If x and y are integers, and N = (x² - y + 3x)(2y + x), is N odd?
1) x + y is even
2) 3xy is odd
Answer: B
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Difficulty level: 600
even/odd question: If x and y are integers, and N = . . .
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Target question: Is N odd?Brent@GMATPrepNow wrote:If x and y are integers, and N = (x² - y + 3x)(2y + x), is N odd?
1) x + y is even
2) 3xy is odd
Given: N = (x² - y + 3x)(2y + x)
Before we examine the statements, it might be useful SYSTEMATICALLY examine all of the possible cases we need to consider:
case a: x is even, and y is even
case b: x is even, and y is odd
case c: x is odd, and y is even
case d: x is odd, and y is odd
There are two ways to analyze each case.
- We can take each case and apply the rules for evens and odd (e.g., even + odd = odd, even x even = even, etc)
- We can take each case and plug in even and odd numbers for x and y. The easiest values are 1 for odd numbers and 0 for even numbers.
When we do apply either of these strategies we get:
case a: x is even, and y is even. N is EVEN
case b: x is even, and y is odd. N is EVEN
case c: x is odd, and y is even. N is EVEN
case d: x is odd, and y is odd. N is ODD
The target question ask whether N is odd. Since N is odd only when x is odd and y is odd, we can rephrase our target question...
REPHRASED target question: Are x and y BOTH odd?
Okay, now onto the statements!!!
Statement 1: x+y is even
If x+y is even, then there are two possible cases:
- x and y are both odd, in which case, x and y ARE both odd
- x and y are both even, in which case, x and y are NOT both odd
Since we can answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3xy is odd
If 3xy is odd, then xy is odd, which means x and y ARE both odd
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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N = (x² - y + 3x)(2y + x)
N = (x * (x - 3) - y) * (x + 2y)
x and (x - 3) must be different parities (if x is even, x - 3 is odd, and vice versa), so x * (x - 3) = odd * even = even. We can also say that 2y is even, since it's 2 * some integer.
From here, replacing those terms with evens, we've got
N = (even - y) * (x + even)
N = x * even + even² - y * even - xy
or
N = even + even - even - xy
So the question is reduced to "is xy odd?"
From there, the statements are a cinch!
N = (x * (x - 3) - y) * (x + 2y)
x and (x - 3) must be different parities (if x is even, x - 3 is odd, and vice versa), so x * (x - 3) = odd * even = even. We can also say that 2y is even, since it's 2 * some integer.
From here, replacing those terms with evens, we've got
N = (even - y) * (x + even)
N = x * even + even² - y * even - xy
or
N = even + even - even - xy
So the question is reduced to "is xy odd?"
From there, the statements are a cinch!
seems way too long to do in under 2 minutes.Brent@GMATPrepNow wrote:Target question: Is N odd?Brent@GMATPrepNow wrote:If x and y are integers, and N = (x² - y + 3x)(2y + x), is N odd?
1) x + y is even
2) 3xy is odd
Given: N = (x² - y + 3x)(2y + x)
Before we examine the statements, it might be useful SYSTEMATICALLY examine all of the possible cases we need to consider:
case a: x is even, and y is even
case b: x is even, and y is odd
case c: x is odd, and y is even
case d: x is odd, and y is odd
There are two ways to analyze each case.
- We can take each case and apply the rules for evens and odd (e.g., even + odd = odd, even x even = even, etc)
- We can take each case and plug in even and odd numbers for x and y. The easiest values are 1 for odd numbers and 0 for even numbers.
When we do apply either of these strategies we get:
case a: x is even, and y is even. N is EVEN
case b: x is even, and y is odd. N is EVEN
case c: x is odd, and y is even. N is EVEN
case d: x is odd, and y is odd. N is ODD
The target question ask whether N is odd. Since N is odd only when x is odd and y is odd, we can rephrase our target question...
REPHRASED target question: Are x and y BOTH odd?
Okay, now onto the statements!!!
Statement 1: x+y is even
If x+y is even, then there are two possible cases:
- x and y are both odd, in which case, x and y ARE both odd
- x and y are both even, in which case, x and y are NOT both odd
Since we can answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3xy is odd
If 3xy is odd, then xy is odd, which means x and y ARE both odd
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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seems way too long to do in under 2 minutes.[/quote]hoppycat wrote: Brent
If you try applying the same strategy to other questions, you'll find you can do so in under 30 seconds, at which point it will take very little time to analyze the statements.
Cheers,
Brent
If you try applying the same strategy to other questions, you'll find you can do so in under 30 seconds, at which point it will take very little time to analyze the statements.Brent@GMATPrepNow wrote:seems way too long to do in under 2 minutes.hoppycat wrote: Brent
Cheers,
Brent[/quote]
Okay thanks
We'll see!