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

It is currently 18 Dec 2014, 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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

1) Series of A(n) is such that A(n) = A(n-1) / n. How many

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 13 Jun 2006
Posts: 7
Followers: 0

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

1) Series of A(n) is such that A(n) = A(n-1) / n. How many [#permalink] New post 18 Mar 2007, 18:26
1) Series of A(n) is such that A(n) = A(n-1) / n. How many elements of the series are bigger than 1/2?

(1) A(2) = 5
(2) A(1) - A(2) = 5

2) On the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square. What is the distance between point (0, 0) and the closest vertex of the square?

a) 1/sqrt (2) b) 1 c) sqrt (2) d) sqrt (3) e) 2*sqrt (3)
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 450
Location: Earth
Followers: 2

Kudos [?]: 40 [0], given: 0

 [#permalink] New post 18 Mar 2007, 19:41
Q1. D
Stmt
Actually plugged in numbers
A2 = A1 / 2
so A1 = 10
A2 = 5
A3 = 5/3
A4 = 5/12 STOP. You can answer Question asked.

Stmt 2
A1 - A2 = 5 implies A1 - (A1/2) = 5
Simplifying A1 = 10
Now we can again do actual calculations and answer the question asked.
Intern
Intern
avatar
Joined: 13 Jun 2006
Posts: 7
Followers: 0

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

 [#permalink] New post 18 Mar 2007, 19:51
What about negative numbers? A(0), A(-1), etc.?
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 450
Location: Earth
Followers: 2

Kudos [?]: 40 [0], given: 0

 [#permalink] New post 18 Mar 2007, 20:11
I clearly assumed n > 0.
But thinking about it..
I would say...n here needs to be greater than 0.
Because otherwise the whole series is undefined as a(0) is always undefined.
Which means question is ambiguous...

I would hate to see answer E here.
Whats OA?

I am working on your second questions...not quite hitting the right approach.
Intern
Intern
avatar
Joined: 13 Jun 2006
Posts: 7
Followers: 0

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

 [#permalink] New post 18 Mar 2007, 20:17
The OA is D but the question did not mention that N > 0, hence my confusion.
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 450
Location: Earth
Followers: 2

Kudos [?]: 40 [0], given: 0

 [#permalink] New post 18 Mar 2007, 21:05
Yes it is confusing.
Whats the source of this question? usually official questions are not ambiguous.
Director
Director
User avatar
Joined: 13 Dec 2006
Posts: 521
Location: Indonesia
Followers: 6

Kudos [?]: 99 [0], given: 0

 [#permalink] New post 18 Mar 2007, 22:09
Either answer should be E or question shoud say only positive integers.

As from the calculation proposed by Kyatin

A(1) = A(1-1)/1 or A(1) = A(0) = 10...

also A(0) = A(-1)/0 or A(0) = infinity

A(0) cannot have two different values hence its insufficient.

regards,

Amardeep
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1808
Followers: 8

Kudos [?]: 94 [0], given: 0

 [#permalink] New post 19 Mar 2007, 02:52
Well.... By convention, we consider a sequence with positive integers.... I would like to say that (D) is justified here :)... Otherwise, we could even consider real numbers.... A(-sqrt(2)) = A(-sqrt(2)-1) / (-sqrt(2))... Makes not so much sense :)

a(-30) or a(-1) sounds like non sense, mathematically speaking :)... Generally, we went to know from a sequence what happens if n tends to be infinite : convergent or divergent :)

Also, as the problem sets a(n) = a(n-1)/n, we cannot have n=0 because the equation simply exists and is definied :)... But, we can have an admitted starting value A(0) for a sequence that serve to calculate the other terms. :)

All to say that we should consider n>0 and A(1) = A(0) a valid element :)
Director
Director
User avatar
Joined: 13 Dec 2006
Posts: 521
Location: Indonesia
Followers: 6

Kudos [?]: 99 [0], given: 0

 [#permalink] New post 19 Mar 2007, 07:02
Good insight fig,

Well its clearly written in GMAT quant section that all the numbers consider are real... though it can be negative integers as well, A(-1) which leads to A(0) = infinity doesnt make sense.

Also, we should understand that GMAT checks for aptitude i.e. avg maths which everybody should know... One shouldnt be Maths honors to solve these tricky but standard formula based probs.

regards,

Amardeep
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1808
Followers: 8

Kudos [?]: 94 [0], given: 0

 [#permalink] New post 19 Mar 2007, 11:36
Amardeep Sharma wrote:
Good insight fig,

Well its clearly written in GMAT quant section that all the numbers consider are real... though it can be negative integers as well, A(-1) which leads to A(0) = infinity doesnt make sense.

Also, we should understand that GMAT checks for aptitude i.e. avg maths which everybody should know... One shouldnt be Maths honors to solve these tricky but standard formula based probs.

regards,

Amardeep


More about it here: http://en.wikipedia.org/wiki/Sequence.... I do agree that one could not know every mathematical term used but ok... Once one of these terms is used, it conveys a certain meaining that we cannot avoid :)... Here, "serie" implies n >= 0 :)

Hope that helps :)

I speak in terms of pure mathematical logic here :)

Also, notice that the GMAT would give the exact domain of definition for n :)... That is, in a sens, missing in the quesiton to be a "whole" GMAT one :)
Director
Director
User avatar
Joined: 19 Mar 2007
Posts: 524
Followers: 2

Kudos [?]: 6 [0], given: 0

 [#permalink] New post 21 Mar 2007, 04:54
What is the answer to the following question?

