Consider the Question and two Statements given below in respect of three cities P,Q and R in a State:
Question: How far is city P from city Q?
Statement-1 City Q is 18 km from city R
Statement-2 City P is 43 km from city R.
Which one of the following is correct in respect of the Question and the Statements?
UPSC - 2022
Statement-I alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are sufficient to answer the Question
Both Statement-1 and Statement-2 are not sufficient to answer the Question
The question asks for the distance between city P and city Q. We are given two statements providing distances between Q and R, and P and R. We need to determine if these statements, individually or together, are sufficient to find the distance between P and Q.
D) Both Statement-1 and Statement-2 are not sufficient to answer the Question
Six persons A, B, C, D, E and P are sitting equidistant from each other around a circular table (facing the centre of the table).
Consider the Question and two Statements given below :
Question: Who is sitting on the immediate left of A?
Statement-1: B is sitting opposite to C and D is sitting opposite to E.
Statement-2: F is sitting on the immediate left of B
Which one of the following is correct in respect of the Question and the Statements?
UPSC - 2022
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 sufficient to answer the Question
Both Statement-1 and Statement-2 are not sufficient to answer the Question
The problem asks us to determine if the given statements are sufficient to identify the person sitting immediately to the left of A. We have six persons (A, B, C, D, E, P) sitting around a circular table, facing the center. We will analyze each statement individually and then combined to see if a unique solution can be found.
Let's represent the six positions around the circular table as 1, 2, 3, 4, 5, 6 in a clockwise direction.
In a circular arrangement of 6 people, opposite positions are (1,4), (2,5), and (3,6).
However, we don't know the exact positions of A and P. A could be at 3 or 6. If A is at 3, P is at 6. If A is at 6, P is at 3.
Let's consider a possible arrangement based on Statement-1:
Let's list the pairs: (B, C), (D, E), (A, P).
Consider A's position. If A is at position 1, P is at position 4. The other two pairs (B,C) and (D,E) can be arranged in two ways for the remaining positions (2,5) and (3,6):
Since we get different answers for who is to the immediate left of A, Statement-1 alone is not sufficient.
The problem states there are six persons: A, B, C, D, E, and P. The person 'F' is not among the six given persons. This indicates that Statement-2 provides irrelevant or incorrect information based on the initial problem statement. Therefore, Statement-2 cannot be used to answer the question.
Since Statement-2 introduces a person 'F' who is not part of the initial group of six (A, B, C, D, E, P), Statement-2 is contradictory or irrelevant to the problem's context. Even if we ignore the 'F' issue and assume it's a typo for one of the other persons, Statement-1 alone was insufficient, and Statement-2 contains an inconsistency. Therefore, combining them will not lead to a sufficient answer.
If we strictly interpret the problem, the set of people is {A, B, C, D, E, P}. Statement-2 mentions 'F', which is not in this set. This makes Statement-2 invalid or unhelpful.
Even if we assume 'F' was a typo for 'P' (the only other person not mentioned in Statement-1), then Statement-2 would be: P is sitting on the immediate left of B. Let's see if this helps.
From Statement-1: Pairs are (B, C), (D, E), (A, P).
If P is to the immediate left of B (assuming everyone faces the center, so immediate left is clockwise):
So, one possible arrangement (clockwise) is: B, P, D, C, A, E. In this case, immediate left of A (position 5) is C (position 4). (Moving clockwise from A, the person at position 4 is to A's immediate left).
Another possible arrangement: B, P, E, C, A, D. In this case, immediate left of A (position 5) is C (position 4).
In both these scenarios (assuming F was P), the person to the immediate left of A is C. This would make the combined statements sufficient. However, this relies on assuming a typo, which is not a standard approach in competitive exams unless explicitly stated.
Given the exact wording, 'F' is not one of the six persons. Therefore, Statement-2 is invalid.
Since Statement-1 is insufficient, and Statement-2 is invalid/irrelevant, neither statement alone nor both combined can answer the question.
D) Both Statement-1 and Statement-2 are not sufficient to answer the Question
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?
UPSC - 2022
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 sufficient to answer the Question
Both Statement-1 and Statement-2 are not sufficient to answer the Question
Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m.
Consider the Question and two Statements given below:
Question: Which lecture is in the third period?
Statement-1: Lecture F is preceded by A and followed by C
Statement-2: There is no lecture after lecture B
Which one of the following is correct in respect of the Question and the Statements?
UPSC - 2022
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 sufficient to answer the Question
Both Statement-1 and Statement-2 are not sufficient to answer the Question
The problem asks us to determine which lecture is in the third period given two statements. We need to evaluate the sufficiency of each statement individually and then combined.
There are six lectures (A, B, C, D, E, F), each of one hour duration, scheduled between 8:00 a.m. and 2:00 p.m. This means there are six periods:
We need to find the lecture in the 3rd period (10:00 - 11:00).
This means the sequence A - F - C must occur consecutively in the schedule. Let's list the possible positions for this sequence:
In these possible arrangements, the lecture in the 3rd period could be C (in case 1), A (in case 2), F (in case 3), or some other lecture (in case 4). Since we cannot uniquely determine the lecture in the 3rd period, Statement-1 alone is not sufficient.
This implies that lecture B is the last lecture, i.e., it is in the 6th period.
This statement only tells us the position of B. The lectures in the 1st, 2nd, 3rd, 4th, and 5th periods are still unknown. Therefore, Statement-2 alone is not sufficient to determine the lecture in the 3rd period.
From Statement-2, we know B is in the 6th period:
_, _, _, _, _, B
From Statement-1, we know the sequence A - F - C. Since B is in the 6th position, the sequence A - F - C cannot start at the 4th position (as it would require 4th, 5th, 6th positions, but B is in 6th). So, the possible arrangements for A - F - C are:
Let's examine the 3rd period in these possibilities:
As we can see, the lecture in the 3rd period could be C, F, or A. Since we still cannot uniquely determine the lecture in the 3rd period even after combining both statements, both statements together are not sufficient.
D) Both Statement-1 and Statement-2 are not sufficient to answer the Question
Consider the Question and two Statements given below:
Question: Is x an integer?
Statement-1: x/3 is not an integer.
Statement-2: 3x is an integer.
Which one of the following is correct in respect of the Question and the Statements?
UPSC - 2022
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 sufficient to answer the Question
Both Statement-1 and Statement-2 are not sufficient to answer the Question
The question asks whether \(x\) is an integer. We need to evaluate if the given statements, individually or together, provide enough information to definitively answer this question as "yes" or "no". We will test different values of \(x\) that satisfy each statement to see if they lead to a consistent answer.
D) Both Statement-1 and Statement-2 are not sufficient to answer the Question
As shown in the step-by-step analysis, neither statement alone nor both statements combined can definitively determine whether \(x\) is an integer. We found scenarios where \(x\) is an integer and scenarios where \(x\) is not an integer, all while satisfying the given conditions.
A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.
Consider the following statements:
1. The middle three floors are painted in different colours.
2. The second (II) and the fourth (IV) floors are painted in different colours.
3. The first (1) and the fifth (V) floors are painted red. To ensure that any two consecutive floors have different colours
UPSC - 2019
Only statement 2 is sufficient
Only statement 3 is sufficient
Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient
Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient
We need to determine which statement or combination of statements is sufficient to ensure that any two consecutive floors have different colours. We will analyze each statement individually and in combination, checking if the condition of different colours for consecutive floors is met.
Let the five floors be F1, F2, F3, F4, F5. We have four colours available.
Correct Option: B) Only statement 3 is sufficient
