Thursday, March 16, 2006

DS - prime numbers

What is the value of the integer x?

(1) x is a prime number.
(2) 31 <= x < 37

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - woman's age (sensitive matter)

In what year was Ellen born?

(1) Ellen's brother Pete, who is 1+1/2 years older than Ellen, was born in 1956.
(2) In 1975 Ellen turned 18 years old.

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - relative movement of two cars

While on a straight road, car X and car Y are travelling at different constant rates. If car X is now 1 mile ahead car Y, how many minutes from now will car X be 2 miles ahead of car Y?

(1) Car X is travelling at 50 miles per hour and car Y is travelling at 40 miles per hour
(2) 3 minutes ago car X was 1/2 mile ahead of car Y

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - algebraic equation

Is ax = 3- bx?

(1) x(a+b)=3
(2) a=b=1.5 and x=1

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - bookrack capacity

I..........x.........I
-------------------
(consider a bookrack with length x)

Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack?

(1) x = 50 centimeters
(2) Twelve of the volumes have an average (average men) thickness of 5 centimeters,

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - number product

If w+z = 28, what is the value of wz?

(1) w and z are positive integers.
(2) w and z are consecutive odd integers

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - triangle internal angles

(consider a triangle with internal angles x, y and z)

Is the triangle equilateral?

(1) x = y
(2) z=60

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - jar with color marbles

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?

(1) Of the marbles removed, the ratio between the number of red ones to the number of blue ones is 2:1.
(2) Of the first 6 marbles removed, 4 are red.

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - sweaters shop inventory

Last Friday a shop sold 3/4 of the sweaters in its inventory. Each sweater sold for $20. What was the total revenue last friday from the sale of these sweaters?

(1) When the shop opened last friday, there were 160 sweaters in its inventory.
(2) All but 40 sweaters in the shop's inventory were sold last friday.


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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

integer, positive int, negative int, whole numbers definition for GMAT

Integers, Natural Numbers and Whole Numbers

The numbers {... −3, −2, −1, 0, 1, 2, 3, ...} form the set of integers.
The notation { } indicates 'set' or collection, and the three dots indicate that the list continues endlessly to infinity.
The numbers {1, 2, 3, 4, ...} form the set of positive integers (also called natural numbers or counting numbers).
The numbers {−1, −2, −3, ...} form the set of negative integers.
The number 0 is an integer which is neither positive nor negative. It is usually not considered a counting number.
The numbers {0, 1, 2, 3, ...} form the set of whole numbers, i.e. the set of positive integers and zero.

Saturday, February 18, 2006

aprender a pensar

Uma das dificuldades que muitos candidatos portugueses sentem diante de uma prova como o GMAT decorre de uma falha cada vez mais manifesta do nosso sistema de ensino: de uma forma geral não ensina a pensar; e falha especialmente no que toca ao desenvolvimento do raciocínio lógico-matemático, ao desenvolvimento de competências discursivas de clareza e objectividade.

Todas estas competências são essenciais não apenas à realização de um trabalho científico em rede, portanto partilhado, mas também a projectos multidisciplinares, plurianuais em que uma parte substancial da comunicação e registo de informação ainda utiliza e utilizará sempre texto.

Daí a grande frequência de problemas que ainda hoje ocorrem por um deficiente uso da linguagem técnica ou... da linguagem, simplesmente. E como se pode exprimir claramente um pensamento quando ele próprio se encontra deficientemente elaborado? Do exposto resulta claramente a importância de provas como o GMAT exigidas a todo os candidatos a MBA e progressivamente a cada vez mais lugares com responsabilidades dirigentes nos sectores público e privado.

Friday, February 17, 2006

EC - Safe Drinking Water Act

Under the Safe Drinking Water Act, the Envronment Protection Agency is required either to approve individual state plans for controlling the discharging of wastes into underground water or that they enforce their own plans for states without adequate regulations.

