Bunuel wrote:
If x = y + 2 and x is an even integer, which of the following could be the sum of x and y?
A. 140
B. 146
C. 148
D. 152
E. 156
We see that x + y must be the sum of 2 consecutive even integers, or y + (y + 2) = 2y + 2. We also see that both x and y are even integers.
If we subtract 2 from each answer choice we have:
138, 144, 146, 150, and 154
When we divide those answers by 2, the only one that provides an even quotient is 144, since 144/2 = 72.
Alternate Solution:
We know that x = y + 2, and x is even, so we know that y is also even. By substitution, we see that x + y = (y + 2) + y = 2y + 2.
Let’s check each answer choice. We are looking for an answer choice that yields an even integer value for y:
Choice A: Does 2y + 2 = 140 yield an even integer value for y? No. In this case, y = 69.
Choice B: Does 2y + 2 = 146 yield an even integer value for y? Yes! In this case, y = 72.
Answer: B
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