GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Nov 2019, 16:33

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.

Close

Request Expert Reply

Confirm Cancel

For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
G
Joined: 04 Sep 2017
Posts: 291
For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1  [#permalink]

Show Tags

New post 21 Sep 2019, 15:20
9
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (02:15) correct 54% (02:26) wrong based on 145 sessions

HideShow timer Statistics

For each positive integer k, let \(a_k = (1 + \frac{1}{k+1})\). Is the product \(a_1a_2 … a_n\) an integer?

(1) n + 1 is a multiple of 3.
(2) n is a multiple of 2.


DS59851.01
Intern
Intern
avatar
B
Joined: 04 Feb 2018
Posts: 44
Re: For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1  [#permalink]

Show Tags

New post 23 Sep 2019, 03:16
gmatt1476 wrote:
For each positive integer k, let \(a_k = (1 + \frac{1}{k+1})\). Is the product \(a_1a_2 … a_n\) an integer?

(1) n + 1 is a multiple of 3.
(2) n is a multiple of 2.


DS59851.01


The correct answer is B. The detailed working can be found in the attached document.
Attachments

My Solution.doc [40 KiB]
Downloaded 47 times

To download please login or register as a user

Intern
Intern
avatar
B
Joined: 04 Feb 2018
Posts: 44
Re: For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1  [#permalink]

Show Tags

New post 23 Sep 2019, 03:33
gmatt1476 wrote:
For each positive integer k, let \(a_k = (1 + \frac{1}{k+1})\). Is the product \(a_1a_2 … a_n\) an integer?

(1) n + 1 is a multiple of 3.
(2) n is a multiple of 2.


DS59851.01
coylahood wrote:
gmatt1476 wrote:
For each positive integer k, let \(a_k = (1 + \frac{1}{k+1})\). Is the product \(a_1a_2 … a_n\) an integer?

(1) n + 1 is a multiple of 3.
(2) n is a multiple of 2.


DS59851.01


The correct answer is B. The detailed working can be found in the attached document.


Sorry I realised a mistake with my detailed solution. I have uploaded the corrected version.
Attachments

Updated Solution.doc [41 KiB]
Downloaded 43 times

To download please login or register as a user

Manager
Manager
avatar
P
Joined: 01 Feb 2017
Posts: 244
Re: For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1  [#permalink]

Show Tags

New post 24 Sep 2019, 02:03
2
for n=1, a1= 3/2
for n=2, a2= 4/3
for n=3, a3= 5/4
for n=4, a4= 6/5

Testing products:
n=even, product is an integer (a1*a2= 2 , a1*a2*a3*a4= 3)
n=odd, product is a non-integer (a1*= 3/2 , a1*a2*a3= 5/2)

St1: n+1 as a multiple of can be either odd or even and hence n can be either as well. Insufficient

St2: n is even. Sufficient.

Ans B
VP
VP
User avatar
D
Joined: 19 Oct 2018
Posts: 1078
Location: India
Premium Member CAT Tests
Re: For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1  [#permalink]

Show Tags

New post 18 Oct 2019, 14:23
\(a_k = (1 + \frac{1}{k+1})\)
\(a_k = \frac{k+2}{k+1})\)

\(a_1a_2 … a_n\)= \(\frac{3}{2}*\frac{4}{3}*\frac{5}{4}*.........*\frac{n+2}{n+1}\)

\(a_1a_2 … a_n\)=\(\frac{n+2}{2}\)

\(a_1a_2 … a_n\)= \(\frac{n}{2}+1\)

\(\frac{n}{2}+1\) is an integer, if \(\frac{n}{2}\) is an integer


So basically question stem is whether n is a multiple of 2 or not.

Statement 1- n+1 is a multiple of 3

if n+1 is 3, n is 2 (even)
if n+1 is 6, n is 5 (odd)

Insufficient

Statement 2- n is multiple of 2 or even

Sufficient


gmatt1476 wrote:
For each positive integer k, let \(a_k = (1 + \frac{1}{k+1})\). Is the product \(a_1a_2 … a_n\) an integer?

(1) n + 1 is a multiple of 3.
(2) n is a multiple of 2.


DS59851.01
GMAT Club Bot
Re: For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1   [#permalink] 18 Oct 2019, 14:23
Display posts from previous: Sort by

For each positive integer k, let ak = (1 + 1/(k+1)). Is the product a1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne