Quiz GAT Test

< n, m > represents nD + nm, where n and m can be integers and fractions and may be positive, negative or zero.
For example,
< 3, 2 > represents 3D + 6
< 1, -5 > represents D - 5
< 6, 1/3 > represents 6D + 2.
Note: The rules for multiplication are:
positive × positive = positive,
negative × positive = negative,
positive × negative = negative,
negative × negative = positive.
What does < 7, 2 > represent?

In its waste management program, a local council collects three types of waste: general rubbish, recyclable materials and green waste. Only one type of waste is collected each week.
The 52 weeks of the year are numbered, in order. Waste is collected according to the following schedule:
If the week is a multiple of four, recyclable materials are collected.
If the week is a multiple of three but not a multiple of four, green waste is collected.
On all other weeks, only general rubbish is collected.
From the start of the year, when green waste has been collected five times, how many times has general rubbish been collected?

The following passage is from a biography of Nobel Prize-winning author Patrick White. For a time Patrick White credited a Romanian crank in the Sydney suburbs with saving his life. Dr Herman Morgenstern was treating his asthma with calcium injections and long sessions under blue lights. The results seemed miraculous. One afternoon in April 1958, White turned up at the Romanian's surgery wanting a little something to help him through the ordeal he faced that evening. Morgenstern gave him a pill and lift to Martin Place, where White was to be given the Miles Franklin Award for Voss. "As it was the first time awarded," he wrote to his friends David and Gwen Moore, "the bull1 that went with it was most alarming".
Among the television cameras and literary bores gathered at the ceremony was Prime Minister, Bob Menzies. Genial, huge with the dewlaps2 of a sea lion, Menzies had been prime minister for a decade. White's late, radical reputation might suggest this meeting was fraught with difficulty … Not at all. Though White had toyed with revolution during the war, such ideas had died on his return home. Revolutions were for elsewhere but not for Australia. Once settled in Sarsaparilla3 with his vegetables and dogs, the conservative instincts of his family reasserted themselves.
bull: nonsense, dewlaps: loose skin on the throat, Sarsaparilla: White's farm near Sydney
Dr Morgenstern's treatment of White's asthma is depicted as

The following information is about an American legal case over whether a deed granting rights to 'minerals' beneath a property in Pennsylvania entitled the deed-holders to gas as well. The property sits above a shale-rock formation. Commercial drilling for the gas trapped within the formation began in 2008. There are now nearly 9000 shale-gas wells in the state of Pennsylvania.
1 John and Mary Butler owned a property in Pennsylvania, which their predecessors had acquired from Charles Powers in 1881. In 2009, the Butlers went to court to 'quiet' a right specified in their 1881 deed of ownership that entitled Charles Powers's heirs to 'one half the minerals and petroleum oils' beneath the property. No heir had ever exercised the right.
2 After they were located, Charles Powers's heirs opposed the Butlers' action, claiming that their right under the deed should entitle them to half of any gas extracted from the shale (a mineral) beneath the Butlers' property.
3 The court dismissed the heirs' claim. The court relied on the precedent set by Dunham v. Kirkpatrick (1882) in the Pennsylvania Supreme Court. Under the 'Dunham Rule', a deed reserving 'minerals' does not include rights to oil or gas unless these terms are specifically mentioned.
4 Charles Powers's heirs appealed to a superior court, arguing that courts in other US states treated 'mineral' rights as including oil and gas. They also pointed to a 1983 Pennsylvania Supreme Court judgement in US Steel Corp v. Hoge, which found that whoever owned the coal owned the gas within it. The deed held by US Steel specified its rights to coal. The heirs believed that this judgement supported their claim: if they half-owned the minerals (shale) beneath the Butlers' property, they also half-owned the gas in it. The superior court ordered that the case return to the lower court for it to consider the heirs' new arguments.
5 The Butlers immediately appealed to the Pennsylvania Supreme Court against the superior court's decision. In 2013, the Supreme Court ruled in their favour by upholding the Dunham Rule. In the court's judgement, one judge wrote: 'I find the original rationale for the Dunham Rule to be cryptic, conclusory and highly debatable. Nevertheless, since Dunham has effectively served to establish a governing rule of property law in Pennsylvania for over a century, too many settled expectations rest upon it for the courts to upset it retroactively.'
John and Mary Butler sought to 'quiet' a right specified in their deed of land ownership (Box 1). By doing this they wanted to

'Who controls the past controls the future. Who controls the present controls the past.' George Orwell The quotation suggests that history

What is the primary purpose of a literacy test?

If a car travels 150 kilometers in 2 hours, what is its average speed in kilometers per hour?

What is the primary purpose of the Internet of Things (IoT)?

What is the primary purpose of digital literacy in today's society?

< n, m > represents nD + nm, where n and m can be integers and fractions and may be positive, negative or zero.
For example,
< 3, 2 > represents 3D + 6
< 1, -5 > represents D - 5
< 6, 1/3 > represents 6D + 2.
Note: The rules for multiplication are:
positive × positive = positive,
negative × positive = negative,
positive × negative = negative,
negative × negative = positive.
What does < 4, 7 > + < -6, 3 > represent?