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25 Apr 2023, 04:47
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If \(a\), \(b\), and \(c\) are constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
(1) \(c >b\)
(2) \(a > 1\)
(1) \(c >b\)
(2) \(a > 1\)
25 Apr 2023, 04:47
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Official Solution:
If \(a\), \(b\), and \(c\) are constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
(1) \(c >b\)
Given \(c - b > 0\), this means \(a*y = some \ positive \ number\).
If \(a = 0\), then no value of \(y\) can satisfy this equation, as \(0*y = positive\ number\) has no solutions for \(y\).
If \(a ≠ 0\), then only 1 value of \(y\) can satisfy this equation, since in this case \(y = \frac{c - b}{a}\).
Not sufficient.
(2) \(a > 1\)
\(y = \frac{c - b}{a} = \frac{c - b}{nonzero \ number}\).
As a result, regardless of the value of \(c - b\), the equation \(a*y = c - b\) will always have only one solution, given by: \(y =\frac{c - b}{nonzero \ number}\).
Sufficient.
Answer: B
If \(a\), \(b\), and \(c\) are constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
(1) \(c >b\)
Given \(c - b > 0\), this means \(a*y = some \ positive \ number\).
If \(a = 0\), then no value of \(y\) can satisfy this equation, as \(0*y = positive\ number\) has no solutions for \(y\).
If \(a ≠ 0\), then only 1 value of \(y\) can satisfy this equation, since in this case \(y = \frac{c - b}{a}\).
Not sufficient.
(2) \(a > 1\)
\(y = \frac{c - b}{a} = \frac{c - b}{nonzero \ number}\).
As a result, regardless of the value of \(c - b\), the equation \(a*y = c - b\) will always have only one solution, given by: \(y =\frac{c - b}{nonzero \ number}\).
Sufficient.
Answer: B
29 Apr 2024, 09:29
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