A. that they enforce their
B. for enforcing their
C. they should enforce their
D. it should enforce its
E. to enforce its

EC - seventeenth-century colonists

Samuel Sewall viewed marriage, as other seventeenth-century colonists, like a property arrangement rather than an emotional bond based on romantic love.

A. Samuel Sewall viewed marriage, as other seventeenth-century colonists, like a property arrangement rather than
B. As did other seventeenth-century colonists, Samuel Sewall viewed marriage to be a property arrangement rather viewing it as
C. Samuel Sewall viewed marriage to be a property arrangement , like other seventeenth-century colonists, rather than viewing it as
D. Marriage to Samuel Sewall, like other seventeenth-century colonists, was viewed like a property arrangement rather than
E. Samuel Sewall, like other seventeenth-century colonists, viewed marriage as a property arrangement rather than

EC (expression correctness) doctor malpractice

A patient accusing a doctor of malpractice will find it dificult to prove damage if there is a lack of some other doctor to testify about proper medical procedures.

A. if there is a lack of some other doctor to testify
B. unless there will be another doctor to testify
C. without another doctor's testimony
D. should there be no testimony fromsome other doctor
E. lacking another doctor to testify

PS - hiker walk

A hiker walked for two days. On the second thay the hiker 2 hours longer and at an average speed 1 mile per hour (mph) faster than he walked the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walkingm what was his average speed on the first day?

A. 2 mph
B. 3 mph
C. 4 mph
D. 5 mph
E. 6 mph

PS - inequality area in a x,y plane












In the rectangular coordinate system shown above, which quadrant, if any, contains NO point (x,y) that satisfies the inequality 2x-3y<=(-6) ?

A. none
B. quadrant I
C. quadrant II
D. quadrant III
E. quadrant IV

PS - car value depreciation

In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original price. By what percentage did the book value for this car decrease from 1986 to 1988?

A. 16(2/3)%
B. 25%
C. 33(1/3)%
D. 50%
E. 75%

PS - ration between decreased quantities

The ratio of two quantities is 3 to 4. If each of these quantities is decreased by 5, what is the ratio of these two new quantities?

A. 3/4
B. 8/9
C. 18/19
D. 23/24
E. It cannot be determined from the information given

PS - tagged fish catch

In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?

A. 400
B. 625
C. 1250
D. 2500
E. 10000

PS - Nationwide poll

In a nationwide poll, N people were interviewed. If 1/4 of them said "yes" to question 1, and of those, 1/3 answered "yes" to question 2, which of the following questions represents the number of people interviewed that did NOT answer "yes" to both questions?

A. N/7
B. 6N/7
C. 5N/12
D. 7N/12
E. 11N/12

PS - powers of 2

If s, u and v are positive integers and 2^s = 2^u + 2^v, which of the following must be true?
I. s=u
II. u (not equal to) v
III. s > v

A. none
B. I only
C. II only
D. III only
E. II and III

PS - student clubs

Club...........number of students
---------------------------------
chess...............40
drama.............30
math...............25


The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are both in chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. Hom many different students are in the three clubs?

A 68
B 69
C 74
D 79
E 84

PS - cube volume to surface relation

If a cube has a volume of 64, what is its total surface area?

A 16
B 24
C 48
D 64
E 96

PS - silver price evolution

During a two week period, the price of an ounce o silverincreased by 25 percent by the end of the first week an then decreased by 20 percent of this new price by the end of the second week. If the price of the silver was x dollars per ounce by the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period?

A 0.8x
B 0.95x
C x
D 1.05x
E 1.25x

PS - bi-variant function

If x * y = xy - 2(x+y) for all integers x and y, then 2 * (-3) = ...

(A) -16
(B) -11
(C) -4
(D) 4
(E) 16

PS - value of a polynomial

What is the value of 2x^2 - 2.4x - 1.7 for x = 0.7?

