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08 Jan 2018, 22:01
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C
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:
68% (01:58) correct
32%
(01:47)
wrong
based on 225
sessions
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If \(x\) and \(y\) are both positive integers, is \(y\) a multiple of 7?
(1) \((x^3)(y^3) = 441^3\)
(2) \(x\) is a single digit integer
(1) \((x^3)(y^3) = 441^3\)
(2) \(x\) is a single digit integer
08 Jan 2018, 22:39
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Statement #1 tells us that \((x^3)(y^3) = 441^3\). This can be mathematically simplified down to \((x)(y)=441\). Therefore, both \(x\) and \(y\) are factors of \(441\).
Factoring \(441\) isn't hard, especially once we realize that \(441\) is not only divisible by \(9\), but \(441 = 450-9\).
Factoring a common \(9\) out of this expression gives us:
\(450-9 = 9(50-1) = 9*49 = 3*3*7*7\)
\(x\) or \(y\) could be any combination of these prime values. \(y\) could be equal to 3 (not a multiple of 7), and it could also be equal to 7 (obviously, a multiple of 7.) Statement #1 is clearly insufficient.
Statement #2 is profoundly insufficient by itself. It tells us nothing about \(y\), so it is easy to eliminate.
As we combine the statements together, we can now ask ourselves the question, "does it matter that \(x\) is a single digit integer?" If \(x\) must be a single digit integer, there are only four possible solutions: \(x\)\(=1,3,7,\) or \(9\).
Given these four values for \(x\), here are the possible values for \(x\) and \(y\) (notice that there is no reason to actually multiply them out, since the problem only wants us to find out if \(y\) is a multiple of 7.)
(\(x\)) *(\(y\))
\(1\) * (\(3*3*7*7\))
\(3\)*(\(3*7*7\))
\(7\)*(\(3*3*7\))
\(9\)*(\(7*7\))
In every case, \(y\) must be a multiple of 7. Combining these two statements together is sufficient.
The answer is C.
Factoring \(441\) isn't hard, especially once we realize that \(441\) is not only divisible by \(9\), but \(441 = 450-9\).
Factoring a common \(9\) out of this expression gives us:
\(450-9 = 9(50-1) = 9*49 = 3*3*7*7\)
\(x\) or \(y\) could be any combination of these prime values. \(y\) could be equal to 3 (not a multiple of 7), and it could also be equal to 7 (obviously, a multiple of 7.) Statement #1 is clearly insufficient.
Statement #2 is profoundly insufficient by itself. It tells us nothing about \(y\), so it is easy to eliminate.
As we combine the statements together, we can now ask ourselves the question, "does it matter that \(x\) is a single digit integer?" If \(x\) must be a single digit integer, there are only four possible solutions: \(x\)\(=1,3,7,\) or \(9\).
Given these four values for \(x\), here are the possible values for \(x\) and \(y\) (notice that there is no reason to actually multiply them out, since the problem only wants us to find out if \(y\) is a multiple of 7.)
(\(x\)) *(\(y\))
\(1\) * (\(3*3*7*7\))
\(3\)*(\(3*7*7\))
\(7\)*(\(3*3*7\))
\(9\)*(\(7*7\))
In every case, \(y\) must be a multiple of 7. Combining these two statements together is sufficient.
The answer is C.
General Discussion
08 Jan 2018, 22:26
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AaronPond
Points to consider..
1) x and y are positive integers..
From statement I,
\(x*y = 441=1*3*3*7*7\)
So x can be 9, and y can be 49.... Yes y is multiple of 7
x can be 49 and y can be 9..... Ans NO
Insufficient
From statement II..
Nothing about y..
Insufficient
Combined...
x can be 1,3,7 or 9
corresponding values of y are 441,3*49,63,49
In each case y will be MULTIPLE of 7
Sufficient
C
