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 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 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 select the most appropriate answer.
C, I, L, N, R, and Y live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on, till the topmost floor is numbered 6. Who among them lives immediately above Y?
(I) Only four people live between N and I. C lives immediately below I.
(II) Only one person lives between C and R. Y lives immediately above N.P and Q are children of S. Who is the father of P? To answer this question which of the statements (1) and (2) is/are necessary?
(1) R is the brother of P and the son of T.
(2) U is the mother of Q.Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question.
Question:
Rajesh's salary is Rs. 12,500. What is Arvind's salary?
Statements
I. Arvind gets $\frac{3}{5}$th of the total salary of his and Rajesh'
II. Two-thirds of Arvind's salary is equal to the average salary of both.
