Question: What is the postcode of a town in Cook County, New South Wales, that is situated approximately 100 km west of the Sydney central business district, and about 8 km east of Katoomba?

Context paragraphs:
Bell, New South Wales: Bell (postcode: 2786) is a small rural and residential village in the Blue Mountains region of New South Wales, Australia.  It is the north-westernmost village in the City of Blue Mountains, located approximately 125 km west of Sydney central business district by road or 137 km by rail, approximately 20 km east of Lithgow and 10 km north of Mount Victoria.  It is a locality on the junction of the Bells Line of Road, Chifley Road and the Darling Causeway, with an elevation of approximately 1100 m   .

Wentworth Falls, New South Wales: Wentworth Falls (postcode: 2782) is a town in the Blue Mountains region of New South Wales, situated approximately 100 km west of the Sydney central business district, and about 8 km east of Katoomba, Australia on the Great Western Highway, with a Wentworth Falls railway station on the Main Western line.  The town is at an elevation of 867 m   .  At the 2011 census , Wentworth Falls had a population of .

Jenolan Caves: The Jenolan Caves (Tharawal: Binoomea, Bindo, Binda) are limestone caves located within the Jenolan Karst Conservation Reserve in the Central Tablelands region, west of the Blue Mountains, in New South Wales, in eastern Australia.  The caves and 3083 ha reserve are situated approximately 175 km west of Sydney, 20 km east of Oberon and 30 km west of Katoomba.

Medlow Bath, New South Wales: Medlow Bath (postcode: 2780) is an Australian small town located near the highest point of the Blue Mountains, between Katoomba and Blackheath.  It has an approximate altitude of 1050 m   and is located approximately 115 km west-north-west of the Sydney central business district and 5 km north-west of Katoomba.  At the 2011 census, Medlow Bath had a population of 517 people.

Leura, New South Wales: Leura (postcode: 2780) is a suburb in the City of Blue Mountains local government area that is located 100 km west of the Sydney central business district in New South Wales, Australia.  It is one of the series of small towns stretched along the Main Western railway line and Great Western Highway that bisects the Blue Mountains National Park.  Leura is situated adjacent to Katoomba, the largest centre in the upper mountains, and the two towns merge along Leura's western edge.

Tank Stream: Tank Stream, a fresh water tributary of Sydney Cove, located in New South Wales, Australia, was the fresh water supply for the fledgling colony of New South Wales in the late 18th century.  Today it is little more than a storm water drain.  It originated from a swamp to the west of present-day Hyde Park and at high tide entered Sydney Cove at what is now the intersection of Bridge and Pitt Streets in the Sydney central business district.  The catchment was 65 ha , corresponding roughly the size of the Sydney central business district.

Dharug National Park: The Dharug National Park is a protected national park that is located in the Central Coast region of New South Wales, in eastern Australia.  The 14850 ha national park is situated approximately 58 km north of the Sydney central business district and 25 km west of Gosford .

Blue Mountains Botanic Garden: The Blue Mountains Botanic Garden is a 28 ha public botanic garden located approximately 100 km west of the Sydney central business district at Mount Tomah in the Blue Mountains, in New South Wales, Australia.  The garden is heritage-listed and is located on the boundary of the UNESCO World Heritage Site Greater Blue Mountains Area and can be accessed via the Bells Line of Road.

Cook County, New South Wales: Cook County was one of the original Nineteen Counties in New South Wales and is now one of the 141 Cadastral divisions of New South Wales.  It includes the area to the west of Sydney in the Blue Mountains, between the Colo River in the north, and the Coxs River in the south and west, encompassing Lithgow, Mount Victoria, Katoomba, Wentworth Falls, Lawson and most of the other towns in the Blue Mountains.  The Nepean River is the border to the east.  Before 1834, the area was part of the Westmoreland, Northumberland and Roxburgh counties.

Blackheath, New South Wales: Blackheath (postcode: 2785) is an Australian town located near the highest point of the Blue Mountains, between Katoomba and Mount Victoria in New South Wales.  The town's altitude is about 1065 m   and it is located about 120 km west north-west of the Sydney central business district, 11 km north-west of Katoomba, and about 30 km south-east of Lithgow

Supporting paragraphs: Cook County, New South Wales Wentworth Falls, New South Wales
Answer: 2782