### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #181 : Data Analysis

The first six terms of a sequence are:

Which is the greater quantity?

(a) The tenth term of the sequence

(b)

**Possible Answers:**

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

**Correct answer:**

(b) is greater.

The terms are generated by alternately subtracting two and adding two. The next four terms are:

Therefore (b) is greater.

### Example Question #29 : Sets

A bag has blue, green, red, and purple balls.

Quantity A: The probability of choosing red ball and blue ball after two consecutive picks, with replacement.

Quantity B: The probability of choosing blue or red ball on one pick.

**Possible Answers:**

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity A is greater.

**Correct answer:**

Quantity B is greater.

Quantity A: There are a total of balls, so the probabilty of choosing red ball AND blue ball is

, which gives us .

Quantity B: The probability of choosing blue ball OR red ball is .

Quantity B is larger.

### Example Question #21 : Sets

If Joe flips a coin twice, what is the probability that at least one tail will occur?

**Possible Answers:**

**Correct answer:**

There are four possible outcomes (with H being heads and T being tails): HH, HT, TT, TH. There are three outcomes that contain a tail: TH, HT, and TT. Therefore the probaility that at least one flip will show tails is .

### Example Question #181 : Data Analysis

An arithmetic sequence begins

What number replaces the square?

**Possible Answers:**

**Correct answer:**

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

### Example Question #182 : Data Analysis

The first two terms of an arithmetic sequence are

Which of the following expressions is equivalent to the fifth term?

**Possible Answers:**

**Correct answer:**

An arithmetic sequence is formed by adding the same expression to each term to get the next term; this common difference is

.

To obtain the fifth term, add to the second term three times - equivalently, add three times this to the second term;

### Example Question #183 : Data Analysis

A geometric sequence begins

.

What number replaces the circle?

**Possible Answers:**

**Correct answer:**

Since this is a geometric sequence, each entry in the sequence is obtained by multiplying the previous entry by the same number - this number is

.

Now we can find the next three entries in the sequence:

This replaces the square.

replaces the triangle.

replaces the circle and is therefore the correct answer.

### Example Question #34 : How To Find The Missing Part Of A List

An arithmetic sequence begins

What number replaces the circle?

**Possible Answers:**

**Correct answer:**

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

.

The next three entries in the sequence are computed as follows:

, which replaces the square

, which replaces the triangle

, which replaces the circle

### Example Question #182 : Data Analysis

A geometric sequence begins

What number replaces the square?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #183 : Data Analysis

The* Fibonacci sequence* is formed as follows:

For all integers ,

Which of the following is true of , the one-thousandth number in this sequence?

**Possible Answers:**

**Correct answer:**

To express , the one-thousandth term of the sequence, in terms of and alone, we note that, by definition of the sequence, each term, except for the first two, is equal to the sum of the previous two. Therefore,

Also

, and, substituting:

and

,

the correct choice.

### Example Question #184 : Data Analysis

The Fibonacci sequence is defined as follows:

For integers , .

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is greater

It is impossible to determine which is greater from the information given.

(a) and (b) are equal

(b) is greater

**Correct answer:**

(a) is greater

The Fibonacci sequence begins as follows:

This sequence is seen to be an increasing sequence. Therefore, each term is greater than its preceding term. In particular,

If we substitute 51 for in the rule of the sequence, we get

, so

This makes (a) greater.

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