Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Dec 2014, 00:00

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the positive integer n?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 23 Dec 2006
Posts: 136
Followers: 1

Kudos [?]: 9 [0], given: 0

What is the positive integer n? [#permalink] New post 16 Aug 2007, 16:31
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (02:13) correct 51% (01:39) wrong based on 63 sessions
What is the positive integer n?

(1) For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-positive-integer-n-1-for-every-positive-126636.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Aug 2012, 12:11, edited 1 time in total.
OA added.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 865
Followers: 12

Kudos [?]: 208 [0], given: 0

 [#permalink] New post 16 Aug 2007, 17:22
I don't think I understand statement 1 but I would be forced to guess C.

Statement two tells us that N is either 4 or 5. and since statement 1 mentions 16 I would guess that the two together would somehow tell us it's 4!

haha, sorry I have no idea. just spitting out my logic
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5081
Location: Singapore
Followers: 19

Kudos [?]: 165 [0], given: 0

 [#permalink] New post 16 Aug 2007, 19:28
St2:
n = 4 or 5. insufficient.

st1:
the product is divisible by 16. say the product is x, then we can write x/16 = 2/2^4. so as long as x has four 2's, we can cancel out 16. the statement says this works for every integer m, so let's say m=1. if m = 5, then x =720 which is divisible by 16. if m = 4, then x = 120, which is not divisible by 16. if m = 7, then x = 2520 which is also divisible by 16. Insufficient.

using st2 and st1, we know n is 5. Sufficient.

Ans C
Director
Director
User avatar
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 57 [0], given: 7

Re: DS: How Many m and n's? [#permalink] New post 16 Aug 2007, 20:07
sludge wrote:
What is the positive integer n?

(1) For every integer m, the product m (m + 1) (m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0


got E.

from 1: m can be any integer but n varies depending upon m till the expression [m(m + 1)(m + 2) ... (m + n)] is divisible by 16.

so if m = 1, n = 5.
if m = 2, n = 4
if m = 3, n = 5
if m = 4, n = 5
if m = 5, n = 4

so, m could be 4 or 5.

from 2: n = 4 or 5.

from 1 and 2 also n = 4 or 5.

so annswer should be E
Manager
Manager
User avatar
Joined: 14 May 2006
Posts: 202
Followers: 1

Kudos [?]: 10 [0], given: 0

 [#permalink] New post 17 Aug 2007, 01:41
Got E.

I used the same method as Fistail:

If m=1, then n > 5
If m=2, then n > 4
and so on...

So (1) is insufficient.

For (2), n = 4 or 5. So (2) is insufficient as well.

(1) and (2) doesn't provide if n is 4 or 5 so E.

Is there a way to do this problem faster?
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 139 [0], given: 0

Re: DS: How Many m and n's? [#permalink] New post 17 Aug 2007, 01:49
sludge wrote:
What is the positive integer n?

(1) For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.


(1) tells us that n is at least 5, as the product of 6 or more consecutive integers is always a multiple of 16. The product of fewer than 6 consecutive integers need not be a multiple of 16.
NOT SUFF
(2) n is either 4 or 5
NOT SUFF
(T) n=5
SUFF
Director
Director
User avatar
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 57 [0], given: 7

Re: DS: How Many m and n's? [#permalink] New post 17 Aug 2007, 06:03
kevincan wrote:
sludge wrote:
What is the positive integer n?

(1) For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.


(1) tells us that n is at least 5, as the product of 6 or more consecutive integers is always a multiple of 16. The product of fewer than 6 consecutive integers need not be a multiple of 16.
NOT SUFF
(2) n is either 4 or 5
NOT SUFF
(T) n=5
SUFF



if m=2, m(m+1)(m+2)(m+3)(m+4) =(2x3x4x5x6) is divided by 16.

so n here is 4.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 139 [0], given: 0

 [#permalink] New post 17 Aug 2007, 06:51
However, is m(m+1)(m+2)(m+3)(m+4) a multiple of 16 for every integer m?
Director
Director
User avatar
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 57 [0], given: 7

 [#permalink] New post 17 Aug 2007, 06:57
kevincan wrote:
However, is m(m+1)(m+2)(m+3)(m+4) a multiple of 16 for every integer m?


nope. in this case n = 4, in some other cases n=5 or could be more or less.

if m = 1, n = 5.
if m = 8, n = 3
if m = 15, n =2
if m = 16, n =1.

the divisibility of the expression m(m+1)(m+2)(m+3)(m+4) by depends upon n.

therefore it is E.

imo, this is really good question.
Intern
Intern
avatar
Joined: 06 Aug 2007
Posts: 46
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: DS: How Many m and n's? [#permalink] New post 17 Aug 2007, 08:04
sludge wrote:
What is the positive integer n?

