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11 Apr 2023, 09:45
Kudos
Bookmarks
B
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:
61% (02:13) correct
39%
(02:28)
wrong
based on 54
sessions
History
Date
Time
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Not Attempted Yet
If \(x\) is an integer and \(|x|+\frac{x}{3}<5\), what is the value of \(x\)?
(1) \(x>-12\)
(2) \(x<-6\)
(1) \(x>-12\)
(2) \(x<-6\)
11 Apr 2023, 14:10
Kudos
Bookmarks
Bunuel
Given
- \(x\) is an integer
- \(|x|+\frac{x}{3}<5\)
\[ f(x) =
\begin{cases}
x +\frac{x}{3}<5 & \quad \text{if } x \geq 0 \\
-x +\frac{x}{3}<5 & \quad \text{if } x < 0
\end{cases}
\]
Solving for x, we get
\[ f(x) =
\begin{cases}
x < \frac{15}{4} & \quad \text{if } x \geq 0 \\
x > \frac{-15}{2} & \quad \text{if } x < 0
\end{cases}
\]
Statement 1
(1) \(x>-12\)
We don't have enough information to comment on whether x is positive or negative. As the sign of x is not known to us, we can not find the range as well.
The statement is not sufficient. We can eliminate A, and D.
Statement 2
(2) \(x<-6\)
This statement tells us that x is negative as x < -6. If x is negative, the value of x should be greater than -7.5 for the information in the premise to hold true.
Hence, -7.5 < x < -6
The only possible value of x that satisfy this inequality is x = -7
The statement is sufficient to find a definite value of x.
Option B
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