### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #11 : Fractions

is a positive number, and . Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

**Possible Answers:**

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

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

**Correct answer:**

(a) is the greater quantity

.

The reciprocal of is therefore - that is, times the reciprocal of . The reciprocal of a positive number must be positive, and , so

The reciprocal of is the greater number.

### Example Question #12 : Fractions

is a positive number. Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

**Possible Answers:**

(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

**Correct answer:**

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

We examine two scenarios to demonstrate that the given information is insufficient.

Case 1:

The reciprocal of this is .

The reciprocal of this is .

, so has the greater reciprocal.

Case 2: .

The reciprocal of this is .

The reciprocal of this is .

, so has the greater reciprocal.

### Example Question #13 : Fractions

is a negative number. Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

**Possible Answers:**

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

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

**Correct answer:**

(b) is the greater quantity

is negative, so we will let , making positive. It follows that .

The reciprocal of is ;

the reciprocal of is .

and are both positive; , so , and . Therefore, the reciprocal of is the greater quantity.

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