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.
Analyzing Statement Sufficiency for Shortest Person
The goal is to determine the shortest person among A, B, C, D, and E using the provided statements.
Statement Analysis
- Statement I: "A is taller than E but shorter than D." This translates to the inequality:
$D > A > E$
This statement alone does not provide enough information about B and C to find the shortest person. - Statement II: "B is shorter than C but taller than E." This translates to:
$C > B > E$
This statement alone is insufficient as it doesn't include A or D. - Statement III: "D is taller than C and A is taller than B." This gives two separate inequalities:
$D > C$
$A > B$
This statement alone is insufficient, as it doesn't connect all individuals or establish the absolute shortest.
Combining Statements
Let's combine the statements to see if we can establish a complete order:
- From Statement II and III: We have $C > B > E$ and $D > C$. Combining these yields $D > C > B > E$.
- From Statement III and II: We also know $A > B$. Combined with $B > E$ (from II), we get $A > B > E$.
- From Statement I: We know $D > A$ and $A > E$.
Determining the Shortest Person
Combining all derived inequalities:
- $D > C > B > E$ (from II & III)
- $D > A > B > E$ (from I & III & II)
From these combined statements, we can see that E is shorter than B, C, and D. Statement I also confirms E is shorter than A. Therefore, E is shorter than A, B, C, and D.
Conclusion: With all three statements combined, we can definitively conclude that E is the shortest person.
Hence, Statements I, II, and III together are sufficient to answer the question.
Similar Questions
- 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 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. - 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 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: 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. - 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 is the total of five natural even numbers?
Statements:
I. The second number is two times the first number.
II. All the five even numbers are consecutive even numbers in increasing order. A question is given, followed by two statements labelled I and II. Decide which of the statements is/are sufficient/necessary to answer the question and select the correct answer.
Question:
Who is the shortest among Shamita, Tanya and Rekha?
Statements:
I. Shamita is taller than Rekha. Rekha is shorter than Tanya.
II. Rekha is shorter than Surbhi. Surbhi is taller than Shamita. Tanya is shorter than Surbhi.
(A) Statement I alone is sufficient to answer the question, whereas Statement II alone is not sufficient to answer the question.
(B) Statement II alone is sufficient to answer the question, whereas statement I alone is not sufficient to answer the question.
(C) Both statements I and II together are not sufficient to answer the question.
(D) Both statements I and II together are necessary to answer the question.
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.
Five, girls, Gauri, Ragini, Navya, Kajal and Lovely, are sitting around a circular table facing towards the centre. Who sits to the immediate left of Lovely?
(I) Gauri is sitting immediately to the right of Lovely. Ragini is sitting immediately to the left of Kajal.
(II) Navya is sitting second to the left of Kajal. Gauri is an immediate neighbour of both Navya and Lovely.
Important Questions from Data Sufficiency
Consider two Statements and a Question:
Statement 1: Priya is 4 ranks below Seema and is 31 st from the bottom.
Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
Question: What is Seema’s rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
