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is x-y odd?
Source: Beat The GMAT — Data Sufficiency |
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Patrick_GMATFix
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Questions about even/odds can often be solved quickly by just logically thinking through the properties of numbers. The full solution below is taken from the GMATFix App.
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[email protected]
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Hi EricKryk,
This DS question is perfect for either TESTing Values or using Number Properties. I'll show you how knowing Number Properties can make this question a pretty easy pick-up.
We're told that X, Y and Z are POSITIVE INTEGERS. We're asked "is X - Y ODD?" This is a YES/NO question. Before we deal with the two Facts, here is something to keep in mind about odds and evens as they relate to this question:
Even - Even = Even (answer is NO)
Odd - Odd = Even (answer is NO)
Even - Odd = Odd (answer is YES)
Odd - Even = Odd (answer is YES)
Fact 1: X = Z^2
This tells us NOTHING about Y, so there's no way to answer the question. However, it does tell us this:
If Z = Odd, then X = Odd
If Z = Even, then X = Even
Fact 1 is INSUFFICIENT
Fact 2: Y = (Z-1)^2
This tells us NOTHING about X, so there's no way to answer the question. It does tell us this though:
If Z = Odd, then Y = Even
If Z = Even, then Y = Odd
Fact 2 is INSUFFICIENT
Combined, we have these two possibilities:
If Z = Odd, then X = Odd and Y = Even (the answer to the question is YES).
If Z = Even, then X = Even and Y = Odd (the answer to the question is YES).
The answer is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This DS question is perfect for either TESTing Values or using Number Properties. I'll show you how knowing Number Properties can make this question a pretty easy pick-up.
We're told that X, Y and Z are POSITIVE INTEGERS. We're asked "is X - Y ODD?" This is a YES/NO question. Before we deal with the two Facts, here is something to keep in mind about odds and evens as they relate to this question:
Even - Even = Even (answer is NO)
Odd - Odd = Even (answer is NO)
Even - Odd = Odd (answer is YES)
Odd - Even = Odd (answer is YES)
Fact 1: X = Z^2
This tells us NOTHING about Y, so there's no way to answer the question. However, it does tell us this:
If Z = Odd, then X = Odd
If Z = Even, then X = Even
Fact 1 is INSUFFICIENT
Fact 2: Y = (Z-1)^2
This tells us NOTHING about X, so there's no way to answer the question. It does tell us this though:
If Z = Odd, then Y = Even
If Z = Even, then Y = Odd
Fact 2 is INSUFFICIENT
Combined, we have these two possibilities:
If Z = Odd, then X = Odd and Y = Even (the answer to the question is YES).
If Z = Even, then X = Even and Y = Odd (the answer to the question is YES).
The answer is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
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Brent@GMATPrepNow
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Patrick's and Rich's solutions (testing cases) are great.EricKryk wrote:If x, y, and z are positive integers, is x-y odd?
1) x = z²
2) y = (z-1)²
Here's a different (algebraic) approach:
Target question: Is x-y odd?
Given: x, y, and z are positive integers
Statement 1: x = z²
There's no information about y, so there's no way to determine whether or not x-y is odd.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y = (z-1)²
There's no information about x, so there's no way to determine whether or not x-y is odd.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: x = z²
Statement 2: y = (z-1)²
Subtract equations to get: x-y = z² - (z-1)²
Expand to get: x-y = z² - [z² - 2z + 1]
Simplify to get: x-y = 2z - 1
Since z is a positive integer, we know that 2z is EVEN, which means 2z-1 is ODD.
If 2z-1 is ODD, we can conclude that x-y is definitely ODD
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
