If x and y are integers, is the product xy odd?
(1) x = -5
(2) x and y are consecutive integers
OA B
Source: Magoosh
If x and y are integers, is the product xy odd?
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\[x,y\,\,{\text{ints}}\,\,\,\left( * \right)\]BTGmoderatorDC wrote:If x and y are integers, is the product xy odd?
(1) x = -5
(2) x and y are consecutive integers
Source: Magoosh
\[{\text{xy}}\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,?\,\,:\,\,\,x,y\,\,\,{\text{odd}}\]
\[\left( 1 \right)\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 5,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 5,1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,{\text{one}}\,\,{\text{odd}}{\text{,}}\,\,{\text{another}}\,\,{\text{even}}\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \]
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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Hi All,
We're told that X and Y are INTEGERS. We're asked if (X)(Y) is ODD. This is a YES/NO question and can be solved with Number Properties and TESTing VALUES.
1) X = -5
With the information in Fact 1, we know the value of X (and that it's ODD). However, we don't know whether Y is odd or even.
IF...
X = -5, Y = 1 then (X)(Y) = -5 and the answer to the question is YES
X = -5, Y = 2 then (X)(Y) = -10 and the answer to the question is NO
Fact 1 is INSUFFICIENT
2) X and Y are CONSECUTIVE integers
By definition, a pair of consecutive integers will ALWAYS include 1 Odd number and 1 Even number, so the product will ALWAYS be (Odd)(Even) = Even and the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that X and Y are INTEGERS. We're asked if (X)(Y) is ODD. This is a YES/NO question and can be solved with Number Properties and TESTing VALUES.
1) X = -5
With the information in Fact 1, we know the value of X (and that it's ODD). However, we don't know whether Y is odd or even.
IF...
X = -5, Y = 1 then (X)(Y) = -5 and the answer to the question is YES
X = -5, Y = 2 then (X)(Y) = -10 and the answer to the question is NO
Fact 1 is INSUFFICIENT
2) X and Y are CONSECUTIVE integers
By definition, a pair of consecutive integers will ALWAYS include 1 Odd number and 1 Even number, so the product will ALWAYS be (Odd)(Even) = Even and the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich