### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Find Percentage

Using the information given in each question, compare the quantity in Column A to the quantity in Column B.

Jack scores a 40 on his first test and improves his score by 80% on his second test. Jill scores 50 on her first test, and her second test is 130% of her first test.

Column A Column B

Jack's 2nd Jill's 2nd

test score test score

**Possible Answers:**

The quantity in Column A is greater.

The quantity in Column B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

**Correct answer:**

The quantity in Column A is greater.

Jack improves by 80%, so we multiply his original score by 1.8 (the 1 to represent his earlier score and the .8 to add on his improvement). 40% times 1.8 equals 72%.

Jill's second test is 130% of her first test (that is, a 30% improvement). To find her new score we multiply her first score by 1.3. 50% times 1.3 equals 65%.

Thus, Jack's second test score is higher.

### Example Question #1 : How To Find Percentage

of 2,001 is 1

of 1,999 is 1

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

(a) is greater

**Correct answer:**

(b) is greater

No calculation is necessary. The whole in (b) is less, so 1 is a greater portion of that whole than the whole in (a). This makes (b) greater.

### Example Question #2 : How To Find Percentage

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:**

(a) is greater

can be rewritten as

### Example Question #3 : How To Find Percentage

1,111 is of 999

999 is of 1,111

Which is the greater quantity?

(a)

(b)

**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) is greater

No calculation is necessary. In (a), the part is greater than the whole, so the percent **must** be greater than 100. In (b) The part is less than the whole, so **must** be less than 100. Therefore,

### Example Question #2 : How To Find Percentage

There were 48 pieces of fruit brought to the brunch. Twelve of the pieces of fruit were bananas. What percentage of the fruit were bananas?

**Possible Answers:**

25%

66%

50%

12%

48%

**Correct answer:**

25%

Percentage involves part over whole. The total number of fruit was 48. The number of bananas was 12. Therefore, you can make a fraction from those numbers: . Then, to find the percentage, divide 12 by 48. This gives you 0.25. To find the percentage, move the decimal point to the right two places. This gives you 25%.

### Example Question #1 : How To Find Percentage

70% of 4,000 is equal to what percent of 6,400?

**Possible Answers:**

**Correct answer:**

70% of 4,000 is equal to , which is

percent of 6,400.

Evaluate:

The correct response is

### Example Question #6 : How To Find Percentage

is a positive number. Which of the following is the greater quantity?

(A) 70% of 40% of

(B) 40% of 70% of

**Possible Answers:**

(A) and (B) are equal

(A) is greater

(B) is greater

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

**Correct answer:**

(A) and (B) are equal

40% of a number is the number multplied by 0.40; 70% of the number is the number multiplied by 0.70.

40% of is ; 70% of that is

70% of is ; 40% of that is

Regardless of the value of , the quantities are equal.

### Example Question #7 : How To Find Percentage

is a positive integer. Which is the greater quantity?

(A) 25% of

(B) 50% of

**Possible Answers:**

(A) and (B) are equal

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

(A) is greater

(B) is greater

**Correct answer:**

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

The greater of the two can be shown to depend on the value of .

Example 1:

Then 25% of is equal to

and 50% of is equal to

This makes (A) greater.

Example 2:

Then 25% of is equal to

and 50% of is equal to

This makes (B) greater.

Therefore, insufficient information is given in the problem to determine which is the greater.

### Example Question #41 : Percentage

is a positive number. Which is greater?

(A) 60% of 40% of

(B) 50% of 50% of

**Possible Answers:**

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

(B) is greater

(A) and (B) are equal

(A) is greater

**Correct answer:**

(B) is greater

40% of is equal to ; 60% of that is

50% of is equal to ; 50% of that is

Since is positive and ,

,

and (B) is greater.

### Example Question #9 : How To Find Percentage

What is 0.5% of 1,000,000?

**Possible Answers:**

**Correct answer:**

Convert the percentage to a decimal:

Multiply by 1,000,000 to get our answer.

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