### 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 #211 : Numbers And Operations

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) and (b) are equal

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

(a) is the greater quantity

**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 #4 : How To Find The Part From The Whole

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:**

(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:**

(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 #5 : 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) and (b) are equal

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

(a) is the greater quantity

**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.

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

150% of what number is 9,000?

**Possible Answers:**

**Correct answer:**

Taking 150% of a number is the same as multiplying that number by 1.5. We can find our number, therefore, by *dividing* 9,000 by 1.5:

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

is a multiple of 2, but not a multiple of 6. If is divided by 6, What could be the remainder?

**Possible Answers:**

**Correct answer:**

If the remainder of dividing by 6 is 0, then must be a multiple of 6, which contradicts what we are given.

Suppose we call and the quotient and remainder, respectively, of dividing by 6. Then

If the remainder is 1, then

, as a product of two integers, one even, is an even number; if 1 is added, the result is odd. Therefore, if 1 is the remainder, is odd, which also contradicts what we are given about . 1 cannot be the remainder, and for similar reasons, neither can 3.

This leaves 2, which can be the remainder; for example, 8, which is a multiple of 2, but not a multiple of 6, yields a quotient of 1 and a remainder of 2 when divided by 2.

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