In which of the following options will the expression P < M be definitely true?
P = A < R < M
Inequalities: Understanding "Definitely True"
Inequalities questions test your ability to determine relationships between different elements based on given symbolic expressions. The key is to find a definite path from one element to another that establishes the required relationship without any ambiguity. An expression is "definitely true" if it holds true under all possible interpretations of the given statements.
Analyzing the Problem Statement
The question asks us to identify the option where the expression \($P < M$\) is definitely true. This means we need to trace the relationship between P and M in each given option and see if a clear, unambiguous "P is less than M" connection can be established.
Step-by-Step Analysis of Each Option
1. Option Analysis: M < R > P > S
- The given expression is \($M < R > P > S$\).
- We need to find the relationship between M and P.
- From the expression, we have \($M < R$\) and \($R > P$\).
- Both M and P are shown to be "less than" R. However, there is no direct relationship or connection established between M and P themselves.
- Consider possible scenarios:
- If R = 10, M = 5, P = 7, then \($M < P$\) (5 < 7).
- If R = 10, M = 7, P = 5, then \($M > P$\) (7 > 5).
- If R = 10, M = 5, P = 5, then \($M = P$\) (5 = 5).
- Since M could be less than, greater than, or equal to P, the expression \($P < M$\) is not definitely true.
2. Option Analysis: M > S < P < F
- The given expression is \($M > S < P < F$\).
- We need to find the relationship between M and P.
- From the expression, we have \($M > S$\) and \($S < P$\).
- Both M and P are related to S, but in opposite directions (M is greater than S, P is greater than S). There is a "common element" S, but the relation "opens" away from S for both M and P.
- Consider possible scenarios:
- If S = 5, M = 10, P = 7, then \($M > P$\) (10 > 7).
- If S = 5, M = 7, P = 10, then \($M < P$\) (7 < 10).
- If S = 5, M = 7, P = 7, then \($M = P$\) (7 = 7).
- Since M could be less than, greater than, or equal to P, the expression \($P < M$\) is not definitely true.
3. Option Analysis: Q < M < F = P
- The given expression is \($Q < M < F = P$\).
- We need to find the relationship between M and P.
- From the expression, we have \($M < F$\) and \($F = P$\).
- Combining these, if \($M < F$\) and \($F = P$\), then it definitively means \($M < P$\).
- The question asks for \($P < M$\) to be definitely true. Here, we found \($M < P$\), which is the opposite.
- Therefore, \($P < M$\) is definitely false in this option.
4. Option Analysis: P = A < R < M
- The given expression is \($P = A < R < M$\).
- We need to find the relationship between P and M.
- Let's break down the relationships:
- \($P = A$\) (P is equal to A)
- \($A < R$\) (A is less than R)
- \($R < M$\) (R is less than M)
- Combining \($P = A$\) and \($A < R$\), we can infer \($P < R$\).
- Now, combining \($P < R$\) and \($R < M$\), we can definitively infer \($P < M$\).
- Since all the inequality signs point in the same direction from P towards M (or from M away from P), a definite relationship is established.
- Therefore, the expression \($P < M$\) is definitely true in this option.
Conclusion
Based on the detailed analysis of all options, only in the expression \($P = A < R < M$\) can we definitively conclude that \($P < M$\).
Important Questions from Critical Reasoning
'Little knowledge is a dangerous thing' is a decision based on:
Which of the following is the assumption for the claim that 'Pleasure is desirable'?
Read the given statements carefully and answer the questions.
Fear of danger is more dangerous than danger itself. Risk is directly proportional= to danger
Which of the following are true according to the given statements?
A. Fear is worse than any fearful threat.
B. There is a trade-off between risk and danger.
C. There should be fear of danger.
D. There is no need to take risks to overcome any danger.
A question has been given in this question and a statement related to it. Read the passage carefully and review the statement based on it.
Amazon has acknowledged the data violation of user names and email ids of some users without giving details of its nature or scope. Although the company has not disclosed the total number of users affected by this violation, it has sent information to all affected users about the technical problem. And now this e-commerce major company is offering Gift Cards as compensation to customers who are victims of their data violation. This e-commerce company headquartered in Seattle is offering Gift Cards between $ 5 to $ 100 for users affected by some of their data violations.
A publication mentioning email communications between Amazon and a customer Paul Gagnon has reported that when he asked the customer service desk to ask the company how his information was leaked, then the company gave him a promotion of $ 100 Certificate offered. When Gagan got no response for the reason of this violation, he was offered $ 100 as an apology. After this violation, many affected users had filed a complaint with the service desk. Many people affected by this violation complained to the company, but none of them got so far. It is being speculated that Amazon Customer Service Supervisors have been instructed not to offer any comments or any kind of compensation to affected Amazon users.
Statement: The company has not told the fixed number of people affected by data violation. Select the most suitable option below.
A-statement is definitely true.
B-Query is probably true.
C-statement can not be determined.
D-statement is completely false.
A question has been given in this question and a statement related to it. Read the passage carefully and review the statement based on it.
Amazon has acknowledged the data violation of the user name and email id of some of its users, without giving details of its nature or scope. Although the company has not disclosed the total number of users affected by this violation, it has sent information to all affected users about the technical problem. And now this e-commerce major company is offering Gift Cards as compensation to customers who are victims of their data violation. This e-commerce company headquartered in Seattle is offering Gift Cards between $ 5 to $ 100 for users affected by some of their data violations.
A publication mentioning email communications between Amazon and a customer Paul Gagnon has reported that when he asked the customer service desk to ask the company how his information was leaked, then the company gave him a promotion of $ 100 Certificate offered. When Gagan got no response for the reason of this violation, he was offered $ 100 as an apology. After this violation, many affected users had filed a complaint with the service desk. Many people affected by this violation complained to the company, but none of them got so far. It is being speculated that Amazon Customer Service Supervisors have been instructed not to offer any comments or any kind of compensation to affected Amazon users.
Statement: Amazon has not instructed its supervisors to not provide any comments or offers of compensation to the affected users.
Select the most suitable option below.
A-statement is definitely true.
B-Query is probably true.
C-statement can not be determined.
D-statement is completely false.