(A) -0.72
(B) -1.42
(C) -1.98
(D) -2.40
(E) -2.89

PS - future airfare spending estimates

A company accountant estimates that airfare next year for business trips of a thounsand miles or less will increase by 20 percent and airfares for all other business trips will increase by 10 percent. This year total airfares for business trips of a thousand miles or less were §9,900 and airfares for all other business trips were §13.000. According to the accountant's estimate, if the same business trips will be made next year as this year, how much will be spent for airfares next year?

(A) $22,930
(B) $26,180
(C) $26,330
(D) $26,490
(E) $29,770

PS - degrees of the circle

The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of teh budget it represents, how many degrees of the circle should be used to represent an item that is 15 percent of the budget?

(A) 15º
(B) 36º
(C) 54º
(D) 90º
(E) 150º

PS - square root of 463

The square root of 463 is between
(A) 21 and 22
(B) 22 and 23
(C) 23 and 24
(D) 24 and 25
(E) 25 and 26

PS - sales comission

On 3 sales John has received comissions of $240, $80, and $110, and he has 1 additional sale pending. If John is to receive an average (arithmetic mean) comission of exactly $150 on the 4 sales, then the 4th comission must be:

(A) $164
(B) $170
(C) $175
(D) $182
(E) $185

PS - relative height of 5 friends

If Sidney is taller than Roger, Roger is taller than ernon, and Billy is taller than both Roger and Felix, then which of the following statements must be true?

A - Felix is shorter than Roger
B - Sidney is taller than Billy
C - Roger is shorter than Felix
D - Sidney is taller than Felix
E - Billy is taller than Vernon

PS (problem solving) copper price

The price of copper rose by 25 percent and then fell by 20 percent. The price after these changes was:

A - 20 percent greater than the original price
B - 5 percent greater than the original price
C - the same as the original price
D - 5 percent less than the original price
E - 15 percent less than the original price

DS - students scores

How many students scored less than the class average on a test?

(1) The class average was 83.
(2) Fourteen students scored above the class average.

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - integer result?

If n is an integer, is (100-n)/n an integer?

(1) n > 4
(2) n^2 = 25

A. Statement (1) ALONE is sufficient, but statement (2) alone is not suffcient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not suffcient.
C. BOTH statements TOGETHER are suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT suffcient.

DS - Men and women in a room

How many more men than women are in the room?

(1) There is a total of 20 women and men in the room.
(2) The number of men in the room equals the square of the number of women in the room.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not suffcient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not suffcient.
C. BOTH statements TOGETHER are suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT suffcient.

DS - (data sufficiency) line segments length

A.......B.........C.......D

In the figure above, is CD > BC?

Given statements:
(1) AD = 20
(2) AB = CD

A. Statement (1) ALONE is sufficient, but statement (2) alone is not suffcient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not suffcient.
C. BOTH statements TOGETHER are suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT suffcient.

Thursday, February 16, 2006

portugueses @ globalização + GMAT + MBA ?


