Digital SAT Math Practice #4

• I only

• I and II only

• I and III only

• I and II and III

For any positive integer n, τ(n) represents the number of positive divisors of n.
What is the value of τ(τ(τ(12)))?

• 2

• 3

• 4

• 6

Answer explanation

Since τ(12) = 6, τ(τ(τ(12))) = τ(τ(6)). Since τ(6) = 4, then τ(τ(6)) = τ(4) = 3.

Which of the following is equal to (7⁸ × 7⁹)¹⁰?

• 7²⁷

• 7⁸²

• 7¹⁷⁰

• 49⁷²⁰

Answer explanation

First, multiply inside the parentheses:

7⁸ × 7⁹ = 7¹⁷;

then raise to the 10th power: (7¹⁷)¹⁰ = 7¹⁷⁰.

• 3

• 4

• 5

• 6

If 0 < x < 1, which of the following lists the numbers in decreasing order?

What is the value of 2⁴ ÷ 2^-4?

Answer explanation

2⁴ : 2^-4 = 2⁸ = 256

What is the value of |(-2 - 3) - (2 - 3)|?

Answer explanation

|(-2 - 3) - (2 - 3)| = |(-5) - (-1)| = |-5 + 1| = |-4| = 4

What is the greatest prime factor of 132?

Answer explanation

The easiest way to find the greatest prime factor of 132 is to find its prime factorization: 132 = 2 × 2 × 3 × 11, so 11 is the greatest prime factor.

If the product of four consecutive integers is equal to one of the integers, what is the largest possible value of one of the integers?

Answer explanation

0; 1; 2; 3

If x and y are positive integers, and (13^x)^y = 13¹³, what is the average (arithmetic mean) of x and y?

Answer explanation

Since 13¹³ = (13^x)^y = 13^xy, then xy = 13. The only positive integers whose product is 13 are 1 and 13. Their average is (13 + 1) : 2 = 7.