Problem Solving

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...

GARGURI wrote: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.

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

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

neoreaves wrote: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

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)

I got it in 1 min. the ans is D.... Thank you for posting question

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.

rajeshsinghgmat wrote: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.

You're absolutely right, rajeshsinghgmat. This is actually a pet peeve of mine.
Students often forget to add brackets (especially with rational expressions), so we get ambiguous posts like 3+x/y+z/y+2, which lead to many different interpretations.

Cheers,
Brent

vexy999 wrote:The question confused me. I thought it was 35^2 -(1/k) when in fact I should have been thinking (35^2-1)/k..Do the questions appear like this on GMAT?

Same here.

sam2312 wrote:

vexy999 wrote:The question confused me. I thought it was 35^2 -(1/k) when in fact I should have been thinking (35^2-1)/k..Do the questions appear like this on GMAT?

Same here.

Yes, questions like this do appear on the GMAT. However, they will be expressed to remove any ambiguity. The question here should look something like this:

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

Cheers,
Brent

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

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

Since (35^2-1)/k is an integer, then (35^2-1) =

35 = 7 * 10/2
So 35^2 - 1 = 49 * 100/4 - 1 = 4900/4 - 1 = 1225 - 1 = 1224 = 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

Answer D