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19 Jun 2022, 08:43
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A sequence S consists of 7 consecutive multiples of a positive integer in increasing sequence. If all the numbers in S are positive, then is the last term of S a multiple of 3?
1) The arithmetic mean of S is a multiple of 3
2) The first term of S is a multiple of 3
1) The arithmetic mean of S is a multiple of 3
2) The first term of S is a multiple of 3
SandeepReddy26
24 Jun 2022, 06:04
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Solution please ThatDudeKnows
24 Jun 2022, 06:31
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figjam786
Is the 7th term a multiple of 3?
Looking at statement (1) alone, since the sequence is evenly spaced and we have an odd number of terms, the average will be equal to the middle term (if you don't know this by rule or intuitively, you could derive it by realizing that the average of terms 1 and 7 will be equal to the average of terms 2 and 6, which will be equal to the average of terms 3 and 5, which will be equal to term 4). That means term 4 is the average, and we are told that the average is a multiple of 3. Therefore, term 4 is a multiple of 3. To get from term 4 to term 7, we are adding 3*something. Since the things that we are adding are both divisible by 3, the sum will be divisible by 3. Does statement (1) alone give us enough information to answer the question? Yes. AD.
Looking at statement (2) alone, the term 1 is a multiple of 3 and then we are adding 6*something in order get to term 7. Since the things that we are adding are both divisible by 3, the sum will be divisible by 3. Does statement (2) alone give us enough information to answer the question? Yes. D.
