### All ISEE Middle Level Quantitative Resources

## Example Questions

### 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 #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?

**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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