Yangpu, meanwhile, said its tests were not related to the enrollment procedure, but were aimed at “relaxing” parents.

The “graphics-based reasoning” was said to be too difficult for most of the test-takers.

An official at Qibao school told The Telegraph that authorities had ordered the school to conduct a “deep investigation”.

The man, who did not want to be named, said allegations were based on a “rumour”, but refused to deny the school tested parents, saying: “We don’t take foreign media interviews.”

Qingpu charges 30,000 yuan (£3,360) a term for six-year-olds entering the school, while Yangpu charges 11,000 yuan (£1,230) and Qibao 12,500 yuan (£1,400).

While many parents took to social media to complain about the strict enrolment procedures, some were less critical.

“Just like some schools in other countries require parents to be Christian, I think the requirements from these private schools are reasonable,” a mother who is hoping to enroll her daughter at the one of the schools told the Global Times newspaper.

China has a catchment area system for public schools, and competition for places has seen desperate parents splurge on extremely poor quality property near elite schools.

The Telegraph last year reported on an insect-ridden alleyway in Beijing being sold for a price similar to plush homes in Kensington and Chelsea because of the desirable catchment area.