Help on released SAT question (Math)

Test Preparation SAT Preparation
1

<p>If x is an odd integer and y is an even integer, which of the following is an even integer?</p>

<p>(A) x+y²
(B) x² + y²
(C) x³ + y³
(D) y(x+y)
(E) y² - x²</p>

<p>I checked the explanation and it gave me these givens: </p>

<pre><code> odd ± odd = even odd * odd = even
odd ± even = odd odd * even = odd
even ± even = even even * even = even
</code></pre>

<p>Since x is odd, x² and X³ are also odd, and since y is even, y³ and y³ are also even. Each of choices (A), (B), and (C) represents the sum of an odd integer and an even integer, which is odd. In choice (E), there is an even integer minus an odd integer, so the difference is odd. In choice (D), the quantity in parentheses is odd, but is even, so the product is even.</p>

<p>the givens seem to go against the explanation. This comes straight from collegeboard's quickstart program for taking the psat so... help?</p>

2

<p>What seems to be the problem? In choice D, you are multiplying x+y by an even number (y). The product of any integer with an even number is also even.</p>

3

<p>Or another solution would be to substitute an even number and a odd number. ex) 3 and 6
This would be a good soultion if you have some time left on you test or if you are great at calculations</p>