# ISEE Middle Level Quantitative : How to find the part from the whole

## 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: 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 #2 : 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) is the greater quantity

(a) and (b) are equal

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

(b) is the greater quantity

(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 #3 : 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

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

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

(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.