A história parece dizer que os portugueses seriam, em princípio, dos povos que estariam mais à-vontade e mais teriam a ganhar com o processo de globalização em curso. A facilidade de trato, o dom das línguas e certa misteriosa capacidade para lançar pontes entre civilizações e culturas muito diferentes poderão constituir outros tantos pontos fortes dum povo com 500 anos de tradição de comércio, negócios e empresas intercontinentais. O que falta então para que Portugal se torne um "exportador" de gestores e executivos internacionais?
Por outro lado, ainda que colectivamente se venha a assuma uma tal estratégia como uma "prioridade nacional", a verdade é que esta "corrida ao ouro" não deixará nunca de ser um somatório de "corridas" individuais. Cada português que decida preparar-se para competir com outros candidatos dos cinco continentes, terá diante de si um conjunto de portas que terá de ser ele próprio a abrir sozinho. Não se trata aqui de um apelo para o regresso «rapidamente e em força»... à emigração, a qual nunca foi verdadeiramente interrompida, mas de uma proposta de emigração com mais "Valor Acrescentado".
Diante do novo "português à solta no mundo", surge então o curso especializado internacionalmente conhecido por MBA (Masters in Business and Administration), para cujo acesso é exigida uma prova bastante exigente em termos de concentração e prontidão de raciocínio e resposta. O esforço de preparação compensa bastante na medida em que o salário médio do primeiro emprego após um MBA de referência pode chegar a 150.000€ ao ano. Não é preciso fazer muitas contas para perceber quão interessantes poderão vir a ser para o estado português as remessas destes "novos emigrantes".
Um óbice actual a uma tal estratégia é a deficiente preparação oferecida pelo sistema de ensino em Portugal, fruto do progressivo relaxamento dos padrões de exigência, de empenho dos agentes em geral e também, necessário é reconhecê-lo, de importantes mutações culturais e sociais que levam as novas gerações a assumir atitudes cada vez mais distanciadas das que uma tal aposta exige. Eis porque muitos candidatos portugueses acabam por falhar actualmente nos seus testes GMAT, apesar do esforço de estudo e preparação, enquanto outros, porventura com menos tempo investido, acabam por ser bem sucedidos. Talvez a razão para isto não ande muito longe das razões por que alguns gestores e empresários enfrentam com tanta angústia a presente realidade da concorrência global e dos mercados mundiais em ebulição enquanto outros parecem navegar com perfeito à-vontade nestes "mares" agitados.
Basta uma visita à página dos rankings do Financial Times para perceber que o investimento num MBA compensa! Daí que a obtenção de uma boa classificação no teste GMAT, condição determinante do acesso, pode fazer toda a diferença entre conseguir ser admitido(a) num MBA que praticamente assegura um rendimento de 150.000 € / ano... e um dos outros.Por tudo isto, e como são cada vez mais os interessados na "sorte grande" do MBA, decidi criar um blogue para afixar e discutir a resolução de exercícios da parte logico-matemática do GMAT (problem solving / data sufficiency) na qual alguns candidatos portugueses que temos vindo a ajudar ao longo do tempo mostram maior fragilidade.
Se ainda assim subsistirem muitas dificuldades, ou a habitual falta de tempo e de apoio para delinear uma estratégia de resolução dos exercícios no tempo disponível, optimizada para cada pessoa, então os retiros de preparação intensiva na Quinta d'Elmano podem ser uma opção. A quinta fica perto do Porto e possui condições para alojar grupos até 7 pessoas. Os contactos são luisbotelhoribeiro@gmail.com. A quinta fica no lugar de Fijô, em Rebordosa - Paredes.

Pode-se optar entre um retiro em língua portuguesa ou em língua inglesa, a língua utilizada no GMAT. O tema do retiro será um ou vários dos que constituem o leque de avaliação do GMAT: Problem solving, Data sufficiency, Word problems, Reading compreension, Sentence correction, Critical reasoning, Analytical Writing Assessment.

treino intensivo

Retiros de treino intensivo:
Periodicamente são organizados retiros de treino intensivo numa quinta a 15 minutos do Porto, no meio da maior tranquilidade do meio rural, propício à máxima concentração e máxima rentabilidade do tempo investido. Outras actividades complementares interessantes são também possíveis: palestras/debates com especialistas académicos e gestores séniores, concertos, sessões de música, caminhadas, percursos de orientação, karts, etc.
Como chegar ao local:
A quinta fica perto da confluência da autoestrada A41 com a A42, entre a localidade de Sobrado (Valongo) e Rebordosa (Paredes). Tomando a saída de Sobrado na direcção de Rebordosa/Lordelo. Cerca de 1 km depois, atravessa-se a nova ponte da Amizade sobre o rio Ferreira, para o lado de Rebordosa. Segue-se para Fijô de Baixo e no antigo lugar de Souto encontra-se a quinta. Esta estende-se ao longo da margem sul do rio Ferreira.