Re: In a sequence of 13 consecutive integers, all of which are
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11 Feb 2019, 10:07
If there are exactly 3 multiples of 6 in a sequence of 13 consecutive integers, then the sequence must begin and end with a multiple of 6. So, the first number in the least possible sequence is the number 6. Because all of the integers in the sequence are less than 100, the first number in the greatest possible sequence is 84. Now, determine "What is needed". To count how many integers in the sequence are prime, the statements need to limit the possible sequences to either one sequence, or multiple sequences that contain the same number of prime numbers. Evaluate the statements one at a time.
Evaluate Statement (1). Because both of the multiples of 5 in the sequence are also multiples of either 2 or 3, there must be only two multiples of 5 in the sequence. Plug In values that satisfy this statement. If the sequence is 6,7,8,9,10,11,12,13,14,15,16,17,18, then there are 4 prime numbers: 7, 11, 13, and 17. However, if the sequence is 66,67,68,69,70,71,72,73,74,75,76,77,78, then there are 3 prime numbers: 67, 71, and 73. When different numbers that satisfy a statement yield different answers to the question, the statement is insufficient. So, write down BCE.
Now, evaluate Statement (2). Because only one of the two multiples of 7 in the sequence is not also a multiple of 2 or 3, one of the two multiples of 7 in the sequence is also a multiple of 2 or 3. Plug In values that satisfy this statement. If the sequence is 6,7,8,9,10,11,12,13,14,15,16,17,18, then there are 4 prime numbers: 7, 11, 13, and 17. However, if the sequence is 66,67,68,69,70,71,72,73,74,75,76,77,78, then there are 3 prime numbers: 67, 71, and 73. When different numbers that satisfy a statement yield different answers to the question, the statement is insufficient. Eliminate choice B.
Now evaluate both statements together. Reuse the numbers that were Plugged In for statements (1) and (2) that satisfy both statements. If the sequence is 6,7,8,9,10,11,12,13,14,15,16,17,18, then there are 4 prime numbers. However, if the sequence is 66,67,68,69,70,71,72,73,74,75,76,77,78, then there are 3 prime numbers. When different numbers that satisfy both statements yield different answers to the question, the statements together are insufficient. Eliminate choice C.
The correct answer is choice E.