SOLUTION: There is a number less than 4,000 that when divided by any number higher than 4 but lower than 10, it leaves a remainder of 3. What is the mystery number?

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Question 1074998: There is a number less than 4,000 that when divided by any number higher than 4 but lower than
10, it leaves a remainder of 3. What is the mystery number?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
My guess is: 2523
I picked my factors as:
+5%2A7%2A8%2A9++=+2520+
I left out +6+ because it is +2%2A3+=+6+,
and those factors are already included in
+2%2A4+=+8+ and +3%2A3+=+9+
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+2520%2F5+=+504+
+2520%2F6+=+420+
+2520%2F7+=+360+
+2520%2F8+=+315+
+2520%2F9+=+280+
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I want a remainder of +3+ after each
of these divisions, so +2520+%2B+3+=+2523+
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Definitely get another opinion on this!

Answer by ikleyn(52824) About Me  (Show Source):