Find the values of x, y and z, if:
Statements:
I. $2x + 3y + z = 16$
II. $x = y$
Sufficiency Analysis for x, y, z Values
The question asks if we can determine unique values for x, y, and z using the provided statements.
Statement I Analysis
- Statement I gives the equation: $2x + 3y + z = 16$.
- This is a single linear equation with three unknown variables ($x, y, z$).
- With only one equation and three variables, there are infinitely many possible solutions, so we cannot find unique values for $x, y,$ and $z$.
- Therefore, Statement I alone is not sufficient.
Statement II Analysis
- Statement II gives the relationship: $x = y$.
- This statement provides a condition relating two variables but does not give any specific values or further constraints.
- Therefore, Statement II alone is not sufficient.
Combined Statement Analysis
- Combine Statement I and Statement II: $2x + 3y + z = 16$ and $x = y$.
- Substitute $x = y$ into the first equation: $2(y) + 3y + z = 16$.
- This simplifies to $5y + z = 16$.
- We now have one equation ($5y + z = 16$) with two unknown variables ($y$ and $z$). Since $x=y$, this equation also involves $x$.
- With one equation and effectively two or three variables (depending on how you view $x=y$), there are still infinitely many possible solutions. For example, $(x, y, z)$ could be $(1, 1, 11)$ or $(2, 2, 6)$ or $(3, 3, 1)$.
- Since we cannot find unique values for $x, y,$ and $z$, both statements together are not sufficient.
Conclusion
The information from both Statement I and Statement II together is not enough to find the unique values of $x, y,$ and $z$.
Important Questions from Data Sufficiency (Notes)
In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.
Q. Five students – Isha, Kavita, Meenal, Nisha, and Priti – scored different marks.Who scored the second highest?
(I) Meenal scored more than Isha but less than Nisha.
(II) Priti scored more than Meenal but less than Nisha.- In light of the statements I and II choose the most appropriate option.
If a group comprises of five persons A, B, C, D and E, then how many persons are taller than E?
Statement (I) A is taller than B and B is shorter than A and E only.
Statement (II) C is shorter than A and A is shorter than E. - In light of the statements I and II choose the most appropriate option.
Eight boxes- A, B, C, D, P, Q, R and S are stacked vertically but not necessarily in the same order. Which among them is kept immediately above R?
Statement (I) Only three boxes are kept above D and only one box is kept between D and Q. Q is kept lower than D and is immediately below P.
Statement (II) Only one box is kept between A and C. C is kept three boxes above Q. As many boxes are kept above B as are kept below R. - A question along with a set of statements is given. Find which of the given statements is/are sufficient to answer the given question.
Question:
Find the perimeter of a triangle given that:
Statements:
I. Area of the triangle is 24 sq. units.
II. Height of the triangle is 4 units. A question along with a set of statements is given below. We have to find which of the given statements is/are sufficient to answer the given question.
Question : Find the area of the triangle PQR.
Statements :
I. PQ = 5 m., PR = 5 m.
II. Length of PO is 4 m.
