The infinite sequence a1, a2 ….aN is such that a1=45, a2= 49 and a(n) = a(n-2) + 7 for n > 2. Which of the following is a term of the sequence?
Ø 323
Ø 463
Ø 498
Ø 533
Ø 598
This was a very tricky question that I came across. Would appreciate if somebody can solve it and help me understand that solution?

Disclaimer: -
I do not know the source of this question, so please do not ask it from me. A friend of mine who just wrote his GMAT and got a cool 750 gave me the pdf files containing some challenging questions. I have the answers to these questions but not the official explanations.

We can write any of the elements of the series in the form of either:

a(x)=45+7(X) such as for a1, a3, a5 etc. or as;
a(x)=49+7(X) such as for a2, a4 etc;
here x goes from 0 to n

Now the thing is any number of the series from either 45 or 49 is subtracted should be divisible by 7. Let us look at each choice:

Ø 323--------Both (323-45) and (323-49) aren't divisible by 7
Ø 463--------Both not divisible by 7
Ø 498--------Both not divisible by 7
Ø 533--------Both not divisible by 7
Ø 598--------(598-45) is divisible by 7 so this could be the answer

Am I correct?

Absolutely, my friend...u r answer is correct and thanks for the fantastic explanation. Would appreciate if u can post answers to the other remainder theory question that i had posted.

The number in the series are of the following form

even numbers - div by 7

odd numbers - when divided by 7 remainder is 3

only E follows this patern.

Very good solution. Nice work.

In the future, per this forum's guidelines, please do not post questions unless you know their sources. Thank you for your understanding.

Rey