### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #54 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

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

**Correct answer:**

(a) is the greater quantity

### Example Question #55 : How To Find The Solution To An Equation

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #56 : How To Find The Solution To An Equation

Solve the equation:

**Possible Answers:**

**Correct answer:**

To solve to the equation isolate the variable on one side of the equation with all other constants on the other side. To accomplish this perform opposite operations to manipulate the equations.

First subtract 18 from both sides.

Now divide by 8 on both sides.

### Example Question #52 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

(b) is the greater quantity

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

(a) is the greater quantity

**Correct answer:**

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

However, without further information, we cannot determine whether this is greater than . For example,

is consistent with the information, and .

is consistent with the information, and .

### Example Question #58 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

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

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

**Correct answer:**

(b) is the greater quantity

It is not necessary to find and to answer this question.

.

### Example Question #53 : How To Find The Solution To An Equation

is positive.

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

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

**Correct answer:**

(b) is the greater quantity

,

so

and

,

so

If , then, since ,

and

.

### Example Question #60 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

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

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

**Correct answer:**

(a) and (b) are equal

### Example Question #181 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve for :

**Possible Answers:**

**Correct answer:**

Apply the properties of equality to both sides of the equation as follows in order to isolate on the left side, keeping in mind the rules for signed integer arithmetic:

Move the decimal points two places right in each of the two numbers, then divide:

### Example Question #62 : Equations

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

**Correct answer:**

(b) is the greater quantity

Isolate on one side of the first equation by dividing both sides by the coefficient of :

Divide by moving the decimal points right two places in order to make the divisor an integer:

Similarly:

, so

;

that is, .

### Example Question #181 : Algebraic Concepts

is a positive number; is the additive inverse of .

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

(b) is the greater quantity

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

(a) is the greater quantity

**Correct answer:**

(b) is the greater quantity

If is the additive inverse of , then, by definition,

.

Therefore, after distribution,

.

If is a positive number, then its additive inverse, , must be negative. Therefore, , as the product of two numbers of unlike sign, is negative. Multiply this by the positive number 7 and the result is also negative, so

,

and

.

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