### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #41 : How To Factor A Number

Which of the following is NOT a factor of ?

**Possible Answers:**

**Correct answer:**

First, we must solve for

While 64 is divisible by 4, 8, and 16, it is not divisible by 7; therefore, 7 is not a factor of 64 and is thus the correct answer.

### Example Question #51 : Numbers And Operations

and are distinct odd primes. Which is the greater quantity?

(a) The number of factors of

(b) The number of factors of

**Possible Answers:**

(b) is greater

(a) is greater

(a) and (b) are equal

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

**Correct answer:**

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

Since and are distinct primes, the prime factorization of is ; therefore, the factors of are 1, , , and . There are four factors.

We show that may or may not have more factors by example.

Case 1: .

Then , which has four factors: 1, 2, 4, 8.

Case 2:

Then , which has six factors: 1, 2, 3, 4, 6, 12.

Therefore, we have at least one situation in which and have the same number of factors, and at least one in which has more. The given infomation is insufficient.

### Example Question #42 : How To Factor A Number

and are distinct odd primes. Which is the greater quantity?

(a) The number of factors of

(b) The number of factors of

**Possible Answers:**

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

(b) is greater

(a) and (b) are equal

(a) is greater

**Correct answer:**

(a) is greater

Since and are distinct primes, the prime factorization of is ; therefore, the factors of are 1, , , and . There are four factors.

Since is a prime, the prime factorization of is ; therefore, the factors of are 1, , and . There are three factors.

This makes (a) greater.