The banana question — lobbed at an applicant for medicine at Cambridge last year — may not be typical, but it highlights the difficulties involved in winning a place at Oxbridge.

More than 10,000 students with straight As were rejected by Oxford and Cambridge last year, and this autumn it will be even more competitive. With entrance papers being introduced in an increasing number of subjects, landing a place has become a fine art.

As a result, an entire industry has sprung up around the process, with companies offering training to candidates and advising on the best subject-by-subject chance of success on a no- acceptance, no-fee basis.

Anthony Smith, the President of Magdalen College, Oxford, may describe such entrepreneurs as “a bunch of grasping, meddling, money-grabbing young men” exploiting parents’ social anxiety about Oxbridge, but their existence reflects a growing reality — crafty number-crunching and naked pragmatism can increase the chances of success.

The old-fashioned image of Oxbridge entry — public school headmaster has a quiet word in the ear of a friendly college tutor about the merits of his star pupil — belongs in the history books. Now a welter of factors needs to be considered as part of an entrance strategy.

The first point to be aware of is that the richest colleges, such as St John’s, Oxford, and Trinity, Cambridge, attract the most competition for places. Combine this with a popular subject, such as English or law, and the odds can be even more daunting.

St John’s, Oxford, for instance, receives 9.7 applications for every place on its economics course. Few of the candidates will be slouches. Compare that with St Hilda’s, an unfashionable all-girls college, which has just 0.3 applications for each offer it makes to read classics.

The same colleges dominate the academic league tables, making them even more keenly sought after. Magdalen, which regularly features in the upper reaches of Oxford’s Norrington table of degree results, receives eight applications per place for medicine; but apply to St Peter’s, a runt of the Oxford litter, and you narrow your odds to just 2.2 against.

Inevitably, the stiffer the competition, the more pressure is placed on admissions tutors. Laura Spence, an applicant from a state comprehensive, became the poster girl for opponents of “the Oxbridge old boy network” — led by Gordon Brown — when she failed to win a place at Magdalen to read medicine in 2000.

Smith has said ever since that Spence was not the only candidate that year to brandish a string of A grades, and that the Government should look at the state of its examination system before it criticises Oxbridge colleges for “arbitrary” decisions.

The cost of various colleges might also be a factor: a room at Jesus, Oxford, will cost £1,541 a year, while the most expensive, at Pembroke, comes to £2,495 — a £3,000 difference over the course of a three-year degree. Meals and other charges can add £2,000 a year to the rents.

Last year, The Times compiled the first value-for-money league table of Oxford colleges, comparing their academic record with the cost of attending them. Exeter College, founded in 1314 and the alma mater of J. R. R. Tolkien, came top, while Pembroke College came bottom.

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