PRACTICE SET
D
The way to tell if a number is even is to look at the last digit to the right—in the ones column. If that digit is divisible by 2, or
is 0, the number is even. Looking at the choices, only (D) ends in a number that isn’t 0 and isn’t divisible by 2, so only it is
not even.
1.
G
A prime number is one that is divisible by only itself and 1. Of the choices, only (G), 53, and (K), 59, are prime. You want
the least prime number greater than 50, so (G) is correct. Using the divisibility rules would quickly show you that 51 and 57
are divisible by 3, while 55 is divisible by 5.
2.
E
If the ones digit of a number can be divided by 2, the number is divisible by 2. All of the answer choices except (E) end in an
odd number, so only choice (E) is a multiple of 2.
3.
H
Before multiplying these expressions out, begin by checking if there are any common factors between the numerator and the
denominator. In the numerator, 15 is the same as 5 times 3 and 9 is the same as 3 times 3, so this expression can be rewritten
as. Common factors of the numerator and the denominator are both the 3s and the 5, resulting in
This method is much simpler than multiplying everything out and then trying to factor after the fact.
4.
C
The least common multiple (LCM) of two integers is the product of their prime factors, each raised to the highest power with
which it appears. The prime factorization of 18 is 2 • 3^2 and that of 24 is 23 • 3. So their LCM is 23 • 3^2 = 8 • 9 = 72. You
could also find their LCM by checking out the multiples of the larger integer until you find the one that’s also a multiple of the
smaller. Check out the multiples of 24: 24? No. 48? No. 72? Yes.
5.
H
If a number is divisible by 3, the sum of its digits will be divisible by 3. Checking the answer choices, only (H), 465, works
since 4 + 6 + 5 = 15, which is divisible by 3.
6.
E
According to PEMDAS, start in the parentheses. As per PEMDAS, perform multiplication before subtraction: −6(3 − 12).
After the subtraction: −6 (−9). Since a negative times a negative is a positive, the answer is 54, (E).
7.
G
If a number is divisible by 10, its last digit will be a 0. Only (G) fits this criterion.
8.
