Cегодня мы рассмотрим некоторые виды задач, в которых приходится иметь дело с множествами (наборами предметов). Большую долю среди таких заданий составляют объемные текстовые задачи. Существует несколько подходов к решению подобных задач. Рассмотрим их на примерах.

Today we will about problems with sets. A certain portion of  such problems is word problems, in which you have to extract the necessary information from the text. There are a few effective ways to deal with these problems.

1. If 78 people work at a factory, how many are women older than 40?

(1) There are twice as many men working at the factory as women
(2) The number of men under age of 40 at the factory is the same as the number of women of the same age

(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 does not help us by itself. We just know that there are 26 women and 52 men.
Statement 2 informs us that there is the same number of men and women under the age of 40.
Combining the two statements still does not help us answer the question.
So, the answer is E.

2. In a certain office 25% of the computers are equipped with built-in modems and infrared ports. What is the percentage of the computers not equipped with either of these devices?

(1) Half of the computers that are equipped with built-in modems do not have infra-red ports
(2) 35% of all computers are equipped with infrared ports but do not have built-in modems

(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

From Statement (1) we know that 25% of all computers have built-in modems but do not have infrared ports. However, without knowing the percentage of computers with infrared ports but without built-in modems, we cannot answer the question.
Statement (2) gives the opposite information. We cannot answer the question without knowing the percentage of the computers with built-in modems but without infrared ports.
From Statement (1) and Statement (2) combined it follows that 25% + 25% + 35% = 85% of all computers are equipped with at least one of the devices. Therefore, 15% are equipped with neither of them.
The answer is C.

3. In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?
A. 2/15 P
B. 3/5 P
C. 3/4 P
D. 5/6 P
E. 13/15 P

The people who answered “yes” to both questions are 1/3 of 2/5 P, so 2/15 P.
Therefore, the people who did not answer “yes” to both questions are P - 2/15 P = 13/15 P. The answer is E.


Resume. In this lesson we talked about problems, in which we have to calculate values of a set. Such problems appear quite often on the test. Usage of simple rules gives you a correct answer and an opportunity to save some time on your GMAT.

Material prepared by Ksenia Zueva,
GMAT consultant at MBA Strategy