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# M15-03

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Manager
Joined: 18 May 2012
Posts: 82

Kudos [?]: 89 [0], given: 21

Concentration: Finance, Marketing

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01 Jun 2013, 22:31
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The sequence A1 , A2 , ... is defined such that $$An+1 = \frac{An}{n+1}$$ for all n>1 . How many terms of the sequence is greater than $$\frac{1}{2}$$ ?

(1) A2 =5

(2) A1 −A2 =5

-Doubt --
1. We are specifically told tha the function is only valid for n>1, however the solution assumes that A2 = $$\frac{A1}{2}$$ then shouldnt we say for all n>=1 ?

Also shouldnt the question say-- how many terms are (not is)
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Kudos [?]: 89 [0], given: 21

Manager
Joined: 27 Feb 2012
Posts: 136

Kudos [?]: 63 [0], given: 22

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02 Jun 2013, 00:41
rohanGmat wrote:
The sequence A1 , A2 , ... is defined such that $$An+1 = \frac{An}{n+1}$$ for all n>1 . How many terms of the sequence is greater than $$\frac{1}{2}$$ ?

(1) A2 =5

(2) A1 −A2 =5

-Doubt --
1. We are specifically told tha the function is only valid for n>1, however the solution assumes that A2 = $$\frac{A1}{2}$$ then shouldnt we say for all n>=1 ?

Also shouldnt the question say-- how many terms are (not is)

I agree with you on this. There should be something said on no. of terms.
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Kudos [?]: 63 [0], given: 22

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128621 [0], given: 12180

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02 Jun 2013, 04:19
rohanGmat wrote:
The sequence A1 , A2 , ... is defined such that $$An+1 = \frac{An}{n+1}$$ for all n>1 . How many terms of the sequence is greater than $$\frac{1}{2}$$ ?

(1) A2 =5

(2) A1 −A2 =5

-Doubt --
1. We are specifically told tha the function is only valid for n>1, however the solution assumes that A2 = $$\frac{A1}{2}$$ then shouldnt we say for all n>=1 ?

Also shouldnt the question say-- how many terms are (not is)

The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1).

The sequence $$A_1$$, $$A_2$$, ... is defined such that $$A_{n+1}=\frac{A_{n}}{n+1}$$ for all n>1. How many terms of the sequence are greater than 1/2?

Basically we have a sequence of numbers which is defined with some formula. For example: $$A_{2}=\frac{A_{1}}{1+1}$$, $$A_{3}=\frac{A_{2}}{2+1}$$, $$A_{4}=\frac{A_{3}}{3+1}$$, ... The question asks: how many numbers from the sequence are greater than 1/2. Notice that if we knew ANY term of the sequence we would be able to get all the other terms/numbers and thus answer the question.

(1) $$A_2=5$$. As discussed above this statement is sufficient as we can write down all the terms. For example: $$A_{2}=\frac{A_{1}}{1+1}=5$$ --> $$A_1=10$$. $$A_{3}=\frac{A_{2}}{2+1}=\frac{5}{3}$$, and so on.

(2) $$A_1-A_2=5$$ --> $$A_1-\frac{A_{1}}{1+1}=5$$ --> we can solve for $$A_1$$ and thus will have the same case of knowing one term. Sufficient.

Hope it helps.
_________________

Kudos [?]: 128621 [0], given: 12180

Manager
Joined: 18 May 2012
Posts: 82

Kudos [?]: 89 [0], given: 21

Concentration: Finance, Marketing

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02 Jun 2013, 10:32
Bunuel wrote:
rohanGmat wrote:
The sequence A1 , A2 , ... is defined such that $$An+1 = \frac{An}{n+1}$$ for all n>1 . How many terms of the sequence is greater than $$\frac{1}{2}$$ ?

(1) A2 =5

(2) A1 −A2 =5

-Doubt --
1. We are specifically told tha the function is only valid for n>1, however the solution assumes that A2 = $$\frac{A1}{2}$$ then shouldnt we say for all n>=1 ?

