Data Analysis and Probability - ISEE Upper Level Quantitative Reasoning

Each term of a geometric sequence is obtained by multiplying the previous one by the same number (common ratio); this number is

.

Let be the number in the square.

Since this is an arithmetic sequence, each entry in the sequence is obtained by adding the same number to the previous entry - this number is

Let be the number in the square. Then

Based on the information given, you can construct the following Venn Diagram:

In order to find the overlap, you need to find out how many are in the circles together. This is easy. Subtract: . Now, since the overlap represents a duplication, you need to subtract out one of those duplicate values. Let's call that ; therefore, we know that:

Solving for , you get:

Based on the information given, you can draw the following Venn Diagram:

To solve this, remember that the total number of values in the two circles is:

(We must do this because of the overlap. You need to subtract out one instance of that overlap.)

If we assign the value for the unknown region, we know:

Based on the information, you can draw the following Venn Diagram:

It is very easy to solve for the number of plants that have green leaves but not large ones. This is merely . We find this by eliminating the large-leaved plants from the green ones (by subtracting the overlap from the green ones).

Based on the information given, you can draw the following Venn Diagram:

Now, you must begin by solving for . You know that the two circles together will have in them. This is arrived at by subtracting the people who have neither books nor pens () from the "universe" of people in the sample space (). Now, we know that . This is because of the overlap of in both groups. We have to get rid of one instance of that. Thus we can solve for :

Now, we can find the number of people with only books by subtracting from the to get .

Carter would not fall in set A, since he was not a President born in Virginia.

He would not fall in B, since he was born before 1850.

He would fall in C, since his first name is James.

He would fall in the region included in set C, but not A or B - this is Region V.

Carter would not fall in set A, since he was not a President born in Virginia.

He would fall in B, since he was born after 1850.

He would fall in C, since his first name is James.

He would fall in the region included in sets B and C, but not A - this is Region III.

The subset must comprise words that fall inside sets and , but not . Therefore, all of the words in the subset must begin with a consonant, end with a vowel, and not have six letters.

Of the given choices, the only set whose elements fit this description is {plateau, portmanteau, calliope, marionette, taco}.

The subset must comprise words that fall inside set , but neither nor .

Therefore, all of the words in the subset must have exactly five letters, but cannot begin with a vowel or end with a consonant - that is, we are looking for a set of five-letter words that begin with a consonant and end with a vowel.

The only set among the five choices that matches this description is the set

{price, value, pinna, trove, three}.

The costs of the beverages will be as follows:

Add these amounts:

20% of this is

, which rounds to $5.30.

The following table illustrates the ways that the dice can come up. The orange cells indicate a roll of 6 or less; the pink cells indicate a roll of eight or more.

Since each of these outcomes are equally likely, and there are fifteen outcomes that are favorable to each of the two events, the probabilities are the same.

The gray portion of the circle graph represents Wells; the yellow portion represents Hawley. The gray portion is larger, so Wells won more votes, making (b) greater.

The portion of the circle graph representing Phelps is light blue; it takes up less than half of the graph, so fewer than half of the votes were won by Phelps. (b) is correct.

(a) Add:

(b) Add:

(a) is the greater quantity.

Out of thirty-six possible rolls, there are five ways to roll a six:

Six ways to roll a seven:

Five ways to roll an eight:

This is sixteen rolls out of thirty-six. Therefore, there are twenty rolls that do not result in one of these three numbers. Since all rolls are equally likely, this makes (b) the greater probability.

The size of the orange portion of the circle, which represents Creighton, is larger than the combined sizes of the dark blue and green portions, which represent Barnes and Yale, respectively. This makes (a) the greater quantity.

(a) The four Turkish coffees cost before the discount. The discount is , so the price after discount is .

(b) The two Cafe Americanos cost ; the two lattes cost . The total cost is .

This makes (b) the greater quantity.

In each case, two espressos are being purchased at a regular price, and a third beverage is being purchased at $1.00. This means both sets of drinks cost the same.