Question: Who is older Rahul or Vishal?
Statements:
I. Rahul was born in the year 1987 and is 5 years younger than Vishal's sister.
II. Vishal is twice as old as his sister.
Statement I Analysis
Statement I provides Rahul's birth year (1987) and states he is 5 years younger than Vishal's sister. This allows us to calculate Rahul's age in any given year. It also establishes a relationship between Rahul's age and Vishal's sister's age. However, it does not provide any information about Vishal's age relative to Rahul or his sister.
Therefore, Statement I alone is not sufficient to determine who is older between Rahul and Vishal.
Statement II Analysis
Statement II states that Vishal is twice as old as his sister. Let Vishal's age be denoted by $V$ and his sister's age by $S$. This statement can be represented as $V = 2S$. This establishes a relationship between Vishal and his sister but provides no absolute ages and no information linking them to Rahul.
Therefore, Statement II alone is not sufficient to determine who is older between Rahul and Vishal.
Combined Statements Analysis
Combining both statements:
- From Statement I, Rahul was born in 1987. Let the current year be $Y$. Rahul's age, $R = Y - 1987$.
- Statement I also tells us that Vishal's sister is 5 years older than Rahul. Sister's age, $S = R + 5 = (Y - 1987) + 5$.
- From Statement II, Vishal's age, $V = 2S$.
- Substituting the expression for $S$ from Statement I into the equation from Statement II: $V = 2 \times S = 2 \times ((Y - 1987) + 5)$ $V = 2 \times (R + 5)$ $V = 2R + 10$
Comparing Rahul's age ($R$) and Vishal's age ($V$): Since $R$ represents Rahul's age, it must be a positive value. The equation $V = 2R + 10$ clearly shows that $V > R$. This means Vishal is always older than Rahul.
Therefore, both statements together are sufficient to answer the question.
Conclusion
Both statements are needed together to determine the age comparison between Rahul and Vishal.
Similar Questions
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Important Questions from Data Sufficiency
Please read the below equation and select an appropriate option from the following.
x + y = 10 ; y = x - 2
Quantity A is x.
Quantity B is y.
A lady wants to buy the following items in the given price range-
1. Tomato between Rs. 40 and Rs. 45 per kg.
2. Grapes in the price range of Rs. 80 and Rs. 90 per kg.
3. Milk packets at Rs. 23 per liter.
In which shop from the following will she definitely get all her items/
A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter.
B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg.
C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
One question and three statements are numbered (I), (II) and (III). You have to decide whether the facts given in the statements are sufficient to answer the question given below.
Question: What is the length of the rectangle?
Statement:
I. The perimeter of the rectangle is 80 meters.
II. The sum of the adjacent sides is 40 meters.
III. The width of the rectangle is 10 meters.
Choose the correct option.
A. Only I is sufficient.
B. Only I and II are sufficient.
C. III and one from I or II are sufficient.
D. II and one from I or III are sufficient.
A question and three statements are numbered (I), (II) and (III). You have to decide whether the facts given in the statements are sufficient to answer the question given below.
Question: Five people A, B, C, D and E are sitting facing each other in a circle. E is seated between whom?
Statement:
I. The person sitting to the left of B and to the right of A is the same.
II. D is to the right of B.
III. A sits between E and C.
Choose the correct option.
A. Only I and II are sufficient.
B. Only I and III are sufficient.
C. Only III is sufficient.
D. Facts are insufficient.
