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 ?
UPSC - 2021
Statement-1 alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are required to answer the question.
Neither Statement-1 alone nor Statement-2 alone is sufficient to required to answer the question.
We need to determine if Statement-1, Statement-2, or both are sufficient to find the day of the week for the 14th of the month. We will analyze each statement independently first, and then consider them together if necessary.
The last day of a month can be the 28th, 29th, 30th, or 31st. Since we don't know the number of days in the month, we cannot uniquely determine the day of the 14th. For example:
Since the day of the 14th changes based on the length of the month, Statement-1 alone is not sufficient.
This statement directly tells us that the 17th of the month is a Saturday.
We need to find the day of the 14th. The 14th is \(17 - 14 = 3\) days before the 17th.
If the 17th is a Saturday, then:
Thus, Statement-2 alone is sufficient to determine that the 14th of the month is a Wednesday.
B) Statement-2 alone is sufficient to answer the Question
As shown in the step-by-step analysis, Statement-2 provides a specific date (17th) and its corresponding day (Saturday). From this, we can directly calculate the day for the 14th of the month.
A) Statement-1 alone is sufficient to answer the Question
Statement-1 specifies the day of the last day of the month, but it does not specify the length of the month. Without knowing whether the month has 28, 29, 30, or 31 days, we cannot uniquely determine the day of the 14th. Therefore, Statement-1 alone is insufficient.
C) Both Statement-1 and Statement-2 are required to answer the question.
Since Statement-2 alone is sufficient, it is not necessary to use Statement-1. Therefore, this option is incorrect.
D) Neither Statement-1 alone nor Statement-2 alone is sufficient to required to answer the question.
This option is incorrect because Statement-2 alone is sufficient to answer 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?
UPSC - 2021
Statement-1 alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are required to answer the question.
Neither Statement-1 alone nor Statement-2 alone is sufficient to required to answer the question.
The problem asks us to identify the heaviest person among A, B, C, D, and E using two given statements. We need to determine if Statement-1 alone, Statement-2 alone, or both statements together are sufficient to answer the question.
Consider two Statements and a Question:
Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom.
Statement-2: Ena is 2 ranks above Seema and is 37th 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 to the Statements and the Question?
UPSC - 2021
Statement-1 alone is not sufficient to anawer the Question
Statement-2 alone is not sufficient to anawer the Question
Either Statement-1 alone or Statement-2 alone is sufficient to answer the question
Both Statement-1 and Statement-2 are required to answer the question
The problem asks us to determine if Statement-1, Statement-2, or both are sufficient to find Seema's rank from the top in a class of 40 students. We will analyze each statement independently to see if it provides enough information to calculate Seema's rank from the top.
The total number of students in the class is 40.
The formula to find the rank from the top when the rank from the bottom and total number of students are known is:
\[ \text{Rank from top} = \text{Total students} - \text{Rank from bottom} + 1 \]From Statement-1, we know Priya's rank from the bottom is 31st.
Since Priya is 4 ranks below Seema, this means Seema is 4 ranks above Priya. Therefore, Seema's rank from the bottom will be:
\[ \text{Seema's rank from bottom} = \text{Priya's rank from bottom} + 4 \]Substituting Priya's rank from the bottom:
\[ \text{Seema's rank from bottom} = 31 + 4 = 35 \]Now we have Seema's rank from the bottom (35th) and the total number of students (40). We can find Seema's rank from the top:
\[ \text{Seema's rank from top} = \text{Total students} - \text{Seema's rank from bottom} + 1 \]Substituting the values:
\[ \text{Seema's rank from top} = 40 - 35 + 1 = 6 \]So, Statement-1 alone is sufficient to answer the question.
From Statement-2, we know Ena's rank from the bottom is 37th.
Since Ena is 2 ranks above Seema, this means Seema is 2 ranks below Ena. Therefore, Seema's rank from the bottom will be:
\[ \text{Seema's rank from bottom} = \text{Ena's rank from bottom} - 2 \]Substituting Ena's rank from the bottom:
\[ \text{Seema's rank from bottom} = 37 - 2 = 35 \]Now we have Seema's rank from the bottom (35th) and the total number of students (40). We can find Seema's rank from the top:
\[ \text{Seema's rank from top} = \text{Total students} - \text{Seema's rank from bottom} + 1 \]Substituting the values:
\[ \text{Seema's rank from top} = 40 - 35 + 1 = 6 \]So, Statement-2 alone is also sufficient to answer the question.
