The search feature was put in for a reason.

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Hi Vijay,

This is a killer of a question but there are lots of discussions about it on the forum. The key to solving this question is knowing that the best way to prove that an expression is divisible by n is to demonstrate that the expression can be written as the product of n * integer. For example, 4!+6 is divisible by 3 because it can be written as the product of 3 * integer >> 4! + 6 = 3*(4*2*1 + 2)

On the other hand, one way to prove that an expression is not divisible by n is to demonstrate that the expression can be written as the sum of (multiple of n) + (non-multiple of n). For instance, 3p+7 cannot be a multiple of 3 (assuming p is an integer) because it equals a multiple of 3 + a non multiple of 3.

We can use this to prove that all numbers from 1 to 40 cannot be factors of h(100)+1.

The answer is E. You can see a detailed explanation and step-by-step video to solve this question at GMATPrep question 1282. To practice similar questions, set topic='Number Properties' and difficulty='700+' in the Drill Generator

Hope that helps,
-Patrick