• Question #1: If a, b and c are consecutive integers, a < b < c, and a + b + c = 96, what is the value of b?

  (a) 30 (b) 31 (c) 32 (d) 33 (e) 34

  • Solution: If a, b and c are consecutive numbers, b = a + 1 and c = a + 2. Then, a + (a + 1) + (a + 2) = 96, so 3·a + 3 = 96. a = (96 - 3)/3 = 31. b = a + 1 = 32.

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• Question #2: The price of wheat was $5/bushel on January 2007 and $9/bushel on January 2008. By what percentage did the price change?(a) 10% (b) 40% (c) 60% (d) 80% (e) 90%
  • Answer: The price change is [(Price₂₀₀₈ - Price₂₀₀₇)/Price₂₀₀₇]·100 = [(9 - 5)/5]·100 = (4/5)·100 = 80%

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• Question #3: In the figure below, angle AMB is 100^o, angle BMD is 40^o and angle CME is 60^o. What is the value of angle CMD? Figure not drawn to scale

  (a) 20^o (b) 30^o (c) 40^o (d) 50^o (e) 80^o

  • Answer: If angle AMB is 100^o, then angle BME is 180^o - 100^o = 80^o BMC + CMD = 40^o BMC + CMD + DME = 80^o If we subtract the 2 equations, DME = 40^o CMD + DME = 60^o BMC + CMD + DME = 80^o If we subtract the 2 equations, BMC = 20^o CMD = BME - BMC - DME = 80^o - 40^o - 20^o = 20^o

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