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: 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 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.
