### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Squares / Square Roots

Give the square root of 256.

**Possible Answers:**

**Correct answer:**

- that is, 16 squared is 256, making 16 the square root of 256 by definition.

### Example Question #2 : Squares / Square Roots

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

(b) is greater

**Correct answer:**

(b) is greater

, so

, so

### Example Question #3 : Squares / Square Roots

Which is the greater quantity?

(a)

(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

(a) , so

(b) , so

,

so

,

and

### Example Question #1 : Squares / Square Roots

Column A Column B

**Possible Answers:**

The quantities are equal.

The quantity in Column B is greater.

There is no relationship between the quantities.

The quantity in Column A is greater.

**Correct answer:**

The quantity in Column A is greater.

The square root of 100 is 10, while the square root of 10 is between the square root of 9 and 16, so about 4. Therefore, Column A has to be greater.

### Example Question #3 : Squares / Square Roots

Which of the following is equal to ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

### Example Question #1 : Squares / Square Roots

Which of the following is equal to ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

### Example Question #4 : Squares / Square Roots

Which of the following is equal to ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

### Example Question #1 : Squares / Square Roots

; is positive.

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(A) and (B) are equal

(B) is greater

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

(A) is greater

**Correct answer:**

(A) is greater

Since is positive, we can compare to 8 by comparing their squares.

and

, so , making (A) greater.

### Example Question #2 : Squares / Square Roots

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(A) and (B) are equal

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

(A) is greater

(B) is greater

**Correct answer:**

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

If , then one of two things is true - either or .

However, and , so it is impossibe to tell whether (A) or (B) is greater.

### Example Question #3 : Squares / Square Roots

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(B) is greater

(A) and (B) are equal

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

(A) is greater

**Correct answer:**

(A) is greater

If , then one of two things is true - either or . Since and , either way, so (A) is greater.

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