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.
The question asks for Arvind's salary, given that Rajesh's salary is Rs. 12,500.
Statement I Analysis
Let Arvind's salary be denoted by $A$ and Rajesh's salary by $R$. We are given $R = 12,500$.
Statement I says: Arvind gets $\frac{3}{5}$th of the total salary of his and Rajesh'.
Mathematically, this can be written as:
$A = \frac{3}{5} \times (A + R)$
Let's solve for $A$:
$A = \frac{3}{5}A + \frac{3}{5}R$
$A - \frac{3}{5}A = \frac{3}{5}R$
$\frac{2}{5}A = \frac{3}{5}R$
$A = \frac{3}{2}R$
Since $R = 12,500$, we can find $A$:
$A = \frac{3}{2} \times 12,500 = 3 \times 6,250 = 18,750$
Therefore, Statement I alone is sufficient to determine Arvind's salary.
Statement II Analysis
Statement II says: Two-thirds of Arvind's salary is equal to the average salary of both.
Mathematically, this can be written as:
$\frac{2}{3}A = \frac{A + R}{2}$
Let's solve for $A$:
$2 \times (\frac{2}{3}A) = A + R$
$\frac{4}{3}A = A + R$
$\frac{4}{3}A - A = R$
$\frac{1}{3}A = R$
$A = 3R$
Since $R = 12,500$, we can find $A$:
$A = 3 \times 12,500 = 37,500$
Therefore, Statement II alone is sufficient to determine Arvind's salary.
Conclusion
Since both Statement I and Statement II are independently sufficient to answer the question, the correct option is that either statement alone is sufficient.
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. The difference between father's age and son's age is 21 years now. What is the present age of the son?
Statements
I. After five years, the ratio of father's age to that of the son would be 5:2.
II. The sum of father's age and son's age after five years would be 66 years.
