BTGmoderatorDC wrote:If x and y are consecutive odd integers such that x < y, what is the value of y + x?
(1) The product of xy is negative.
(2) The sum x + y is the square of an integer.
OA A
Source: Magoosh
Another approach for those who are the fan of Algebra.
Given: x and y are consecutive odd integers such that x < y
Question: What is the value of y + x?
Some examples of the consecutive odd integers x and y are -3, -5; -1, 1; 1, 3; 101, 103, etc.
Say the consecutive odd integers are (2n - 1) and (2n + 1). I did not choose expressions such as (2n + 1) and (2n + 3) since, upon multiplication, they would render three terms, while that with (2n - 1) and (2n + 1) would render only two terms [(2n - 1)*(2n + 1) = 4n^2 - 1], easier to manage.
Let's take each statement one by one.
(1) The product of xy is negative.
=> (2n - 1)*(2n + 1) < 0
4n^2 - 1 < 0
n^2 < 1/4
=> -1/2 < n < 1/2
=> n = 0; since n is an integer
Thus, the consecutive odd integers are x = 2n - 1 = 2*0 - 1 = -1 and y = 2n + 1 = 2*0 + 1 = 1
Thus, y + x = 1 - 1 = 0. Sufficient.
(2) The sum x + y is the square of an integer.
x + y = (2n - 1) + (2n + 1) = 4n
n itself can take may value such as 0, 1, 4, etc, making 4n, not a unique value. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
_________________
Manhattan Review
Locations:
Manhattan Review Bangalore |
GMAT Prep Chennai |
GRE Prep Himayatnagar |
Hyderabad GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
