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
- A question and three statements labelled (I), (II) and (III) are given. You have to decide which statement(s) is/are sufficient to answer the question.
Question: Who is the shortest among A, B, C, D and E?
Statements:
I. A is taller than E but shorter than D.
II. B is shorter than C but taller than E.
III. D is taller than C and A is taller than B. - You are given a question and two statements. Identify which of the statements is/are necessary/sufficient to answer the question.
Question:
Who is the father of M?
Statements:
I - P and Q are brothers.
II - Q's wife is the sister of M's wife. - A question is given, followed by two statements labelled 1 and 2. Identify which of the statements is/are sufficient/necessary to answer the question.
Question:
Is Mohita younger or older than Shubham?
Statements:
1. Mohita is, at present, exactly 35 years younger than her father.
2. Mohita's brother, Shubham, who was born in 1954, is exactly 34 years younger than his father. - A question is given, followed by two statements labelled I and II. Identify which of the statements is/are sufficient to answer the question.
Question:
What is Preetee's age?
Statements:
I. Preetee is 10 years younger to her sister Arpita.
II. Arpita is 25 years younger to her mother and 30 years younger to her father. - A question is given, followed by three statements labelled I, II and III. Identify which of the statements is/are sufficient to answer the question.
Question:
Who ranked first in the class?
Statements:
I. Sreeja ranked $2^{\text{nd}}$.
II. Aman ranked one rank below Sreeja.
III. Rohit ranked better than Aman. - A question is given, followed by two statements labelled I and II. Identify which of the statements is/are sufficient to answer the question.
Question:
In a certain code language, 'pu ma kas' means 'we eat mangoes'. What is the code of 'mangoes'?
Statements:
I. 'la ti kas' means 'we are graduate'.
II. 'hum tup pu' means 'they eat bananas'. - A question is given, followed by two statements labelled I and II. Identify which of the statements is/are sufficient/necessary to answer the question.
Question:
What will be the total price of 10 chairs, each of which is of the same price?
Statements:
I. One-fourth of the price of each chair is ₹140.
II. The total price of 3 chairs is ₹560 more than the total price of 2 chairs.
Important Questions from Data Sufficiency
Which of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
\(\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right) \) \(\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)\) is \(k^{16}- \frac{1}{k^{16}}\).
Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question.
Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D?
(I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
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.
