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It must be solve as (35^2 - 1) because in the other form 35^2 - 1 there are many wrong answers so you have to assume the form.
35x35 -1/k >> 1125-1= 1124 , with this number you can't answer the question.

35^2 - 1 = 1225 - 1 = 1224/k

prime factorization for 1224 is 2*2*2*3*3*17

A: 8 = 2*2*2
B: 9 = 3*3
C: 12 = 2*2*3
D: 16 = No possible solution
E: 17 = 17

The only answer without the correct prime is D

Incidentally enough, for those who do not know the trick, there is a VERY easy way to solve for any 2 digit number that ends in five when squaring the number:

To solve for 35^2, simply take the number in the tens digit (in this case, 3), add 1 to that number (making it 4) and multiply it by the original number in the tens place (so 3*4 = 12). After that, simply add 25 to the end (so 35^2 = 3*4 = 12, add 25 to the end and you get 1225). This works for ALL 2 digit numbers that end in 5:

25^2 = 625 (2*3=6, add 25 to the end)
45^2 = 2025 (4*5=20, add 25 to the end)
55^2 = 3025 (5*6=30, add 25 to the end)
etc...

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"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." ~ Antoine de Saint-Exupery

Your math on 35*35 is off... see my post above

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"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." ~ Antoine de Saint-Exupery

i understood the problem as 35^2 -1/k and hence arrived at wrong answer,
But problem is (35^2 -1) / k . which is much more easier than what i assumed
then in that case D is the answer

IMO : D

This is how i solved it

(35^2 -1)/K = (5^2*7^2-1)/K = (25*49-1)/K = (24*49+48)=24*51

A - 24 is divided by 8
B - 9 is not divided by 24 and 51
C - 24 is divided by 12
D - 16 is not divisible by 24*51
E - 51 is divisible by 51

(35-1)(35+1)/k= 34*36/k

(2*17)(2*2*3*3)/k

8= 2*2*2= Divisible
9= 3*3= Divisible
12= 2*2*3
16= 2*2*2*2= one too many 2's so this is not divisible
17= 17= divisible

Thus, D would be the answer in my opinion

This question is written poorly. As written, k must equal 1 which isn't an answer. We'll assume the poster meant to write (35^2 - 1)/k

To solve this problem, we want to find possible factors of 35^2 - 1. These factors are the possible values for k.

(35^2 - 1) = (35^2 - 1^2) = (35-1)(35+1) = 34*36 = (2*17)(2*2*3*3) = 2^3 * 3^2 * 17

So factors: 8, 9, 12, and 17 are all possible.

16 = 2^4 which isn't a possible factor.
Answer is E.

I thought it was 35^2 - 1/k and could not make any headway!

I tried the question several ways. As there is no answer choice available for (35^2)-(1/K or 35^((2)-1/K) I had to form the question like ((35^2)-1)/K.
Answer: D (16)

The question is wrong.
It should read,

If k is an integer, and (35^2-1)/k is an integer, then k could be each of the following, EXCEPT

P is significant in PEMDAS.

Now C is the answer.

Same here.