Either-Or Cases in Inequality

The either-or case is the highest-value trick in inequality, because it turns a question that looks unanswerable into a definite 'either follows'. It appears when the chain gives no direct relation between two letters, yet the two conclusions offered on those same letters are exact opposites that together cover every possibility. SBI Clerk loves this pattern precisely because candidates who only check each conclusion in isolation mark 'neither follows' and lose the mark, while the paired view scores it cleanly.

The Three-Point Test

An either-or answer is correct only when all three conditions hold together. First, neither conclusion is individually definite from the chain. Second, both conclusions relate the very same pair of letters. Third, the two conclusions form a complementary pair that leaves no gap, such as greater-than paired with less-than-or-equal. If even one condition fails — different letters, or a gap where equal is not covered — the answer collapses back to 'neither follows'. Run this checklist whenever a single question shows two conclusions on the same two letters.

Which Pairs Are Complementary

Only exact opposites qualify. Greater-than with less-than-or-equal is complementary, and less-than with greater-than-or-equal is complementary, because each pair together covers all three of bigger, smaller and equal. The dangerous near-miss is greater-than paired with less-than, which leaves the 'equal' case uncovered and is therefore not complementary, so neither follows. The second common form is a common-element chain giving one letter at least as large as another, split into greater-than and equal on the same pair. Both forms reduce to the same idea: the two conclusions must jointly account for every way the two letters could compare. A neat way to remember the valid pairs is that each one puts a strict sign against its own 'or-equal' opposite — greater-than against not-greater, and less-than against not-less — so no third case can slip between them. Any pairing that leaves a case loose, however natural the two conclusions look side by side, is a decoy the paper-setter planted to draw a wrong either-or.

Solved Examples

Example 1: From A > B < C there is no relation between A and C. Conclusions A > C and A ≤ C are complementary, so the answer is either I or II follows. Example 2: From M ≥ N ≥ O the chain gives M ≥ O. Conclusions M > O and M = O together equal M ≥ O, which is established, so either follows again.

✗ Marking 'neither follows' because each conclusion alone is uncertain  |  ✓ Checking if the two conclusions are complementary → either I or II follows

The Equal-Sign Gap

The most common way candidates misfire on either-or is ignoring the equal case. Greater-than and less-than feel like opposites, but between two quantities there is a third possibility — they might be equal — and a pair that skips it is not complementary. So 'P > Q or P < Q' is not an either-or answer, because nothing rules out P = Q, and the correct verdict is neither follows. Conversely, whenever a common-element chain leaves an 'or equal' sign on the linking letter, the resulting relation carries an equal possibility, and a greater-than-plus-equal split on the end letters becomes a textbook either-or. Always ask whether 'equal' is covered before you commit to either side. A fast way to check any pair: write the two conclusions on the same letters and mentally list the three outcomes — bigger, smaller, equal. If the two conclusions together tick all three boxes, they are complementary and the answer is either-or; if any box is left unticked, the answer drops to neither follows. This box-ticking check takes about five seconds and removes every doubt about the trickiest verdict in the whole chapter.