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 carefully and decide the appropriate answer. Among 5 people, A, B, C, D and E, each of a different height, who is the second-tallest? I: E is shorter than A. B is taller than D but shorter than E. II: Only C is taller than A. D is shorter than E.
Second-Tallest Person: Data Sufficiency Analysis
The problem requires determining the second-tallest person among five individuals (A, B, C, D, E) with different heights. We must evaluate the sufficiency of data provided in two statements.
Statement I Analysis: Partial Height Ordering
Statement I provides the following height relationships:
- E is shorter than A: $E < A$
- B is taller than D but shorter than E: $D < B < E$
Combining these inequalities yields a partial order: $D < B < E < A$. This establishes the relative heights of A, B, D, and E, indicating A is the tallest among this group. However, the position of person C is not specified in relation to A, B, D, or E. C could be taller than A, or shorter than A. Without definitive information on C's position relative to A, we cannot determine the overall second-tallest person.
Conclusion for Statement I: Insufficient.
Statement II Analysis: Determining Tallest and Second-Tallest
Statement II provides two pieces of information:
- "Only C is taller than A": This crucial phrase implies that the set of individuals taller than A consists solely of C. Given that all individuals have different heights, this means C is the tallest person overall, and A is the second-tallest person overall. The relationships derived are $C > A$, and $A$ is taller than all others ($B, D, E$).
- "D is shorter than E": This is stated as $D < E$. This fact helps to order the individuals shorter than A ($B, D, E$), but it does not alter the determination that C is the tallest and A is the second-tallest.
The ordering is established as C (tallest) > A (second-tallest) > {B, D, E in an order where $D < E$}.
Conclusion for Statement II: Sufficient.
Overall Conclusion on Data Sufficiency
Since Statement II alone provides enough information to identify the second-tallest person (A), while Statement I alone does not, the data in Statement II alone is sufficient.
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.
