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The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v
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^2+3-6)^B=1[/m] can be made true for certain v](https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/imageset/icon_post_target_unread.png "The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v")
28 Mar 2024, 06:43
28 Mar 2024, 06:43
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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.
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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.
| A | B | |
| -2 | ||
| -1 | ||
| 0 | ||
| 1 | ||
| 2 | ||
| 3 |
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The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v
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28 Mar 2024, 12:50
28 Mar 2024, 12:50
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Expert Reply
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
_________________
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Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v
[#permalink]
29 Mar 2024, 21:29
29 Mar 2024, 21:29
\(((5−3−A)^2+3−6)^B=1\)
=> \(((2-A)^2-3)^B = 1\)
A value of A that would make the equation true irrespective of whatever value B has
=> \((2-A)^2 - 3 = 1\)
=> \((2-A)^2 = 4\)
=> 2- A = 2 or 2-A=-2
=> A=0 of A =4
==> Given the answer choices, A = 0
A value of B that would make the equation true irrespective of value of A
=> B = 0
=> \(((2-A)^2-3)^B = 1\)
A value of A that would make the equation true irrespective of whatever value B has
=> \((2-A)^2 - 3 = 1\)
=> \((2-A)^2 = 4\)
=> 2- A = 2 or 2-A=-2
=> A=0 of A =4
==> Given the answer choices, A = 0
A value of B that would make the equation true irrespective of value of A
=> B = 0
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v
[#permalink]
31 Mar 2024, 21:09
31 Mar 2024, 21:09
any number raised to the power of zero always equals 1
so why can't we take B=0 while A can have any value?
so why can't we take B=0 while A can have any value?
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v
[#permalink]
31 Mar 2024, 21:16
31 Mar 2024, 21:16
Expert Reply
Aditya8624 wrote:
any number raised to the power of zero always equals 1
so why can't we take B=0 while A can have any value?
so why can't we take B=0 while A can have any value?
You are correct and that is what the answer is.
Posted from my mobile device
_________________
gmatclubot
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink]
31 Mar 2024, 21:16
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