В этом  уроке мы разберем некоторые математические задачи, в которых речь идет о таких статистических параметрах, как разброс (Range) и мода (Mode).

In this lesson we consider some Math problems with the Range and the Mode.   
The mode of a list of numbers is the number that occurs most frequently in the list. For example, the mode of 1, 3, 6, 4, 3, 5 is 3. A list of numbers may have more than one mode. For example, the list 1, 2, 3, 3, 3, 5, 7, 10, 10, 10, 20 has two modes, 3 and 10.

The range is defined as the greatest value in the numerical data minus the least value. For example, the range of 11, 10, 5, 13, 21 is 21 − 5 = 16. Note how the range depends on only two values in the data. The range can be 0 if all members of the set are equal or if the set consists of one member.

1. What is the value of X?

(1) X is a mode of [3, 0, 1, - 1, 0, 5, 1]
(2) X is neither positive nor negative

(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.

Statement 1 tells us that X can be either 0 or 1, because this set has two modes: 0 and 1. Insufficient.
Statement 2 tells us that X is 0. Sufficient.
The answer is B.

2.  Are all elements of set S smaller than 20?

(1) The smallest element of S is 0
(2) The range of S is 20

(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

Statement (1) alone is obviously not sufficient: all other elements can have any value greater then 0, they can be greater or less than 20. Insufficient.
Statement (2) gives us information about the difference between the greatest and the lowest numbers in this set. But they can have any values, for example 0 and 20 or 50 and 70. Insufficient.
Using Statement (1) + Statement (2) we can conclude that the biggest element in S is 20. Therefore, not all elements of S are smaller than 20 (the answer to the question is NO).
C is the right answer.

 3. Which of the following cannot be a range of a non-empty set of odd integers?

(A) 0
(B) 2
(C) 4
(D) 5
(E) 8

The range of a set is a difference between the biggest and the smallest member. If all members are odd, this difference will be odd-odd=even. Choice (D) is impossible. Choice (A) is possible because the set can contain only one member and thus have a range of 0. The answer is D.

Resume.  This lesson covers some problems, that are connected with Range and Mode. You should know their statistical meaning  in order to finish the GMAT on time.

Material prepared by Ksenia Zueva,    
GMAT consultant at MBA Strategy