### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : Sets

Which quantity is greater?

(a) The number of even integers that satisfy the inequality

(b) The number of multiples of 4 that satisfy the inequality

**Possible Answers:**

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given.

**Correct answer:**

(a) and (b) are equal

The easiest way to answer this is to try to match each element in the first set to one the second set as follows:

...

In other words, each element in the set in (a) is paired with the element in the set in (b) that is its double. Since there is a one-to-one correspondence, the two sets are of equal aize, and (a) and (b) are equal quantities.

### Example Question #8 : How To Find The Missing Part Of A List

Which quantity is greater?

(a) The number of even integers that satisfy the inequality

(b) The number of odd integers that satisfy the inequality

**Possible Answers:**

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

**Correct answer:**

(a) and (b) are equal.

The easiest way to answer this is to try to match each element in the first set to one in the second set as follows:

...

Since there is a one-to-one correspondence between the elements of the two sets, (a) and (b) are equal.

### Example Question #9 : How To Find The Missing Part Of A List

A pair of fair dice are tossed. Which is the greater quantity?

(a) The probability that the product of the numbers will be at least .

(b)

**Possible Answers:**

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

**Correct answer:**

(b) is greater.

Out of a possible thirty-six rolls, the following result in a product of or greater:

This is ten equally probable rolls out of thirty-six, resulting in a probability of

.

Since , (b) is the greater quantity.

### Example Question #161 : Data Analysis

Which is the greater quantity?

(a) The number of odd integers such that

(b) The number of even integers such that

**Possible Answers:**

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

(a) and (b) are equal.

**Correct answer:**

(a) is greater.

This question can be most easily answered by matching each element in the set in (a) with the next consecutive integer, which is in the set in (b):

...

Every element in the second set has a match, but there is an unmatched element in the first set. Therefore (a) is the greater quantity.

### Example Question #12 : How To Find The Missing Part Of A List

Which of the following is the greater quantity?

(a) The sum of the even integers from to

(b) Twice the sum of the integers from to

**Possible Answers:**

It is impossible to tell from the information given.

(a) and (b) are equal.

(a) is greater.

(b) is greater.

**Correct answer:**

(a) and (b) are equal.

The quantities are equal. This can be proved as follows:

The sum of the integers from to is

.

(b) is twice this:

This is the same value as (a), the sum of the even integers from to .

### Example Question #11 : Sets

An arithmetic sequence begins as follows:

Which is the greater quantity?

(a) The fourth term of the sequence

(b) 200

**Possible Answers:**

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given

**Correct answer:**

(a) is greater

The common difference of the sequence is , so the next two terms of the sequence are:

215 is the fourth term. This makes (a) greater.

### Example Question #14 : How To Find The Missing Part Of A List

A geometric sequence begins as follows:

Which is the greater quantity?

(a) The fourth element of the sequence

(b) 30

**Possible Answers:**

(a) is greater

It is impossible to tell from the information given

(b) is greater

(a) and (b) are equal

**Correct answer:**

(a) is greater

The common ratio of the sequence is

The next two terms of the sequence can be found as follows:

This is the fourth term, which is greater than 30.

### Example Question #651 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

A geometric sequence begins as follows:

Which is the greater quantity?

(a) The fourth term of the sequence

(b) The sixth term of the sequence

**Possible Answers:**

(b) is greater

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

**Correct answer:**

(a) is greater

The common ratio of the geometric sequence is

The next four terms of the sequence are:

- the fourth term

- the sixth term

, so the fourth term, which is (a), is greater

### Example Question #162 : Data Analysis

An arithmetic sequence begins as follows:

Which of the following is the greater quantity?

(a) The tenth element of the sequence

(b) 70

**Possible Answers:**

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

**Correct answer:**

(a) is greater

The common difference of the sequence is ; then tenth element is

,

which is greater than 70.

### Example Question #163 : Data Analysis

A standard deck of cards is altered by removing the red queens and the three of the jacks. A card is drawn at random from this altered deck.

Which is the greater quantity?

(a) The probability of drawing a red card

(b) The probability of drawing a black card

**Possible Answers:**

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

**Correct answer:**

(b) is greater.

The three removed jacks must either comprise two red cards and one black card, or one red card and two black cards. Since the two red queens are also removed, the net result is either the removal of four red cards and one black card, or three red cards and two black cards. Either way, more black cards than red cards are left in the altered deck, and (b) must be greater.

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