**********************
1/(2 – sqrt(3)) = ?

(a) sqrt(3) - 2
(b) 2 + sqrt(3)
(c) sqrt(2) + sqrt(3)
(d) 2 - sqrt(3)
(e) sqrt(3) + 4
**********************
Manager
Manager
User avatar
Joined: 22 Feb 2007
Posts: 165
Followers: 2

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

 [#permalink] New post 21 Mar 2007, 05:10
1/(2 – sqrt(3)) = ?

We have rationalize the denominator. Multiply both numerator and denominator by (2 + sqrt(3))

1/(2 – sqrt(3))

= (2 + sqrt(3))/[(2 + sqrt(3))*(2 – sqrt(3))]

The denominator is now of the form (a+b)*(a-b) = a^2-b^2

Hence

1/(2 – sqrt(3))

= (2 + sqrt(3))/[(2 + sqrt(3))*(2 – sqrt(3))]

= (2 + sqrt(3))/[2^2 -(sqrt(3))^2]

= (2 + sqrt(3))/[4-3]

= (2 + sqrt(3))

Hence B
Manager
Manager
avatar
Joined: 15 Dec 2005
Posts: 60
Followers: 1

Kudos [?]: 2 [0], given: 0

 [#permalink] New post 21 Mar 2007, 08:00
...In the term a(n)...n represents the number of the term ..a sequence will have finite/infinite number of terms ..so when we are talking about the first term of the sequence ...n = 1....hence n cannot be zero ..(since always first term means n=1)....
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 450
Location: Earth
Followers: 2

Kudos [?]: 40 [0], given: 0

 [#permalink] New post 21 Mar 2007, 14:56
Answer to the second question of the post http://www.gmatclub.com/phpbb/viewtopic.php?t=43543
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2007
Posts: 257
Followers: 1

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

 [#permalink] New post 22 Mar 2007, 22:08
kyatin wrote:
Q1. D
Stmt
Actually plugged in numbers
A2 = A1 / 2
so A1 = 10
A2 = 5
A3 = 5/3
A4 = 5/12 STOP. You can answer Question asked.

Stmt 2
A1 - A2 = 5 implies A1 - (A1/2) = 5
Simplifying A1 = 10
Now we can again do actual calculations and answer the question asked.


Kyatin, could you please explain it again? I am sorry I could not get it.

Thanks.
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 450
Location: Earth
Followers: 2

Kudos [?]: 40 [0], given: 0

 [#permalink] New post 22 Mar 2007, 22:27
Summer3

Which step did you not get?

Let me know and I can elaborate.
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2007
Posts: 257
Followers: 1

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

 [#permalink] New post 24 Mar 2007, 00:44
all of it :cry: :oops:
Director
Director
User avatar
Joined: 14 Jan 2007
Posts: 781
Followers: 2

Kudos [?]: 65 [0], given: 0

 [#permalink] New post 24 Mar 2007, 03:05
The answer to the second question - the distance between the origin and the nearest vertex of square is sqrt(2).

Solving the equations lead to the nearest vertex as (1,1).
Distance between (0,0) and (1,1) is sqrt(2).

Approach,
Let the nearest vertex is (x,y)
the length of the diagonal is = distance between (0,6) and (6,2) = sqrt(52). Hence the length of each side of the square = sqrt(26)
Now the distance between the each of the known vertices and the nearest vertex should be the length of a side. Equalise them will end up in the equation: 3x-2y =1
distance between (0,6) and (x,y) is sqrt(26), solving this y = 1 or 7. Putting the values of y in 3x-2y =1 , possible values of x are 1, 5.
Hence the nearest vertex is (1,1).
distance between (0,0) and (1,1) is sqrt(2).


Can somebody suggests me the quicker approach.
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1808
Followers: 8

Kudos [?]: 94 [0], given: 0

 [#permalink] New post 24 Mar 2007, 04:29
vshaunak@gmail.com wrote:
The answer to the second question - the distance between the origin and the nearest vertex of square is sqrt(2).

Solving the equations lead to the nearest vertex as (1,1).
Distance between (0,0) and (1,1) is sqrt(2).

Approach,
Let the nearest vertex is (x,y)
the length of the diagonal is = distance between (0,6) and (6,2) = sqrt(52). Hence the length of each side of the square = sqrt(26)
Now the distance between the each of the known vertices and the nearest vertex should be the length of a side. Equalise them will end up in the equation: 3x-2y =1
distance between (0,6) and (x,y) is sqrt(26), solving this y = 1 or 7. Putting the values of y in 3x-2y =1 , possible values of x are 1, 5.
Hence the nearest vertex is (1,1).
distance between (0,0) and (1,1) is sqrt(2).


Can somebody suggests me the quicker approach.


If u are fine with vectors :)... Have a look at my post : http://www.gmatclub.com/phpbb/viewtopic.php?t=43543
  [#permalink] 24 Mar 2007, 04:29
    Similar topics Author Replies Last post
Similar
Topics:
A geometric sequence 1, 1/2 an is such that an=1/2*a(n-1), arjtryarjtry 2 29 Aug 2008, 17:51
2 Series of A(n) is such that A(n) = A(n-1) / n. How many bmwhype2 5 25 Jan 2008, 08:43
Consider the series : a(1), a(2), ....a(15). a(n) = a(n-1) + ikaytas 5 08 Jun 2006, 09:23
A sequence is such that An=(1/n)- . What is the sum of the getzgetzu 5 23 Nov 2005, 22:25
A0=1, A1=2. A(n+1)=3*(An - 1)*A(n-1). A5= pb_india 4 18 May 2005, 08:55
Display posts from previous: Sort by

1) Series of A(n) is such that A(n) = A(n-1) / n. How many

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.