The worked question on this page is original educational practice. It is not represented as a question from an official previous-year examination paper.
01 / UNDERSTANDING
Review the question
Create original paired quantities whose relation changes across a domain boundary. Ask what extra condition makes the relation definite, teaching the role of information rather than only selecting an option.
02 / UNDERSTANDING
The concept in context
Bounds can settle a comparison without fully solving both sides. However, squaring, multiplying or dividing an inequality requires attention to signs and possible zero values. A counterexample can reject an always-greater claim, while several examples supporting it still do not establish a universal result. Explain the domain condition on which the conclusion depends.
03 / UNDERSTANDING
A worked learning case
Original educational case. In an original comparison, Quantity A is x² and Quantity B is x for a positive x. If x=2, A exceeds B; if x=0.5, A is smaller. Positivity alone does not determine one relation. An added condition x>1 would change the conclusion, showing why the domain is essential rather than optional background.
ORIGINAL EDUCATIONAL PRACTICE
Try it before you check.
Original practice: For every real x > 1, compare x² with x.
Show the answer and reasoning
x² is greater than x.
Because x is positive and greater than one, multiplying x by x increases it. Algebraically, x² − x = x(x − 1), and both factors are positive, so the difference is positive. The domain matters: for a positive x below one, the relation would reverse, so it cannot be omitted from the explanation.
Two traps to watch for.
- Assuming a positive variable must be at least one.
- Treating one supporting numerical example as universal proof.
YOUR TOPIC-SPECIFIC LEARNING MAP
Learn from the attempt
Write the domain before comparing.
Look for boundary and counterexample values.
State the condition making a relation definite.
Explain the idea, apply it to a new situation, then check what changed in your reasoning.
BANKERS TUTORIAL · SOURCE NOTES
Keep the source alongside your notes.
Official links provide subject context and authoritative reference material. This guide’s explanation, scenario and question are original Bankers Tutorial learning content.
- www.ibps.in https://www.ibps.in/
- www.ibps.in https://www.ibps.in/index.php/faq/
For IBPS & RRB preparation, check the current official notice before relying on changing dates, rules or examination requirements.
