Inequality Questions in Reasoning: A Method That Never Fails

Inequality questions appear in almost every banking prelims paper. They look like algebra, but they are really about one skill: deciding whether a relationship is certain. Once you learn the method below, you can solve most of them in under 20 seconds.

The question format

You get a statement such as:

P > Q ≥ R = S < T

and two conclusions, for example I. P > S and II. T > R. You must say whether only I follows, only II, either of them, neither, or both.

Rule 1: Walk along the chain from one letter to the other

To compare two letters, read the signs between them in order.

• All signs point the same way (all > / ≥ / =, or all < / ≤ / =): the relationship is certain.
  • If at least one sign is strict (> or <), the result is strict. P > Q ≥ R gives P > R.
  • If there is no strict sign but there is a ≥ or ≤, the result is ≥ or ≤. Q ≥ R = S gives Q ≥ S.
  • If every sign is =, the letters are equal.
• The signs point in opposite directions, for example R = S < T > U: no relationship can be concluded between R and U.

Rule 2: Test the conclusion against what is certain

A conclusion follows only if it is true in every possible case.

What the chain gives	Conclusion	Follows?
P > S	P > S	Yes
P > S	P ≥ S	Yes (P > S is enough for ≥)
Q ≥ S	Q > S	No (Q could equal S)
Q ≥ S	Q = S	No (Q could be greater)
No relation	Anything	No

Rule 3: The either-or case

Sometimes neither conclusion is certain, but one of them must be true. This happens when:

1. both conclusions use the same two letters, and
2. together they cover every possibility without overlapping.

Example: the chain gives Q ≥ S. Conclusions: I. Q > S, II. Q = S. Neither is certain, but since Q ≥ S means “greater or equal”, one of them must hold. Answer: either I or II.

The same applies when the relation cannot be determined at all and the conclusions are, say, X ≥ Y and X < Y: between them they cover every case.

Common trap: I. Q > S and II. Q < S are not an either-or pair when the chain gives Q ≥ S, because Q = S makes both false.

A worked example

Statement: M ≥ N > O = P ≤ Q

Conclusions: I. M > P II. Q > N

• M to P: ≥, >, =, all pointing the same way, with one strict sign, so M > P. I follows.
• Q to N: reading from Q back to N, the signs are ≥ (Q ≥ P), = and < (O < N). The directions are mixed, so no relation. II does not follow.

Answer: only I follows.

Speed tips

1. Don’t redraw the chain. Put your finger on the first letter and slide to the second.
2. Look for a strict sign as you slide; it decides whether you get > or ≥.
3. Check for an either-or pair whenever both conclusions use the same two letters and neither is certain.

Practise with our inequality MCQs. Every answer there was worked out by a small logic program that applies exactly these rules, so you can trust the key while you learn.