- If x and y are both integers and x(y +3) is odd, then which of the following
must be true?
A x is even
B y is even
C xy is odd
D xy is even
E x is odd
F y is odd - If a, b, and c are positive integers, a + b = 12, and bc = 15, then which of
the following must be true?
A b + c is even
B ab is even
C ac is odd
D a – c is even
E abc is odd
Exercise Answers
- C Exponents are irrelevant when considering properties of odds and evens. So
if 3x^2 is even, then 3x is even. If 3x is even, then 3x must have an even factor. 3
is not even, so x must be even. If x is even, then x + 4 is always even. You may
be wondering about Choice D: note that even when x is even, x 2 is not always
even. For example, if x = 6, x 2 = 3, which is not even. - B Plug in values for x that would satisfy the given information. Try x = 14. In
this case, –14 7 = –2. –2 is even, so 14 is a possible value for x. Thus choices B and
D are possibilities. However, if x = –14, the given information will still be true:
–(–14)
7 = 2 = even. Thus x can be positive or negative. Eliminate Choice D. The
correct answer is B. An important takeaway from this question is that the sign
is irrelevant in odd and even questions. - A, B, C, and F Since exponents are irrelevant when working with odds and
evens, the fact that x^2 – y^2 is even implies that x – y is even. If the difference
between two numbers is even, then x and y must both be odd or both be even.
For cases where they are both odd or both even, A, B, C, and F will always be
true. (You can plug in numbers to confirm.) - A, D, and E Evaluate each choice.
Choice A: An even number to any power yields an even. An even + even =
even. → A is true.
Choice B: If x is 4, then x 2 = 2 = even. If x = 6, then x 2 = 3, which is odd.
→ B is not always true.
Choice C: If x is 4, then^4 x = 1, which is odd. → C is not always true.
Choice D: An even to any power yields an even. → D is true.
188 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 188 12/05/17 11:51 am