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If x^y = 1 then what is the value of x?
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16 Sep 2018, 09:07
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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 value of x?
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16 Sep 2018, 09:33
OA: E Given: \(x^y = 1\) Statement 1: \(x < 0\) taking \(x = 1\), and \(y = 2\) , It satisfies the \(x^y = 1\) as \((1)^2\) is equal to \(1\). taking \(x = 2\), and \(y = 0\) , It satisfies the \(x^y = 1\) as \((2)^0\) is equal to \(1\). Statement \(1\) alone is insufficient as we are not getting a unique value of \(x\). Statement 2: \(y\) is even integer taking \(x = 1\), and \(y = 2\) , It satisfies the \(x^y = 1\) as \((1)^2\) is equal to \(1\). taking \(x = 100\), and \(y = 0\) , It satisfies the \(x^y = 1\) as \((100)^0\) is equal to \(1\). Statement \(2\) alone is insufficient as we are not getting a unique value of \(x\). Combining \((1)\) and \((2)\) will also be insufficient.
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If x^y = 1 then what is the value of x?
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17 Sep 2018, 03:59
Most important element to answer this question is to know that any number raise to "0" is 1. (e.g. 1^0 =1 or 1^0=1)
Now let's work this out.
x^y=1, x=?
St 1: x<0 (x is ve)
Case 1: 1^2 = 1 Case 2: 2^0 = 1
Therefore X could be 1,2,3 or any ve number if the power is 0. Insufficient AD/BCE
St 2: Y is even
(Note: 0 is an even number)
Case 1: x=1, y=2 1^2=1 Case 2: x=2, y=0 2^0=1
Hence B is insufficient. AD/BCE
St1 + St2
x^y=1 (x<0, y is even)
Case 1: x=1 and y=2 => 1^2=1
Case 2: x=2 and y=0 => 2^0=1
From statement 1 and 2, we have proved that x can have multiple values. AD/BCE
Therefore the answer is E
Thank you Arjun



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Re: If x^y = 1 then what is the value of x?
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17 Sep 2018, 14:51
GMATPrepNow wrote: If \(x^y = 1\), then what is the value of x?
(1) x < 0 (2) y is even integer
\({x^y} = 1\) \(? = x\) Let´s ALGEBRAICALLY BIFURCATE statements (1) and (2) together, to be "shielded" that the right answer is (E) immediately! \(\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {x,y} \right) = \left( {  1,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? =  1 \hfill \\ \,{\text{Take}}\,\,\left( {x,y} \right) = \left( {  2,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? =  2 \hfill \\ \end{gathered} \right.\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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Re: If x^y = 1 then what is the value of x?
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17 Sep 2018, 14:59
ArjunJag1328 wrote: Most important element to answer this question is to know that any number raise to "0" is 1. (e.g. 1^0 =1 or 1^0=1) Hi ArjunJag1328! You are correct for any real number... except zero. More explicitly: \({0^0}\,\,{\text{is}}\,\,{\text{not}}\,\,{\text{defined}}\) Curiosity: there are some cases in Mathematics that it is CONVENIENT to admit this expression is also equal to 1 (when you are dealing with multiindices, for example). But this is just a "local convention" to help you present, in that context, formulas in a much more pleasant way... I hope you find this interesting! Regards, Fabio. P.S.: in the GMAT you will NOT be asked to evaluate 0^0 , of course.
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Re: If x^y = 1 then what is the value of x?
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23 Sep 2018, 15:08
GMATPrepNow wrote: If \(x^y = 1\), then what is the value of x?
(1) x < 0 (2) y is even integer Target question: What is the value of x? 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 nonzero 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 = 1Case b: x = 3, and y = 0. Notice that x^y = (3)^0 = 1. In this case, the answer to the target question is x = 3Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: y is even integerLet's TEST some values. PROTIP: 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 = 1Case b: x = 3, and y = 0. Notice that x^y = (3)^0 = 1. In this case, the answer to the target question is x = 3Since 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 counterexamples to show that each statement ALONE is not sufficient. So, the same counterexamples 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 = 1Case b: x = 3, and y = 0. Notice that x^y = (3)^0 = 1. In this case, the answer to the target question is x = 3Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent
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