prime factors of 6 and 8. Though a could equal 6 × 8 = 48, a must equal the
LCM of 6 and 8, which is 24. Since a must be a multiple of 24, it must contain
the factors of 24. 4 is a factor of 24, so Choice A is true. 12 is a factor of 24, so
Choice B is true. 48 is not a factor of 24, so Choice C is not necessarily true.
The correct answer is A and B.- D For the purpose of this question, let’s express “the product of the integers
from 1 through 24, inclusive” as 24!. For 5k to be a factor of 24!, 5k must divide
evenly into 24!. For this to be true, the value of k cannot exceed the number
of times 5 appears in the prime factorization of 24!. The greatest value for k
will thus equal the number of times that 5 appears in the prime factorization
of 24!. To determine the number of times that 5 appears in the prime
factorization of 24!, look at the multiples of 5 from 1–24, inclusive: 5 = 5(1).
10 = 5(2). 15 = 5(3). 20 = 5(4). There are thus four 5s in the prime factorization
of 24!. The maximum value for k is thus 4. The correct answer is D.
Quantitative Comparison Questions
- C If x is a multiple of 12, then the factors of 12 must be factors of x. Since 3 is a
factor of 12, 3 is a factor of x. Thus x divided by 3 yields a remainder of 0. Since
6 is a factor of 12, 6 is a factor of x. Thus x divided by 6 yields a remainder of 0. - D Since 18 is a factor of x, the prime factors of 18 must be prime factors of
x. The prime factorization of 18 is 3 × 3 × 2. Thus 18 has two unique prime
factors, meaning x must have at least two unique prime factors. However,
since you have no additional information about x, you do not know whether it
has additional prime factors. For example, x could equal 90, which has a prime
factorization of 3 × 3 × 2 × 5. In this case, x has three unique factors. The
relationship cannot be determined. - B The remainder must always be smaller than the divisor. Thus the value in
quantity A must be less than 4. - D Plug in the numbers. If y = 7, the value in Quantity A is 2. In this case, the
two quantities are equal. If y = 13, the value in Quantity A is 3. In this case,
Quantity A is greater. The relationship cannot be determined.
Odds and Evens
An even number is any integer that has 2 as a factor; for example, 4, 28, –12, –6,
and so on.Zero is an even number!An odd number is simply the opposite: any number that does not have 2 as
a factor, for example, 1, 9, –13, and so on. The GRE will expect you to know the
following rules. Though testing numbers is certainly helpful on these questions,
you will ultimately save time on the test by committing these rules to memory!184 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 184 12/05/17 11:51 am