Smallest Sufficient, Largest Possible

A superlative with a condition attached is two tests, and the order matters. Suppose you need five gigabytes of room and the files are two, four, six and eight. Test one asks which are big enough: two and four fail straight away. Test two asks which of the survivors is smallest: six beats eight. So six is the answer. Run test two on its own and you pick two, which is the smallest and frees nowhere near enough. The smallest option is almost never the answer to the smallest that works, and the way to avoid the trap is to work out the requirement before you even read the options.

Fifty-eight pencils, eight to a packet, gives seven remainder two — and that one division answers two different questions. How many packets are needed to hold them all? Eight, because the last two pencils still have to go somewhere. How many packets can be completely filled? Seven, because two pencils do not fill a packet. The arithmetic is identical; the sentence decides which way the remainder pushes you. So read the sentence before you decide what to do with the remainder, not after.

There is a short list of words that settle the direction. Needed, required, least, at least and enough all push you up, because something is left over and it still has to be handled. Complete, whole, afford and fit all push you down, because a partial one does not count. Underline the governing word before you divide, and then the rounding decides itself rather than being a judgement call you make while tired at question twenty-eight.

The mirror image is largest possible, and it has the same two-test structure with the direction flipped. A lift takes at most four hundred and fifty kilograms: four hundred and ninety-five is over, so it is out, and of what remains four hundred and fifty is the largest. Notice that exactly equal to the limit is allowed, because at most four hundred and fifty includes four hundred and fifty. If the question had said under four hundred and fifty, that would exclude it. Always read whether the boundary itself counts, because option writers put the boundary value in deliberately.

Three steps, always in this order. First, work out exactly what is required, as a number on its own, ignoring the options completely. Second, cross out every option that fails it — usually two of the four go. Third, and only now, take the smallest or largest of what survives. Doing that third step first is the single commonest error on this question type, and the options are written so that the plausible wrong answer is always sitting there waiting. Quiz and exercises now.