Reading the Question: and, or, not, only

Both and means every condition at once, so the answer lives in the overlap. Take these seven capital letters. C, O and S are made of curved lines only. E and T are straight lines only. P and R have a straight stem and a curved bowl, so they contain both — and P and R are the answer. Notice that five of the seven letters satisfy half the condition, which is exactly why the wrong options look reasonable. Draw the two groups before you choose.

Now the opposite move. Either or but not both means one condition or the other, and never the overlap. Of the same seven letters, the ones that are only curved or only straight are C, O, S, E and T — five of them. P and R are thrown out precisely because they satisfy both. This is the trap, because in ordinary speech or usually includes the overlap: if someone offers you tea or coffee you would not be shocked to be handed both. On this paper the phrase but not both is doing all the work, so underline it.

The word only changes meaning depending on what it is attached to. Only P means P and nothing else — one letter. P and R only means exactly those two, no more and no fewer, so an option listing P, R and S is wrong even though P and R are in it. But letters containing only curved lines is a different sense entirely: here only describes the lines, not the list, and it means this property and no other property. Option lists on this paper use both senses in the same question, and that is deliberate. Ask yourself what the word only is attached to.

Must means true in every case you can construct. Could means true in at least one. Cannot means true in none. The useful consequence is that both are settled by a single case: to knock out a must you need one counter-example, and to confirm a could you need one example. That is fast work, and it is faster than reasoning in the abstract. So test each option by trying to break it rather than by trying to believe it — find the one arrangement that makes it false, and if you cannot, it probably must be true.

A superlative with a condition attached is two tests, not one. Suppose you need five gigabytes of room and the options are two, four, six and eight. Test one asks which are big enough: two and four fail immediately. Test two asks which of the survivors is smallest: six and eight both pass, and six is smaller, so six is the answer. If you run only the second test you pick two, which is the smallest and completely useless. Work out the requirement first, then read the options. That is the whole lesson — connectives, only, must and could, and smallest-that-works. Quiz and exercises now.