is 1. Statement (1), by itself, is insufficient to answer the question; eliminate answer choices (A) and (D).

Next, examine statement (2) by itself. This statement indicates that is an integer but tells you nothing about the value of a. As a result, you cannot tell what the greatest common factor of the two might be. Statement (2), by itself, is insufficient to answer the question; eliminate answer choice (B).

Finally, examine the two statements together. Statement (2), is an integer, indicates that b is a multiple of 4, though it does not tell you an exact value for b. Statement (1) tells you that, whatever b is, a is exactly 4 greater than b. If a is always 4 greater than b, then a must also be a multiple of 4, and a must also be the next consecutive integer multiple of 4. For example, if b is 4, a is 8. If b is 8, a is 12.

You can solve this problem if you know a certain number principle (one that you are expected to know for the GMAT): for any two positive consecutive multiples of an integer n, n is also the greatest common factor of those multiples. Because you know that b and a, respectively, represent two positive consecutive multiples of the integer 4, then 4 is the greatest common factor of b and a.

Bonus exercise: see if you can figure out why the principle discussed in the previous paragraph is always true.

Optional Break #2

The second of the two optional breaks occurs between the Quantitative and Verbal sections. The procedure will be the same as during the first optional break. Again, it is strongly recommended that you take the break.