If k is an integer

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Wed May 19, 2010 1:17 am

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

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Source: Beat The GMAT — Problem Solving | Wed May 19, 2010 1:17 am

rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Wed May 19, 2010 1:26 am

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 ?

"Know thyself" and "Nothing in excess"

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Wed May 19, 2010 1:34 am

Given expression can be written as (35^2 - 1^2)/k = (35 - 1)(35 + 1)/k = (34)(36)/k
(34)(36)/k = (2^3)(3^2)(17)/k
From the given answer choices, k = 8, 9, 12, 17 will give (2^3)(3^2)(17)/k as an integer.
But k = 16 does not give an integer.

The correct answer is (D).

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Wed May 19, 2010 1:40 am

Today is the day for making silly mistakes .

@Rahul you are right answer should be D .

"Know thyself" and "Nothing in excess"

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Mogorosi: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Nov 21, 2010 1:38 am; Location: Johannesburg; Thanked: 3 times; GMAT Score:550

by Mogorosi » Fri Nov 26, 2010 6:11 am

Hello guys,

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

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Fri Nov 26, 2010 6:34 am

The latter

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rishab1988: Master | Next Rank: 500 Posts; Posts: 332; Joined: Tue Feb 09, 2010 3:50 pmFollowed by: 7 members; Thanked: 41 times; GMAT Score:720

by rishab1988 » Fri Nov 26, 2010 7:06 am

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.

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Mogorosi: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Nov 21, 2010 1:38 am; Location: Johannesburg; Thanked: 3 times; GMAT Score:550

by Mogorosi » Fri Nov 26, 2010 3:28 pm

kevincanspain wrote:The latter

Ok, I solved a wrong problem - the former!

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sumit.sinha: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Sat Aug 21, 2010 8:18 am; Location: India; Thanked: 5 times

by sumit.sinha » Thu Dec 02, 2010 9:45 am

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.

Cheers,
Sumit

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blaster: Master | Next Rank: 500 Posts; Posts: 233; Joined: Mon Jun 09, 2008 1:30 am; Thanked: 5 times

by blaster » Thu Dec 02, 2010 10:23 am

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

what is the source, by the way?

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anirudhbhalotia: Master | Next Rank: 500 Posts; Posts: 123; Joined: Tue Nov 23, 2010 7:18 pmFollowed by: 4 members; Location: Mumbai, India; Thanked: 5 times

by anirudhbhalotia » Mon Dec 13, 2010 1:12 am

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!

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pmFollowed by: 1 member; Thanked: 14 times

by frank1 » Mon Dec 13, 2010 8:05 am

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

GMAT score is equally counted as your GPA and 78 clicks can change you life.

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Taran: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Fri Oct 01, 2010 7:34 am; Location: Pune, India; Thanked: 1 times; GMAT Score:680

by Taran » Fri Dec 17, 2010 5:59 am

@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...

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ajayd: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Dec 15, 2010 8:07 am; Thanked: 1 times; GMAT Score:740

by ajayd » Fri Dec 17, 2010 6:45 am

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

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tomada: Master | Next Rank: 500 Posts; Posts: 406; Joined: Mon Jan 25, 2010 11:36 amFollowed by: 4 members; Location: Syracuse, NY; Thanked: 23 times; GMAT Score:740

by tomada » Tue Jan 04, 2011 7:57 am

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

I'm really old, but I'll never be too old to become more educated.

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