Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT
Hopefully I can help someone understand this question better. Testing values is the wrong way to approach this problem. Not learning the fundamentals for an easy question will hurt you.
For this questions, let's simply test divisibility rules - that's all it's asking. But instead, let's not actually solve anything here. Let's just try to take it at face value and test divisibility of the
terms of the equation, not necessarily the difference of the equation.
Let's leave the terms separated as they are.
10^14 - 120
(A) 2
Is 10^14 divisible by 2? Yes, it's even
Is 120 divisible by 2? Yes, it's even
(B) 3
Is 10^14 divisible by 3? Hard to tell, let's not waste time here and move on
Is 120 divisible by 3? Yes (3 * 40)
(C) 4
Is 10^14 divisible by 4? Yes, 4 evenly goes into 100. (25 * 4)
Is 120 divisible by 4? Yes (4 * 30)
(D) 8
Is 10^14 divisible by 8? Yes, because it's divisible by both 2 and 4.
Is 120 divisible by 8? Yes (8 * 15)
(E) 10
Is 10^14 divisible by 10? Of course
Is 120 divisible by 10? Yes
We see that easily, 3 must be the answer