(A)  Derek is singing and Jenny has a headache.
(B)  Jenny has a headache but Derek is not necessarily singing.
(C)  Derek is singing, but Jenny does not necessarily have a headache.
(D)  Derek has been singing and Jenny is beginning to get a headache.
(E)  Derek is not singing.

ANSWER: E

EXPLANATION:

We're told that if Derek sings, then Jenny gets a headache and Karen groans. Then we're told that Karen is not groaning. Using the contra positive, we get the following logic: If Jenny doesn't have a headache and/or if Karen isn't groaning, then Derek must not be singing. So if Karen is not groaning, then there is no way that Derek is singing, and choice (E) is our answer.

2.   John will eat the apple if Danny does not cook.

Based only on the information above, which of the following must be true?

(A)  John will not eat the apple if Danny cooks.
(B)  If John did not eat the apple, Danny did cook.
(C)  If John eats the apple, then Danny did not cook.
(D)  If Danny does not cook, John will not eat the apple.
(E)  If John did not eat the apple, Danny did not cook.

ANSWER: B

EXPLANATION: The sentence can be rearranged to read: "If Danny does not cook, then John will eat the apple. Whenever a Logical Reasoning question gives you an "If...then"sentence, the only thing that must be true is called the "contra positive"—take the opposite of each half of the statement, and flip the two halves. Here, the contra positive is "If John did not eat the apple, then Danny did cook." Hence, choice (B) is the right answer.

3.   A jury reaches a verdict when all of its members have come to a unanimous agreement. In one recent well-publicized trial, the judge thought that the jury had reached a verdict. Eventually, it was learned that one juror had never been able to agree with the others. The proceeding was ultimately declared a mistrial by the judge.

(A)  The jury never actually reached a verdict.
(B)  The jury had reached a verdict but had been disrupted by a single juror.
(C)  There have been other trials in which the jury failed to reach a verdict.
(D)   Only trials in which the jury fails to reach a verdict are declared mistrials.
(E)  The judge's role is not as important as that of the individual jurors.

ANSWER: A

EXPLANATION: If one juror had never been able to agree with the others, then the members of the jury never came to a unanimous agreement; they never reached a verdict (A). (B) is wrong because it contradicts this idea. (C), (D), and )E) may all be true statements, but we have no way of knowing for sure from the information in the question stem.

4.   The maximum time a member is allowed to run on a treadmill at the gym is 30 minutes. Ben has been running on a treadmill for at least 45 minutes.

(A)  The time limit has been established to give every member a chance to run.
(B)  If Ben is not violating the gym rules, then he is not running at the gym
(C)  If Ben is running at the gym, he will have his membership revoked.
(D)   Ben will be getting off the treadmill as soon as possible.
(E)   Ben is not running on a treadmill at the gym

ANSWER: B

EXPLANATION: The trick here is to recognize that the second sentence does NOT say where Ben's treadmill is;it may or may not be at the gym. Only if the treadmill is at the gym is he violating the rules; in other words, if he is not violating the rules, he is not running at the gym (B). (E), the closest wrong answer, is out because Ben could be running at the gym and just flouting the rules.

(A)   Modern medicine is now capable of curing disease X.
(B)  Most people no longer die from disease X.
(C)  Disease X is more easily cured than other serious diseases.
(D)   Progress has been made in the treatment of disease X.
(E)   The worst outbreak of disease X was in the 1940s.

ANSWER: D

EXPLANATION: (D)This Verbal Deduction question revolves around an improvement in medicine. We're told that people diagnosed with disease X lived only six months to a year in the 1940s—whereas nowadays with treatment they can live five years or longer. (D) is the valid conclusion.

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