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what is the sum of all three digit natural numbers that are multiples of 14, but not 21? What is a quick way of doing sums like these, as i cannot rely on intuition during timed exams

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    $\begingroup$ What do you mean by "cannot rely on intuition"? In a well constructed timed exam you have to rely on intuition to get everything right, because "well constructed" implies that it can distinguish between students who have developed a good intuition for the subject and those who just hammer formulas mindlessly. $\endgroup$ – hmakholm left over Monica Dec 8 '15 at 11:35
  • $\begingroup$ Ok thats not exactly what i meant, what i meant was i cannot rely on innovation, and the more i have sorted put the better it is $\endgroup$ – Atharva Dec 8 '15 at 12:58
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The three-digit numbers that are divisible by 14 are $$ 112, 126, \ldots, 994 $$ There are $\frac{994-112}{14}+1 = 64$ of them, so their sum is $$ 64\times\frac{112+994}2 $$

Compute the sum of the numbers that are multiples of 42 (the least common multiple of 14 and 21) in the same way, and subtract them out.

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