Also shouldnt the question say-- how many terms are (not is)

The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1).

The sequence $$A_1$$, $$A_2$$, ... is defined such that $$A_{n+1}=\frac{A_{n}}{n+1}$$ for all n>1. How many terms of the sequence are greater than 1/2?

Basically we have a sequence of numbers which is defined with some formula. For example: $$A_{2}=\frac{A_{1}}{1+1}$$, $$A_{3}=\frac{A_{2}}{2+1}$$, $$A_{4}=\frac{A_{3}}{3+1}$$, ... The question asks: how many numbers from the sequence are greater than 1/2. Notice that if we knew ANY term of the sequence we would be able to get all the other terms/numbers and thus answer the question.

(1) $$A_2=5$$. As discussed above this statement is sufficient as we can write down all the terms. For example: $$A_{2}=\frac{A_{1}}{1+1}=5$$ --> $$A_1=10$$. $$A_{3}=\frac{A_{2}}{2+1}=\frac{5}{3}$$, and so on.

(2) $$A_1-A_2=5$$ --> $$A_1-\frac{A_{1}}{1+1}=5$$ --> we can solve for $$A_1$$ and thus will have the same case of knowing one term. Sufficient.

Hope it helps.

Hi Bunuel,
I am still not convinced. -- "The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1)" -- because in the function given you put n=1 to get A2 = A1/2 - yet in the next line we are told the function is only valid for all n>1.
Shouldnt it say n>=1
_________________

Focusing on apps..
|GMAT Debrief|TOEFL Debrief|

Kudos [?]: 89 [0], given: 21

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128621 [0], given: 12180

### Show Tags

04 Jun 2013, 07:26
rohanGmat wrote:
Bunuel wrote:
rohanGmat wrote:
The sequence A1 , A2 , ... is defined such that $$An+1 = \frac{An}{n+1}$$ for all n>1 . How many terms of the sequence is greater than $$\frac{1}{2}$$ ?

(1) A2 =5

(2) A1 −A2 =5

-Doubt --
1. We are specifically told tha the function is only valid for n>1, however the solution assumes that A2 = $$\frac{A1}{2}$$ then shouldnt we say for all n>=1 ?

Also shouldnt the question say-- how many terms are (not is)

The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1).

The sequence $$A_1$$, $$A_2$$, ... is defined such that $$A_{n+1}=\frac{A_{n}}{n+1}$$ for all n>1. How many terms of the sequence are greater than 1/2?

Basically we have a sequence of numbers which is defined with some formula. For example: $$A_{2}=\frac{A_{1}}{1+1}$$, $$A_{3}=\frac{A_{2}}{2+1}$$, $$A_{4}=\frac{A_{3}}{3+1}$$, ... The question asks: how many numbers from the sequence are greater than 1/2. Notice that if we knew ANY term of the sequence we would be able to get all the other terms/numbers and thus answer the question.

(1) $$A_2=5$$. As discussed above this statement is sufficient as we can write down all the terms. For example: $$A_{2}=\frac{A_{1}}{1+1}=5$$ --> $$A_1=10$$. $$A_{3}=\frac{A_{2}}{2+1}=\frac{5}{3}$$, and so on.

(2) $$A_1-A_2=5$$ --> $$A_1-\frac{A_{1}}{1+1}=5$$ --> we can solve for $$A_1$$ and thus will have the same case of knowing one term. Sufficient.

Hope it helps.

Hi Bunuel,
I am still not convinced. -- "The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1)" -- because in the function given you put n=1 to get A2 = A1/2 - yet in the next line we are told the function is only valid for all n>1.
Shouldnt it say n>=1

Edited the question:
Attachment:

M15-03.png [ 5.46 KiB | Viewed 898 times ]
Is it clearer now?
_________________

Kudos [?]: 128621 [0], given: 12180

Re: M15-03   [#permalink] 04 Jun 2013, 07:26
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# M15-03

Moderator: Bunuel

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