First, let's get a handle on the sequence by seeing what the first few term should be. If Sx=8x-6, then S1 = 2, and S2 = 10, and S3 = 18, and S4 = 26. So those are our first four terms: 2, 10, 18, 26.manik11 wrote:If each term in an infinite sequence is found by the equation Sx=8x-6, and S1=2 , is every term in the sequence divisible by y?
(1) y is an even integer.
(2) At least 2 of the first 4 terms in the sequence are divisible by y
OA : B
Source : Veritas Prep
Now statement 1 tells us that y is even. If y =2, then every terms is divisible by y and the answer to the question is YES. If y = 4, the terms above are not divisible by y, so the answer to the question is NO. Not sufficient.
Statement 2 tell us that at least 2 of the first four terms are divisible by y. So we can see that y could be 2, in which case, YES every term is divisible by y. The question, then, is whether there are any other possible values for y. Well, y could be 1, but that would still give us a YES, as every integer is divisible by 1. So the thing to see here is that the terms above don't share any other factors:
Factors of 2: 1, 2
Factors of 10: 1, 2, 5, 10
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 26: 1, 2, 13, 26
Because y must be 1 or 2, and both 1 and 2 yield an answer of YES, this statement alone is sufficient. And the answer is B.
