find the least multiple of 23 , which when divided by 1821 and 24 leaves remainders 710 and 13 respectively . Choose the correct answer.
A) 3002 B) 3013 C) 3024 D) 3036 E) none of these

Rationale: solution here ( 18 - 7 ) = 11 , ( 21 - 10 ) = 11 and ( 24 - 13 ) = 11 . l . c . m . of 1821 and 24 is 504 . let required number be 504 k - 11 . least value of k for which ( 504 k - 11 ) is divisible 23 is k = 6 . so , required number = 504 × 6 - 11 = 3024 - 11 = 3013 . answer b
Answer: B