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28 Mar 2024, 06:43
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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:
70% (01:57) correct
30%
(02:07)
wrong
based on 662
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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
14 Dec 2024, 09:47
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Bunuel
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"
Attachment:
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General Discussion
28 Mar 2024, 12:50
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The equation \(((5-3-A)^2+3-6)^B=1\) can be made true for certain values of variables A and B independent of each other. The variables A and B are both integers.
Select for A a value that would make the equation true irrespective of whatever value B has, and select for B a value that would make the equation true irrespective of value of A. Make only two selection, one for each column.
The equation will be true for any \(B\) if the expression in the parentheses equals \(1\) since \(1\) raised to any power is \(1\). So, we can find the answer choice for \(A\) such that the expression in the parentheses equals \(1\).
The expression in the parentheses simplifies to
\(((2 - A)^2 - 3)\)
For \(((2 - A)^2 - 3)\) to equal \(1\), \((2 - A)^2\) must be \(4\), and thus \(2 - A\) must be \(2\), and \(A\) must be \(0\).
Select \(0\) for \(A\).
The equation can be true for any \(A\) if \(B\) equals \(0\) since any number to the \(0\) power equals \(1\).
Select \(0\) for \(B\).
Correct answer: 0, 0
Select for A a value that would make the equation true irrespective of whatever value B has, and select for B a value that would make the equation true irrespective of value of A. Make only two selection, one for each column.
The equation will be true for any \(B\) if the expression in the parentheses equals \(1\) since \(1\) raised to any power is \(1\). So, we can find the answer choice for \(A\) such that the expression in the parentheses equals \(1\).
The expression in the parentheses simplifies to
\(((2 - A)^2 - 3)\)
For \(((2 - A)^2 - 3)\) to equal \(1\), \((2 - A)^2\) must be \(4\), and thus \(2 - A\) must be \(2\), and \(A\) must be \(0\).
Select \(0\) for \(A\).
The equation can be true for any \(A\) if \(B\) equals \(0\) since any number to the \(0\) power equals \(1\).
Select \(0\) for \(B\).
Correct answer: 0, 0
