Conditional Combination Questions
How do you answer "which two statements prove this" logic questions?
Break the statement to be proven into its smallest component parts before reading the numbered conditions, then check each answer option against every part. A pair of conditions is only correct if it proves the statement exactly as worded — including qualifiers like "most," "only," or a specific name — not just something similar to it. When no pairing satisfies every part, the correct answer is "none."
Why precision matters more here than anywhere else
These questions ask which two numbered statements, combined, prove a target sentence — for example, "Jacob enjoys apples most." They're not frequent, but they're disproportionately missed, because the wrong options are built to be almost right. A pairing that proves "Jacob enjoys apples" without the word "most" does not prove the full statement. Small qualifying words are never accidental.
Worked example
Find the two statements which together prove: Jacob enjoys apples most.
- Apples are the most delicious fruit
- Jacob and his twin, Jason, have the same tastes
- Jacob is least likely to dislike eating apples
- Jacob and his twin, Jason, have exactly opposite tastes
- Jacob enjoys apples
A. 1 & 2 B. 2 & 3 C. 4 & 5 D. 2 & 5 E. None
Break the target into parts: Jacob (specifically him) — enjoys (not merely tolerates) — apples (the fruit alone) — most (above every other option, not just highly).
Every pairing fails at least one part. Options with statement 1 never establish that Jacob himself likes apples — only that apples are broadly delicious. Options built around Jason's tastes (whether same or opposite) introduce a sibling who has no bearing on Jacob's own preference unless the pairing explicitly transfers it, which none of these do. Statement 3, "least likely to dislike," describes tolerance, not enjoyment — a common substitution trap. No combination proves all four parts, including the superlative "most." Option E, none, is correct.
Working outside the given conditions
A statement can only be proven using the exact information given in the numbered conditions — never outside knowledge, however obviously true it might seem. If the question asks you to prove "wood can be hard," and none of the given conditions establish that directly, you cannot rely on already knowing that wood is sometimes hard. Only what's stated in the options counts.
Steps
- Break the target statement into its individual components before reading the options
- Note any qualifying words (most, only, exactly, never) — these must be proven exactly, not approximately
- Check each option against every component in turn, not just the parts that seem to fit
- Discard any pairing that relies on information not actually stated in the conditions
- Select "none" when no pairing satisfies every component — this is a genuinely correct answer, not a last resort
This is one chapter of the Scholarship & Entrance English Assessment Guide. The complete guide — every technique, collected in one document — is available as a free PDF from the guide's main page.