### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Find The Part From The Whole

Harvey bought a suit at a 25% employee discount at the store where he works. The suit originally cost $350.00. How much did he end up paying?

**Possible Answers:**

**Correct answer:**

Finding 25% of a number is the same as multiplying it by 0.25; to get the discount, multiply 0.25 by the original purchase price of $350.00

To get the price Harvey paid, subtract the discount from the original price:

### Example Question #2 : How To Find The Part From The Whole

Which of the following is true if ?

**Possible Answers:**

**Correct answer:**

Two expressions are equivalent in modulo 9 arithmetic if and only if, when each is divided by 9, the same remainder is yielded.

,

so

, so

is the correct choice.

### Example Question #3 : How To Find The Part From The Whole

is a positive integer. Which is the greater quantity?

(a) The remainder if is divided by 5

(b) The remainder if is divided by 4

**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:**

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

The information is insufficient.

For example, if :

.

.

This gives the division in (b) the greater remainder.

But if :

.

.

This gives the division in (a) the greater remainder.

### Example Question #1 : Whole And Part

is a positive even integer. Which is the greater quantity?

(a) The remainder if is divided by 6

(b) The remainder if is divided by 3.

**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:**

(a) and (b) are equal

Since is an even integer, by definition, there is an integer such that

.

; therefore,

; the remainder is 0.

Also,

; the remainder is 0.

The two remainders are both equal to 0.

### Example Question #4 : How To Find The Part From The Whole

is a positive odd integer. Which is the greater quantity?

(a) The remainder if is divided by 8

(b) The remainder if is divided by 4

**Possible Answers:**

(b) is the greater quantity

(a) is the greater quantity

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

(a) and (b) are equal

**Correct answer:**

(a) is the greater quantity

, with a remainder of 0.

If were to yield a remainder of 0, then must be a whole number; this can only happen if is even. Since is odd, it follows that is not a whole number, and must yield a nonzero remainder. (a) must be the greater quantity.