Problem Solving

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

(A) 8(B) 9(C) 12(D) 16(E) 17

Using the formula (x^2 - y^2 ) = (x+y)(x-y)

35^2 -1 = 35^2 - 1^2

We can write this as (35+1)(35-1)= 36 x 34

So the question becomes (36 x 34)/ k = int .

K is an integer .

so only number that can not divide completely is 8 .

[spoiler]Ans : A .[/spoiler]

whats the OA ?

Today is the day for making silly mistakes .


@Rahul you are right answer should be D .

Hello guys,

is this expression 35^2 - 1/k or (35^2 - 1)/k?

The latter

jeez.I got confused and thought it was (35)^(2-1/k). I thought man its a crazy problem.After seeing how you approached the problem,I was relieved that it was a normal problem.

kevincanspain wrote:The latter

Ok, I solved a wrong problem - the former!

Mogorosi wrote:Hello guys,

is this expression 35^2 - 1/k or (35^2 - 1)/k?

The expression is 35^2 - 1/k and NOT (35^2 - 1)/k. The actual question does not contain brackets.
So,
The Correct answer is (B) 9.

that would be useful if you place ques. as a screenshot .

what is the source, by the way?

sumit.sinha wrote:

Mogorosi wrote:Hello guys,

is this expression 35^2 - 1/k or (35^2 - 1)/k?

The expression is 35^2 - 1/k and NOT (35^2 - 1)/k. The actual question does not contain brackets.
So,
The Correct answer is (B) 9.

So if the answer is B, can we have the steps to solve it in the most easy and efficient way.

Thanks!

sumit.sinha wrote: The expression is 35^2 - 1/k and NOT (35^2 - 1)/k. The actual question does not contain brackets.
So,
The Correct answer is (B) 9.

You are right but from the left only....not actually
just kidding
see this
https://www.beatthegmat.com/35-2-1-k-is- ... 66222.html

any way if question was so i think it could be solved but may be options will have to be different then
but have not tried.

thanks

@Sumit: I agree that the problem should not be (35^2-1)/K, but rather be 35^2 - 1/k. Please help me derive the answer to the later. I tried to solve it this way:

35^2-1/K ---> ((5x5x7x7xK)-1) /K

Now i can see that 5x5x7x7xK is a multiple of K and is therefore always divisible by K. But when you subtract 1 from it, it cannot be divisible by K. Thus for any integer value of K, i dont see that the overall expression will lead to an Integer.

Please help me. I guess i'm missing something here !!!!!

Cheers...

the question is wrong. it should be (35^2-1)/k

Thank you, Ajayd, for confirming that I'm not losing my mind.

Somewhere in my distant past, I learned about "order of operations", such as multiplication and division taking precedence over addition and subtraction.

As expressed, 35^2 - 1/k = (35*35) - (1/k) = 1225 - (1/k)
If k=9, this would equal 1225 - 1/9 = 1224 + 8/9

ajayd wrote:the question is wrong. it should be (35^2-1)/k