(1) For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

I think it's 'A'. n=15 always holds good, it's not really asking for a minimum value of n.
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 120 [0], given: 0

Re: DS: How Many m and n's? [#permalink] New post 17 Aug 2007, 09:38
sludge wrote:
What is the positive integer n?

(1) For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.


C for me.
16= 2*2*2*2
(1) If we know that there are at least 4 even numbers, then you know that it will be divisible by 16. However, you don't have to have 4 even numbers because if m=2, then next even term is m=4. The next even term after that is m=6. This will only require 3 even terms to satisfy the equation; thus, if m is odd, n=6 will satisfy the equation. If m is even, n=4 will satisfy the equation. In sum, n=4 or n=6
INSUFFICIENT.

(2) n=5 or n=4. INSUFFICIENT.

Together, we know that n=4
SUFFICIENT
Manager
Manager
User avatar
Joined: 15 Aug 2007
Posts: 70
Followers: 2

Kudos [?]: 5 [0], given: 0

[#permalink] New post 17 Aug 2007, 09:46
Fistail wrote:
dahcrap wrote:
It is clearly C


how is that?

i wait for OA.


From 1st alone we cant say. n can has so many values depends on m.
From 2nd option we got n 4 and 5...

2nd is also insufficient...

When we put both value of n in 1st.It satisfied quation on diff value of m not every value of m.

We are trying only +ve value of m.. m can be -ve also.When we put m as -1,-2,-3,-4 and n as 4 or 5.we get the product m(m + 1)(m + 2) ... (m + n) =0 which is not divisible by 16.

Answer should be E....
1 KUDOS received
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 865
Followers: 12

Kudos [?]: 208 [1] , given: 0

 [#permalink] New post 17 Aug 2007, 09:46
1
This post received
KUDOS
Here's my attempt at it:

1.
Quote:
For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16


this doesn't tell you anything specific about n. plug in 1 for m (since 1 is simple and M can be any integer) and see what works.

1(2) = 2
1(2)(3) = 6
1(2)(3)(4) = 24
1(2)(3)(4)(5) = 120
1(2)(3)(4)(5)(6) = 720

720 is divisible by 16, which means n = 5 works. this is just one example of an N that works, so you can't be sure that 5 is it, but you can be sure that 1, 2, 3 and 4 do not work (since 2, 6, 24, 120 are not divisible by 16)

as you can see, this is the same as (n+1)! = 16n. We know that 5 works, but there are tons of other possibilities greater than 5 that could be divisible by 16. Since it's DS and not PS we don't need to find them, just know that they exist and that A is NOT SUFFICIENT.

2.
Quote:
(2) n^2 - 9n + 20 = 0


break this down:

(n-4)(n-5) = 0

this means that N is = to either 4 or 5. obviously this isn't sufficient on it's own since we get two possible answers. NOT SUFFICIENT

but put them together and see what happens!

we already know that 4 does not work from the first statement, but 5 does. this gives 5 as the only possible answer and we get C is SUFFICIENT.

now if you went through statement 1 without testing for possibilities you could see from statement 2 that the answer is 4 or 5. then just go back to statement one and plug in 4 and 5 and see if one of them works.

m = 1 n = 4

1(1+1)(1+2)(1+3)(1+4)
1(2)(3)(4)(5) = 120
120 is not divisible by 16.

m = 1 n = 5

1(1+1)(1+2)(1+3)(1+4)(1+5)
1(2)(3)(4)(5)(6) = 720
720/16 = 46

so using both statements we see that the only possible answer is 5. C is sufficient!
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 120 [0], given: 0

Re: DS: How Many m and n's? [#permalink] New post 17 Aug 2007, 09:47
kevincan wrote:
sludge wrote:
What is the positive integer n?

(1) For every integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n^2 - 9n + 20 = 0

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.


