Basic Mathematics

Reasoning Skills

Logic

         

Several friends are planning a road trip. If John goes on the road trip, then Kelly goes on the road trip. If Kelly does not go on the road trip, then Lawrence does not go on the road trip. Which of the following statements must be true?

(A)  \ \ If John goes on the road trip, then Lawrence goes on the road trip.
(B)  \ \ If John does not go on the road trip, then Kelly does not go on the road trip.
(C)  \ \ If John does not go on the road trip, then Lawrence goes on the road trip.
(D)  \ \ If Lawrence goes on the road trip, then John goes on the road trip.
(E)  \ \ If Lawrence goes on the road trip, then Kelly goes on the road trip.

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If Danny owns at least 44 bikes, then Edward owns 33 bikes. If Edward owns a bike, then Freddy owns 55 bikes. If Danny owns 55 bikes, which of the following statements must be true?

I.Edward owns at least one bike.II.Freddy owns at least one bike.III.Freddy does not own any bike.\begin{array}{r r l} &\text{I.} & \text{Edward owns at least one bike.}\\ &\text{II.} &\text{Freddy owns at least one bike.}\\ &\text{III.} & \text{Freddy does not own any bike.}\\ \end{array}

(A)  \ \ I only
(B)  \ \ II only
(C)  \ \ III only
(D)  \ \ I and II only
(E)  \ \ I and III only

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If Aria went to the school play, then Barney also went to the school play.
If Barney went to the school play, then Carie also went to the school play.
If Barney did NOT go to the school play, which of the following must be true?

I.Aria went to the school play.II.Carie went to the school play.III.Aria did not go to the school play.\begin{array}{r r l} &\text{I.} &\text{Aria went to the school play.}\\ &\text{II.} & \text{Carie went to the school play.}\\ &\text{III.} & \text{Aria did not go to the school play.}\\ \end{array}

(A)  \ \ I only
(B)  \ \ III only
(C)  \ \ I and II only
(D)  \ \ II and III only
(E)  \ \ None of the statements

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If John calls May in class, May looks back. If Matthew pricks John in class, John calls May. If John did NOT call May in class, which of the following statements must be true?

I.Matthew did not prick John.II.May did not look back.III.Matthew pricked John.\begin{array}{r r l} &\text{I.} &\text{Matthew did not prick John.}\\ &\text{II.} & \text{May did not look back.}\\ &\text{III.} & \text{Matthew pricked John.}\\ \end{array}

(A)  \ \ I only
(B)  \ \ III only
(C)  \ \ I and II only
(D)  \ \ II and III only
(E)  \ \ None of I, II or III

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The union of sets XX and YY is the set ZZ. Which of the following statements must be true?

I.If 5 is in X, then 5 is in Y.II.If 6 is in Y, then 6 is in Z.III.If 7 is in Z,then 7 is in X.\begin{array}{r r l} &\text{I.} & \text{If}\ 5\ \text{is in}\ X,\ \text{then}\ 5\ \text{is in}\ Y.\\ &\text{II.} & \text{If}\ 6\ \text{is in}\ Y,\ \text{then}\ 6\ \text{is in}\ Z.\\ &\text{III.} & \text{If}\ 7\ \text{is in}\ Z, \text{then}\ 7\ \text{is in}\ X.\\ \end{array}

(A)  \ \ I only
(B)  \ \ II only
(C)  \ \ III only
(D)  \ \ II and III only
(E)  \ \ I, II, and III

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