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Re: Are you ready for GMAT? then try this [#permalink] New post 03 May 2010, 14:37
I am seriously stuck with the following one:

Question (4) page 23:

How many positive integers less than 10,000 ae there in which the sum of the digits equalis 5?

A) 31
B) 51
C) 56
D) 62
E) 93

Official answer (C) = 56

couldnt find a way to solve this one so went ahead and listed all possible options (yes there are 56 answers!!!) but any1 who can provide the proper solution please do so !
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Re: Are you ready for GMAT? then try this [#permalink] New post 03 May 2010, 15:01
Expert's post
zisis wrote:
I am seriously stuck with the following one:

Question (4) page 23:

How many positive integers less than 10,000 ae there in which the sum of the digits equalis 5?

A) 31
B) 51
C) 56
D) 62
E) 93

Official answer (C) = 56

couldnt find a way to solve this one so went ahead and listed all possible options (yes there are 56 answers!!!) but any1 who can provide the proper solution please do so !


Discussed here: integers-less-than-85291.html
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Re: Are you ready for GMAT? then try this [#permalink] New post 05 May 2010, 07:04
anyone get this one? I know i'm missing something very silly here, it's just not clicking, please help me out.

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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Re: Are you ready for GMAT? then try this [#permalink] New post 05 May 2010, 07:20
Expert's post
firang wrote:
anyone get this one? I know i'm missing something very silly here, it's just not clicking, please help me out.

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


\frac{35^2-1}{k}=\frac{(35-1)(35+1)}{k}=\frac{34*36}{k}=\frac{2^3*3^2*17}{k}

From the answer choices only 16=2^4 is not a factor of numerator, hence in case k=16, \frac{35^2-1}{k} won't be an integer, hence k can not be 16.

Answer: D.


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Re: Are you ready for GMAT? then try this [#permalink] New post 05 May 2010, 07:23
Thanks for the quick response, stupid mistake on my part (a^2-b^2).

Also sorry if I violated any rule, but I thought we were discussing the pdf posted at the start of the thread that's why i posted the question here.
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Re: Are you ready for GMAT? then try this [#permalink] New post 05 May 2010, 07:26
firang wrote:
anyone get this one? I know i'm missing something very silly here, it's just not clicking, please help me out.

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

Let me try to explain how I would approach a problem like this. First take a quick look about the answer. What do you notice?
you have a prime number that is 17 and the other are multiples of 4 or 3.
Then I did 35*35 - 1 = 1224
First, I find out if the number is divisible by 17. Because if not you have your answer here.
1224/ 17 = 72
cross out option e
now you have to check with of the answer is multiple of 72, that is easy
A and B are multiple
C too
so the answer must be D

Other option you can know that 1224 is multiple of 9 because the digits of the numbers is multiple of 9 and of course is multiple of 2. To be multiple of 4 the last digit must be multiple of 4 in this case 24 is multiple of 4. For eight the last 3 digits. (224/8 = 28)

for me the first way was really fast, but of course other approaches must be there
so I am open to suggestions!!
I hope it helps
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Re: Are you ready for GMAT? then try this [#permalink] New post 05 May 2010, 07:27
Bunuel wrote:
firang wrote:
anyone get this one? I know i'm missing something very silly here, it's just not clicking, please help me out.

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


\frac{35^2-1}{k}=\frac{(35-1)(35+1)}{k}=\frac{34*36}{k}=\frac{2^3*3^2*17}{k}

From the answer choices only 16=2^4 is not a factor of numerator, hence in case k=16, \frac{35^2-1}{k} won't be an integer, hence k can not be 16.

Answer: D.

As always, nice approach to the problem Bunuel
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Re: Are you ready for GMAT? then try this [#permalink] New post 05 May 2010, 09:46
Bunuel wrote:
firang wrote:
anyone get this one? I know i'm missing something very silly here, it's just not clicking, please help me out.

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


\frac{35^2-1}{k}=\frac{(35-1)(35+1)}{k}=\frac{34*36}{k}=\frac{2^3*3^2*17}{k}

From the answer choices only 16=2^4 is not a factor of numerator, hence in case k=16, \frac{35^2-1}{k} won't be an integer, hence k can not be 16.

Answer: D.


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Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
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No posting of PS/DS questions is allowed in the main Math forum.




RESPECT !!!

i did the following very similar to the above but mine was longer:
35*35 - 1 = 1224 then found the prime numbers of 1224 and realised that 16 (=2^4) is not part of 1224
but clearly the best way is Bunuel's ! kudos
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Re: Are you ready for GMAT? then try this [#permalink] New post 09 May 2010, 14:20
thanks for the material
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Re: Are you ready for GMAT? then try this [#permalink] New post 14 May 2011, 21:36
great work. +1.

does anyone have something similar for the verbal section?
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Re: Are you ready for GMAT? then try this [#permalink] New post 23 May 2011, 15:30
Ah geez, only got about half right... I guess I'm not as ready as I thought I would
Re: Are you ready for GMAT? then try this   [#permalink] 23 May 2011, 15:30
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