What is the smallest number H which when increased by 5 is completely divisible by 8, 11 and 24?
Choose the correct choice from the following answers:
A) 264 B) 259 C) 269 D) 270 E) 282

Rationale: this question includes a number of great number property shortcuts that you can take advantage of : 1 ) the question asks for the smallest number that , when increased by 5 is divisible by 8 , 11 and 24 . since the answers are numbers , we can test the answers . 2 ) any number that is divisible by 24 is also divisible by 8 , so we really just need to consider the 11 and the 24 . 3 ) to be divisible by 24 , the end number must be even . since we ' re adding 5 to get to that end number , the starting number must be odd . the last shortcut allows us to eliminate answers a , d and e . between answers b and c , testing b first will prove that , when increased by 5 , the end sum is divisible by both 11 and 24 . final answer : b
Answer: B