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A: 0
B: 0
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (02:27) correct
33%
(01:16)
wrong
based on 6
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A and B are integers, and the equation \(((5 - 3 - A)^2 + 3 - 6)^B = 1\) must hold true.
Select for A a value of A that ensures the equation is true for any integer value of B, and select for B a value of B that ensures the equation is true for any integer value of A. Make only two selection, one for each column.
Select for A a value of A that ensures the equation is true for any integer value of B, and select for B a value of B that ensures the equation is true for any integer value of A. Make only two selection, one for each column.
| A | B | |
| -2 | ||
| -1 | ||
| 0 | ||
| 1 | ||
| 2 | ||
| 3 |
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Official Answer
A: 0
B: 0
04 Sep 2024, 02:20
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Official Solution:
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of B, the expression in the parenthesis, the base, must be 1: \(1^{any \ integer} = 1\)
\((5 - 3 - A)^2 + 3 - 6=1\)
\((5 - 3 - A)^2 =4\)
\(5 - 3 - A =2\) or \(5 - 3 - A =-2\)
\(A =0\) or \(A=4\)
Since only 0 is present among the options, select 0 for A.
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of A, the exponent must be 0: \((any \ nonzero \ number)^0 = 1\)
Thus, B must be 0. Note that \((5 - 3 - A)^2 + 3 - 6 = 0\) when A is not an integer, specifically when \(A = 2 + \sqrt{3}\) or \(A = 2 - \sqrt{3}\). This ensures that we avoid the case of \(0^0\) (a scenario not tested on the GMAT) for integer values of A.
Correct answer:
A "0"
B "0"
Bunuel
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of B, the expression in the parenthesis, the base, must be 1: \(1^{any \ integer} = 1\)
\((5 - 3 - A)^2 + 3 - 6=1\)
\((5 - 3 - A)^2 =4\)
\(5 - 3 - A =2\) or \(5 - 3 - A =-2\)
\(A =0\) or \(A=4\)
Since only 0 is present among the options, select 0 for A.
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of A, the exponent must be 0: \((any \ nonzero \ number)^0 = 1\)
Thus, B must be 0. Note that \((5 - 3 - A)^2 + 3 - 6 = 0\) when A is not an integer, specifically when \(A = 2 + \sqrt{3}\) or \(A = 2 - \sqrt{3}\). This ensures that we avoid the case of \(0^0\) (a scenario not tested on the GMAT) for integer values of A.
Correct answer:
A "0"
B "0"
14 Dec 2024, 09:40
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