Since both Statement-1 alone and Statement-2 alone are sufficient to answer the question, the correct option is C.
C) Either Statement-1 alone or Statement-2 alone is sufficient to answer the question. Both statements independently provide enough information to calculate Seema's rank from the top.
Two Statements S1 and S2 are given. below with regard to two numbers followed by a Question:
S1: Their product in 21.
S2: Their sum is 10.
Question:
What are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?
UPSC - 2020
S1 alone is sufficient to answer the Question.
S2 alone is sufficient to answer the Question.
S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor 52 alone is sufficient to answer the Question.
S1 and S2 together are not sufficient to answer the Question.
The problem asks us to determine if the given statements (S1 and S2) are sufficient, individually or together, to find two unknown numbers. We will analyze each statement separately and then combine them to see if a unique solution can be found.
C) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question. This is correct because, as shown above, combining both statements leads to a unique set of two numbers (3 and 7).
Two Statements S1 and S2 are given below with regard to four numbers. P, Q, R and S followed by a Question:
S1 : R is greater than P as well as Q.
S2: S is not the largest one.
Question: Among four numbers P, Q, Rand S which one is the largest?
Which one of the following is correct in respect of the above Statements and the Question?
UPSC - 2020
S1 alone is sufficient to answer the Question.
S2 alone is sufficient to answer the Question.
S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor 52 alone is sufficient to answer the Question.
S1 and S2 together are not sufficient to answer the Question.
The problem asks us to determine if the given statements (S1 and S2) are sufficient to identify the largest among four numbers P, Q, R, and S. We need to analyze each statement individually and then combined.
Analyze Statement S1: "R is greater than P as well as Q."
This can be written as: \(R > P\) and \(R > Q\).
From this statement, we know that R is definitely larger than P and Q. However, we don't have any information about S. S could be larger than R, or smaller than R. For example:
Since we cannot definitively identify the largest number using S1 alone, S1 alone is not sufficient.
Analyze Statement S2: "S is not the largest one."
This means that the largest number must be P, Q, or R. However, S2 gives no information about the relative order of P, Q, and R. For example:
Since we cannot definitively identify the largest number using S2 alone, S2 alone is not sufficient.
Analyze Statements S1 and S2 together:
From S1: \(R > P\) and \(R > Q\). This implies that R is greater than both P and Q. So, P and Q cannot be the largest number among P, Q, R, S.
From S2: S is not the largest number.
Combining these two, we have eliminated P, Q, and S as potential largest numbers. Therefore, the only remaining number, R, must be the largest.
Thus, S1 and S2 together are sufficient to answer the question.
C) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
As determined in the step-by-step analysis, S1 alone is not sufficient, S2 alone is not sufficient, but when combined, they allow us to uniquely identify R as the largest number.
A) S1 alone is sufficient to answer the Question.
This is incorrect because S1 only tells us that R is greater than P and Q. It provides no information about S, so S could potentially be the largest or smaller than R.
B) S2 alone is sufficient to answer the Question.
This is incorrect because S2 only tells us that S is not the largest. It does not provide any information about the relative order of P, Q, and R, so any of them could be the largest.
D) S1 and S2 together are not sufficient to answer the Question.
This is incorrect because, as shown in the combined analysis, S1 establishes R as greater than P and Q, and S2 eliminates S as the largest. This leaves R as the only possible largest number.
Two Statements S1 and S2 are given below followed by a Question:
S1: n in a prime number.
S2: n leaves a remainder of 1 when divided by 4.
Question:
If n is a unique natural number between 10 and 20, then what is n?
Which one of the following is correct in respect of the above Statements and the Question?
UPSC - 2020
S1 alone is sufficient to answer the Question
S2 alone is sufficient to answer the Question.
S1 and S2 together are sufficient to answer the Question, but neither 81 alone nor S2 alone is sufficient to answer the Question.
S1 and S2 together are not sufficient to answer the Question.
We need to determine if the given statements (S1 and S2) are sufficient, individually or together, to uniquely identify a natural number \(n\) between 10 and 20. We will list the numbers that satisfy each statement and then check for uniqueness.
D) S1 and S2 together are not sufficient to answer the Question.
