### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #81 : Equations

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

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

(B) is greater

(A) is greater

(A) and (B) are equal

**Correct answer:**

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

The two equations are actually equivalent, as is proved here:

Therefore, we need only test the first equation. However, it can be shown that it is possible for either of the two to be greater or both to be equal; as can be determined from that third equation , any two values of and that add up to will solve the system, such as , , or .

### Example Question #82 : Equations

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(B) is greater

(A) and (B) are equal

(A) is greater

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

**Correct answer:**

(A) is greater

, so , making (A) greater.

### Example Question #83 : Equations

Give the -coordinate of the point on the graph of the equation that has -coordinate .

**Possible Answers:**

No such point exists.

**Correct answer:**

The point is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating for . Substitute, and we get:

The -coordinate is therefore .

### Example Question #81 : How To Find The Solution To An Equation

Give the -coordinate of the point on the graph of the equation that has -coordinate 64.

**Possible Answers:**

No such point exists.

**Correct answer:**

The point is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating for . Substitute, and we get:

### Example Question #85 : Equations

Give the -coordinate of the point on the graph of the equation that has -coordinate 64.

**Possible Answers:**

No such point exists.

**Correct answer:**

No such point exists.

The point is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating for . Substitute, and we get:

Since the square root of a number must be positive, there is no solution. Therefore, there is no point on this graph with -coordinate 64.

### Example Question #86 : Equations

Give the -coordinate of the point on the graph of the equation that has -coordinate .

**Possible Answers:**

No such point exists.

**Correct answer:**

No such point exists.

However, there is no number that can be divided into 3 to yield a quotient of 0, so there is no solution. Therefore, there is no point on this graph with -coordinate .

### Example Question #87 : Equations

What is ?

**Possible Answers:**

**Correct answer:**

Substitute for in the second equation:

### Example Question #88 : Equations

What is ?

**Possible Answers:**

**Correct answer:**

Solve for in the top equation:

Substitute for in the second equation:

### Example Question #81 : Equations

If , then what is an expression for x in terms of y?

**Possible Answers:**

**Correct answer:**

To solve this problem, isolate for x. First, move the y term over to the left side. This gives you . Then, multiply both sides by 4. This gives you . Then, distribute the four to the terms inside the parantheses. This gives you a final answer of .

### Example Question #90 : Equations

Evaluate .

**Possible Answers:**

The answer cannot be determined from the information given.

**Correct answer:**

Substitute for in the second equation as follows:

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