True Statements on Card

Here is a card with the four statements that you see, and no others. Assume that each statement on the card is either true or false; then find and identify each false statement. (Refer to them as a, b, c, d if you want, to speed things up.)

On this card exactly one statement is true.
On this card exactly two statements are true.
On this card exactly three statements are true.
On this card exactly four statements are true.

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Wind Farm

Denmark is a major manufacturer of energy-producing wind turbines. Suppose both the following statements are true:

1. Some wind turbines in Ohio are not from Denmark, but are American-built.
2. All of the wind turbines in Lorain County are indeed from Denmark.

From these two statements, which of the following can be concluded?

  1. Some American-built wind turbines are in Lorain County.
  2. All Lorain county wind turbines are not American-built.
  3. Some American-built wind turbines are not in Lorain County.
  4. No Lorain County wind turbine is American-built.
  5. Some wind turbines in Ohio, but not in Lorain County, were built in Denmark.

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Driving to Atlanta

Manzy’s car, that he had in the 1980’s, had a 24-gallon gas tank. When he started driving one morning with a full tank, heading for Atlanta, the odometer read 3208 miles. He drove for most of the day, having stopped at lunch to buy 5 gallons of gas. The gas gauge said exactly � of a tank at the point where the odometer read exactly 3668. He still had 130 miles of driving to do to get to Atlanta. Back then, gas cost only $1.09 per gallon, and he had only $2.00 left on him and no credit cards. Did he make it into the city? (Give all details.)

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