The sum of seven consecutive natural numbers is 1617. How many of these numbers are prime? · ABC26GN1635
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: S.S.C. 2006
The sum of seven consecutive natural numbers is 1617. How many of these numbers are prime?
Answer
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Explanation
Let the seven consecutive numbers be x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5) and (x + 6). Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 1617 ⇒ 7x + 21 = 1617 ⇒ 7x = 1596 ⇒ x = 228. Thus, the numbers are 228, 229, 230, 231, 232, 233 and 234. Of these numbers, only two numbers i.e. 229 and 233, are prime.
Explanation as extracted from the printed page; notation may be imperfect.
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