Question 19This question is dependent on the understanding of the vocabulary in the question. The key vocabulary is: Integer = positive and negative whole numbers plus the number 0. Examples: -3, -2, -1, 0, 1, 2, 3
Divisor = number 1 is a divisor of number 2 if number 1 divides
into number 2 without a remainder. Prime = a number with exactly two different positive divisors 1 and itself. Examples: 2, 3, 5, 7, 11
The issue is whether one can determine if r is a prime number. Statement (1) by itself: We know that 5 is a positive integer and that each of 5 and t is positive. The relationship 5r = t be will satisfied whether r is or is not prime. Test it this way. 3 is a prime number. 5 times 3 = 15. 6 is not a prime number. 5 times 6 = 30. Since both 15 and 30 are positive integers, statement (1) does not allow one to determine whether r is a prime. This rules out choices (A) and (D). Statement (2) by itself: Remember that r divides evenly into t and that r and t are positive integers. The smallest integer that is greater than 1 is 2. It is possible for t to be an even integer. If t is an even integer then 2 is the smallest divisor of t. Since 2 is a prime number the question can be answered from statement (2) alone. Hence, the answer is (B).
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