# ISEE Middle Level Quantitative : Whole and Part

## Example Questions

### Example Question #1 : Whole And Part

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: Explanation: 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 #1 : How To Find The Part From The Whole

Which of the following is true if ?

Explanation:

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 #1 : 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

(a) and (b) are equal

(a) is the greater quantity

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

(b) is the greater quantity

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

Explanation:

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 #2 : 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.

(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

(a) and (b) are equal

Explanation:

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 #1 : 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

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

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

(a) is the greater quantity

Explanation:

, 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?

Explanation:

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 #1 : 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?

Explanation:

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.