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 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.
