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# M15-03

Author Message
Intern
Joined: 18 May 2012
Posts: 21
Concentration: Finance, Marketing
GMAT 1: 670 Q49 V32
GMAT 2: 750 Q50 V41
Followers: 2

Kudos [?]: 1 [0], given: 2

M15-03 [#permalink]  01 Jun 2013, 21:31
00:00

Difficulty:

5% (low)

Question Stats:

50% (01:01) correct 50% (00:52) wrong based on 4 sessions
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)
[Reveal] Spoiler: OA
Manager
Joined: 27 Feb 2012
Posts: 140
Followers: 1

Kudos [?]: 11 [0], given: 22

Re: M15-03 [#permalink]  01 Jun 2013, 23:41
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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Please +1 KUDO if my post helps. Thank you.

Math Expert
Joined: 02 Sep 2009
Posts: 16878
Followers: 2776

Kudos [?]: 17638 [0], given: 2233

Re: M15-03 [#permalink]  02 Jun 2013, 03:19
Expert's post
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.
_________________
Intern
Joined: 18 May 2012
Posts: 21
Concentration: Finance, Marketing
GMAT 1: 670 Q49 V32
GMAT 2: 750 Q50 V41
Followers: 2

Kudos [?]: 1 [0], given: 2

Re: M15-03 [#permalink]  02 Jun 2013, 09:32
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
Math Expert
Joined: 02 Sep 2009
Posts: 16878
Followers: 2776

Kudos [?]: 17638 [0], given: 2233

Re: M15-03 [#permalink]  04 Jun 2013, 06:26
Expert's post
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 249 times ]
Is it clearer now?
_________________
Re: M15-03   [#permalink] 04 Jun 2013, 06:26
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# M15-03

Moderators: Bunuel, WoundedTiger

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