cnsih1532
Is |x + 1| + |x - 2| < 4 ?
(1) x is between -0.5 and 4
(2) x is between -2 and 2.5
Here we can easily find our answer by subsituting values within the given range in the statements. We just need to see what values to pick.
Lets start with Statement 1 -
Statement 1 -> x is between -0.5 and 4 Lets take \(x = 3\) and substitute in the prompt to check the condition;
\(|x + 1| + |x - 2| < 4\)
\(|3 + 1| + |3 - 2| < 4\)
\(|4| + |1| < 4\)
\(5<4\);
This proves the statement false.
Now lets substitute \(x = 0\)
\(|x + 1| + |x - 2| < 4\)
\(|0 + 1| + |0 - 2| < 4\)
\(|1| + |-2| < 4\)
\(3<4\);
This statement is true.
As two different answers in the same range.
Statement 1 is InsuffucientStatement 2 -> x is between -2 and 2.5 Lets take \(x = -1.9\) and substitute in the prompt to check the condition;
\(|x + 1| + |x - 2| < 4\)
\(|-1.9 + 1| + |-1.9 - 2| < 4\)
\(|0.9| + |-3.9| < 4\)
\(4.8<4\);
This proves the statement false.
Now lets substitute \(x = 0\)
\(|x + 1| + |x - 2| < 4\)
\(|0 + 1| + |0 - 2| < 4\)
\(|1| + |-2| < 4\)
\(3<4\);
This statement is true.
As two different answers in the same range.
Statement 2 is InsuffucientNow Combining Statement 1 and Statement 2 The new range becomes : x is between -0.5 and 2.5
Now we can try and substitute directly the end points. If they satisfy, then the value within the range will surely be satisfied.
Lets take \(x = -0.5\) and substitute in the prompt to check the condition;
\(|x + 1| + |x - 2| < 4\)
\(|-0.5 + 1| + |-0.5 - 2| < 4\)
\(|0.5| + |-2.5| < 4\)
\(3<4\);
This satisfies the equation.
Now lets substitute \(x = 2.5\)
\(|x + 1| + |x - 2| < 4\)
\(|2.5 + 1| + |2.5 - 2| < 4\)
\(|3.5| + |0.5| < 4\)
\(4<4\);
Although this is not true but notice that this equal. If we select any value than this, then the equation will be satisfied.
And from the range we surely know that we need to take someting less than 2.5
Hence
Combining Statements is Sufficient and answer is therefore,
C