, , and are positive integers. When is divided by , the remainder is . If when is divided by , the remainder is , which of the following must be true?
(A) is even
(B) is divisible by
(C) is divisible by
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Politician: Fewer people are entering the labor market now than previously. If the economy grows, the demand for motivated and educated people will far outstrip the supply. Some companies have already started to respond to this labor-market situation by finding better ways to keep their current employees. Their concern is a sure indicator that the economy is growing.
Which of the following is the best criticism of the politician’s reasoning?
(A) The fact that companies are making prudent preparations for a possible future development does not mean that this development is already taking place.
(B) The fact that some companies now try harder to keep their employees does not mean that they used to be indifferent to employee morale.
(C) The fact that demand will outstrip supply does not mean that there will be no supply at all.
(D) The fact that the number of new entrants into the labor market is declining does not mean that the number of new entrants is lower than it has ever been.
(E) The fact that current employees have become more valuable to some companies does not mean that those employees will do their jobs better than they used to.
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