If x^y = 1, then what is the value of x?
(1) x < 0
(2) y is even integer
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If x^y = 1 then what is the
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Brent@GMATPrepNow
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\[{x^y} = 1\]Brent@GMATPrepNow wrote:If x^y = 1, then what is the value of x?
(1) x < 0
(2) y is even integer
\[? = x\]
Let´s ALGEBRAICALLY BIFURCATE statements (1) and (2) together, to be "shielded" that the right answer is [spoiler]__(E)____[/spoiler] :
\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 1,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = - 1 \hfill \\
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 2,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = - 2 \hfill \\
\end{gathered} \right.\,\,\,\,\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Brent@GMATPrepNow
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Target question: What is the value of x?Brent@GMATPrepNow wrote:If x^y = 1, then what is the value of x?
(1) x < 0
(2) y is even integer
Given: x^y = 1
If x^y = 1, then there are 3 possible cases:
case i: x = 1, and y = any value (e.g., 1^9 = 1)
case ii: x = -1, and y = an even integer (e.g., (-1)^4 = 1)
case iii: x = any non-zero value, and y = 0 (e.g., 7^0 = 1)
Statement 1: x < 0
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -1, and y = 2. Notice that x^y = (-1)^2 = 1. In this case, the answer to the target question is x = -1
Case b: x = -3, and y = 0. Notice that x^y = (-3)^0 = 1. In this case, the answer to the target question is x = -3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y is even integer
Let's TEST some values.
PRO-TIP: When testing values, always check to see if you can reuse previous values.
In this case, we can reuse BOTH cases:
Case a: x = -1, and y = 2. Notice that x^y = (-1)^2 = 1. In this case, the answer to the target question is x = -1
Case b: x = -3, and y = 0. Notice that x^y = (-3)^0 = 1. In this case, the answer to the target question is x = -3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = -1, and y = 2. Notice that x^y = (-1)^2 = 1. In this case, the answer to the target question is x = -1
Case b: x = -3, and y = 0. Notice that x^y = (-3)^0 = 1. In this case, the answer to the target question is x = -3
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
