Question: If |y−1/2| < 11/2, which of the following could be a value of y?
- -11
- -11/2
- 11/2
- 11
- 22
Correct Answer: C
Solution and Explanation
Approach Solution 1:
The Model answer has two methods through which it can be solved.
The first approach is based on how the problem can be solved focusing on the given condition that stands as\( |y−1/2| < 11/2.\)
In order to find the solution, it is important to find the equivalence of the given condition to a more simplified equation. This can be elaborated from the fact that \(|y−1/2| < 11/2\) can also be written as
\(-11/2 < y - ½ < 11/2\)
Significantly, the inequalities in the above evaluation of the problem can be solved by adding ½ to each of the sides that would give us the following condition:
\(-11/2 + ½ < y < 11/2 + ½\)
When the above problem is solved, it can be evaluated in the following manner:
\(=|y−1/2| < 11/2\)
\(= -5 < y < 6\)
Hence, the correct answer to the question\( |y−1/2| < 11/2\) is \(11/2\) which implies for option C.
Approach Solution 2
Based on the given condition of \(|y−1/2| < 11/2\) the value of y needs to be identified. It becomes important to state that the condition has inequalities in both sides. Accordingly, it is important to resolve these inequalities for both the cases. This can be done in the following manner:
Case 1:\( |y−1/2| \)which is positive
In order to solve the equation of modulus of y - 1/2 , it important to evaluate that it is less than 11/2.
Therefore, to resolve the inequality, it is important to add ½ from modulus of y - ½ and 11/2
This implies that
\(y - ½ + ½ < 11/2 + ½\)
= y < 12/2
= y < 6
Case 2: y - ½ is negative
The given condition states that |y−1/2| < 11/2
Considering that it has to be negative, it can be evaluated that the given condition is
\(-|y−1/2| < 11/2\)
\(= -(y - ½ ) < 11/2\)
\(= -(y - ½ ) < 11/2\)
Again the given inequalities need to be resolved. In this case, considering which is negative, the problem needs to be subtracted by ½ from both sides. This implies the following:
\(- y + ½ < 11/2\)
\(= - y + ½ - ½ < 11/2 - ½\)
\(= ½ - ½ - 11/2 + ½ < y\)
\(= y > -11/2 + ½\)
= y > -10/2
= y > -5
Hence, it can be stated from both the situations that y is greater than -5 and less than 6. Therefore, it can be evaluated that -5 < y < 6 is the answer to the problem which implies only for 11/2 that is option C.
“If |y−1/2| < 11/2, which of the following could be a value”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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