8. CAPÍTULOS DE LA INVESTIGACIÓN DE MERCADOS
8.1. CAPITULO I
Solve the following problems and choose the best answer. (Answers and explanations are at the end of the chapter.)
Basic
How many odd integers are between and Nineteen Eighteen Ten Nine Eight
What is the greatest integer that will divide evenly into both 36 and 54? 6 9 12 18 27
35 42
Which of the following is a multiple of all three integers 2, 3, and 5? 525 560 615 620 660
What is the smallest positive integer that is evenly divisible by both 21 and 9? 189 126 63 42 21
If the sum of three different prime numbers is an even number, what is the smallest of the three? 2 3 5 7 It cannot be determined from the information given.
The integers A, B, and C are consecutive and A < B < C. If A2 = C, which of the following could be the value of A? –1 0 2 I only III only I and II only
I and III only I, II, and III Intermediate
If n is an odd number, which of the following must be even? What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10? 21 41 121 241 481
If the product of two integers is odd, which of the following must be true? The sum of the two integers is an odd number. The difference between the two integers is an odd number. The square of either integer is an odd number. The sum of the squares of the two integers is an odd number. The difference between the squares of the two integers is an odd number.
For how many positive integers x is an integer? 8 7 6 5 3
In the repeating decimal 0.097531097531…, what is the 44th digit to the right of the decimal point? 0 1 3 7 9
What is the greatest integer that will always evenly divide the sum of three consecutive even integers? 2 3 4 6 12
The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers? 315 321 330 415 424
36
divided by 9, all of the following must be true EXCEPT The number that is 4 less than P is a multiple of 9. The number that is 5 more than P is a multiple of 9. The number that is 2 more than P is a multiple of 3. When divided by 3, P will leave a remainder of 1. When divided by 2, P will leave remainder of 1. Advanced If the product of two integers is an even number and the sum of the same two integers is an odd number, which of the following must be true? The two integers are both odd. The two integers are both even. One of the two integers is odd and the other is even. One of the integers is 1. The two integers are
consecutive.
If both the product and sum of four integers are even, which of the following could be the number of even integers in the group? 0 2 4 I only II only III only II and III only I, II, and III
A wire is cut into three equal parts. The resulting segments are then cut into 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire? 24 36 48 54 72 How many positive integers less than 60 are equal to the product of a positive multiple of and an even number? Four Five Nine Ten Eleven
AVERAGES
The average (arithmetic mean) of a group of numbers is defined as the sum of the values divided by the number of values.
On the GRE you might see a reference to the median. If a group of numbers is arranged in numerical order the median is the middle value. For instance, the median of the numbers 4, 5, 100, 1, and 6 is 5. The median can be quite different from the average. For instance, in the above example, the average was $1.00, while the median is simply the middle of the three prices given, or $0.75.
If we know the average of a group of numbers, and the number of numbers in the group, we can find the sum of the numbers. It’s as if all the numbers in the group have the average value.
37
Example: The average daily temperature for the first week in January was 31 degrees. If the average temperature for the first six days was 30 degrees, what was the temperature on the seventh day? The sum for all 7 days = 31 × 7 = 217 degrees. The sum of the first six days = 30 × 6 = 180 degrees. The temperature on the seventh day = 217 – 180 = 37 degrees. For evenly spaced numbers, the average is the middle value. The average of consecutive integers 6, 7, and 8 is 7. The average of 5, 10, 15, and 20 is (midway between the middle values 10 and 15).
It might be useful to try and think of the average as the “balanced” value. That is, all the numbers below the average are less than the average by an amount that will “balance out” the amount that the numbers above the average are greater than the average. For example, the average of 3, 5 and 10 is 6. 3 is 3 less than 6 and 5 is 1 less than 6. This in total is 4, which is the same as the amount that 10 is greater than 6.