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## If k is an integer

tagged by: Brent@GMATPrepNow

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GARGURI Just gettin' started!
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Sun Nov 06, 2011 11:36 pm
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.

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fueledGMAT Just gettin' started!
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Sat Dec 03, 2011 8:18 am
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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fueledGMAT Just gettin' started!
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Sat Dec 03, 2011 8:20 am
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

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Sharma_Gaurav Really wants to Beat The GMAT!
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Mon Jan 09, 2012 5:04 pm
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

happymanocha Rising GMAT Star
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Tue Jan 24, 2012 1:21 am
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

tisrar02 Really wants to Beat The GMAT!
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Mon Jun 18, 2012 5:46 am
(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

jcnasia Just gettin' started!
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Mon Jul 09, 2012 1:42 am
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.

Ganesh hatwar Rising GMAT Star
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Tue Jul 10, 2012 2:40 am
I thought it was 35^2 - 1/k and could not make any headway!

mba404 Just gettin' started!
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Thu Aug 16, 2012 6:59 am
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.

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hemant_rajput GMAT Destroyer!
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Thu Sep 06, 2012 2:14 am
I got it in 1 min. the ans is D.... Thank you for posting question

rajeshsinghgmat Really wants to Beat The GMAT!
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Fri Jan 25, 2013 1:13 am
The question is wrong.

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.

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Brent@GMATPrepNow GMAT Instructor
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Fri Jan 25, 2013 8:30 am
rajeshsinghgmat wrote:
The question is wrong.

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.

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

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sam2312 Just gettin' started!
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Tue Feb 26, 2013 1:26 am
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.

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Brent@GMATPrepNow GMAT Instructor
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Tue Feb 26, 2013 8:14 am
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

_________________
Brent Hanneson, BSc, BEd, MEd
- Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
- Use our video course in conjunction with
- Watch hours of free videos on DS, RC and AWA
- Our top 3 free videos:
1) The Double Matrix method
3) Managing your time on the GMAT

Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.

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