(1) tells us that n is at least 5, as the product of 6 or more consecutive integers is always a multiple of 16. The product of fewer than 6 consecutive integers need not be a multiple of 16.
NOT SUFF
(2) n is either 4 or 5
NOT SUFF
(T) n=5
SUFF


I got the same answer, but n can be less than 5 for (1). For example, say m=2 and n=4. You have: 2*3*4*5*6, which satisfy the multiplication.

In fact, if m is even, you only need n=4. This is true for all cases. Try it out.
Manager
Manager
User avatar
Joined: 15 Aug 2007
Posts: 70
Followers: 2

Kudos [?]: 5 [0], given: 0

m negative [#permalink] New post 17 Aug 2007, 10:00
Why are you guys not considering the vaule of m negative....

M is juss a interger.It can be negative and zero also

The integers (Latin, integer, literally, "untouched," whole, entire, i.e. a whole number) are the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 120 [0], given: 0

Re: m negative [#permalink] New post 17 Aug 2007, 10:01
chiya wrote:
Why are you guys not considering the vaule of m negative....

M is juss a interger.It can be negative and zero also

The integers (Latin, integer, literally, "untouched," whole, entire, i.e. a whole number) are the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.


I consider m negative and zero. I break it down to even and odd, which consider all.
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 865
Followers: 12

Kudos [?]: 208 [0], given: 0

Re: m negative [#permalink] New post 17 Aug 2007, 10:07
chiya wrote:
Why are you guys not considering the vaule of m negative....

M is juss a interger.It can be negative and zero also

The integers (Latin, integer, literally, "untouched," whole, entire, i.e. a whole number) are the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.


because the stem tells us that N is positive.
and Statement 1 tells us that "for every integer m, the product..."

so we're looking for a positive n and we can plug any integer we want into the equation. plugging in -1, -2, -3 etc will just give us 0 for the answer as long as n > m. -1(-1 +1) = -1(0), and so on

and since 0 is divisible by everything it will work for 16
Manager
Manager
User avatar
Joined: 15 Aug 2007
Posts: 70
Followers: 2

Kudos [?]: 5 [0], given: 0

Re: m negative [#permalink] New post 17 Aug 2007, 10:07
bkk145 wrote:
chiya wrote:
Why are you guys not considering the vaule of m negative....

M is juss a interger.It can be negative and zero also

The integers (Latin, integer, literally, "untouched," whole, entire, i.e. a whole number) are the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.


I consider m negative and zero. I break it down to even and odd, which consider all.


But when m = 0 the product m(m + 1)(m + 2) ... (m + n) =0 which is not divisible by 16.
Manager
Manager
User avatar
Joined: 08 Oct 2006
Posts: 215
Followers: 1

Kudos [?]: 5 [0], given: 0

 [#permalink] New post 17 Aug 2007, 11:12
I agree with Fistail here and my pick is E.
According to 1st statement M can be any integer thus there is no fiexed value for n.
from 2. n can be 4 or 5.

Thus it has to be E. Unless i am missing some logic in statement 1 but i cannot see any way where we can assign a fixed value for m or n.
I think this is one of 700+ questions where you tend to pick C because you know it is a high score question.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 139 [0], given: 0

 [#permalink] New post 17 Aug 2007, 12:24
excelgmat wrote:
I agree with Fistail here and my pick is E.
According to 1st statement M can be any integer thus there is no fiexed value for n.
from 2. n can be 4 or 5.

Thus it has to be E. Unless i am missing some logic in statement 1 but i cannot see any way where we can assign a fixed value for m or n.
I think this is one of 700+ questions where you tend to pick C because you know it is a high score question.


(1) For every integer m, m(m+1)...(m+n) is a multiple of 16 for EVERY integer m if and only if n>4. (1) tells us that n is at least 5. NOT SUFF
(2) n is either 4 or 5 NOT SUFF
(T) n=5 SUFF
  [#permalink] 17 Aug 2007, 12:24
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic What is the value of the positive integer n ? Bunuel 5 03 Jan 2014, 05:17
20 Experts publish their posts in the topic What is the positive integer n? enigma123 13 27 Jan 2012, 15:08
7 Experts publish their posts in the topic What is the positive integer n? enigma123 3 27 Jan 2012, 14:44
1 What is the value of positive integer n? Madelaine88 7 28 Feb 2011, 01:31
N is a positive integer, what is the probability that tweakxc03 1 20 Sep 2009, 14:14
Display posts from previous: Sort by

What is the positive integer n?

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 37 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.