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# Some people form a joint account for one year with the condi

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Manager
Joined: 18 Dec 2012
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Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32
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WE: Manufacturing and Production (Manufacturing)
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Some people form a joint account for one year with the condi [#permalink]

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03 Sep 2013, 07:03
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65% (hard)

Question Stats:

60% (04:38) correct 40% (03:11) wrong based on 91 sessions

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Some people form a joint account for one year with the condition that every month each member deposits an amount equal to the number of members in the account in that month. Also, the person who withdraws from the account before the end of the year get his/her amount at the end of the year. After 6 months, 1/4th of the people withdraw and 1/3rd of the remaining withdraw after 3 months. At the end of the year there is an amount of Rs. 4860 in the account before paying of the withdrawn amounts. Find out the number of people in the beginning of the year.

A. 12
B. 24
C. 36
D. 48
E. 60
[Reveal] Spoiler: OA

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Last edited by Bunuel on 03 Sep 2013, 07:08, edited 1 time in total.
Renamed the topic and edited the tags.
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Joined: 04 Aug 2013
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Re: Some people form a joint account for one year with the condi [#permalink]

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03 Sep 2013, 17:41
Qoofi wrote:
Some people form a joint account for one year with the condition that every month each member deposits an amount equal to the number of members in the account in that month. Also, the person who withdraws from the account before the end of the year get his/her amount at the end of the year. After 6 months, 1/4th of the people withdraw and 1/3rd of the remaining withdraw after 3 months. At the end of the year there is an amount of Rs. 4860 in the account before paying of the withdrawn amounts. Find out the number of people in the beginning of the year.

A. 12
B. 24
C. 36
D. 48
E. 60

Need the solution, cant reach to B as the solution
Manager
Joined: 06 Jul 2013
Posts: 116
GMAT 1: 620 Q48 V28
GMAT 2: 700 Q50 V33
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Kudos [?]: 22 [1] , given: 42

Re: Some people form a joint account for one year with the condi [#permalink]

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03 Sep 2013, 19:42
1
KUDOS
N people in the start.

first 6 months there would 6.N.N money deposited.
1/4 members are gone so 3/4 left
Then next 3 month 3.3N/4.3N/4

then 1/3 of remaining gone = 3N/4*2/3 = N/2
so money deposited 3.N/2.N/2

total = 6N^2+27/16N^2+3/4N^2 = 4860
solve for N = 24
Manager
Joined: 18 Dec 2012
Posts: 96
Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32
GMAT 2: 530 Q37 V25
GPA: 3.32
WE: Manufacturing and Production (Manufacturing)
Followers: 1

Kudos [?]: 30 [1] , given: 34

Re: Some people form a joint account for one year with the condi [#permalink]

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03 Sep 2013, 23:30
1
KUDOS
Let x be the number of people in the beginning.
Amount deposited for 6 months = 6*x*x = 6x^2

Number of people for the next 3 months = x -x/4 = 3x/4

Amount deposited for the next 3 months = 3 * (3x/4)^2

Number of people for the last 3 months = 3x/4 - (1/3 * 3x/4) = x/2

Amount deposited for the last 3 months = 3* (x/2)^2

Total amount = 6x^2 + 27x^2/16 + 3x^2/4 = 4860

x= 24 (option B)
_________________

I'm telling this because you don't get it. You think you get it which is not the same as actually getting it. Get it?

GMAT Club Legend
Joined: 09 Sep 2013
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Re: Some people form a joint account for one year with the condi [#permalink]

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08 Nov 2014, 08:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Some people form a joint account for one year with the condi [#permalink]

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14 Apr 2015, 04:37
Qoofi wrote:
Let x be the number of people in the beginning.
Amount deposited for 6 months = 6*x*x = 6x^2

Number of people for the next 3 months = x -x/4 = 3x/4

Amount deposited for the next 3 months = 3 * (3x/4)^2

Number of people for the last 3 months = 3x/4 - (1/3 * 3x/4) = x/2

Amount deposited for the last 3 months = 3* (x/2)^2

Total amount = 6x^2 + 27x^2/16 + 3x^2/4 = 4860

x= 24 (option B)

Why are we multiplying things two times(^2)?
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Re: Some people form a joint account for one year with the condi [#permalink]

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15 Apr 2015, 00:00
ssriva2 wrote:
Why are we multiplying things two times(^2)?

Because at the end of each month, each person deposits an amount equal to the number of people. For example, if there are 24 people, each would deposit $24 (or whatever currency the question is asking), meaning a total of 24*24 dollars is deposited. So if you start out with $$n$$ people: > After month 1: ($$n$$ x $$n$$) deposited = $$n^2$$ > After month 2: +$$n^2$$ deposited > After month 3: +$$n^2$$ deposited > After month 4: +$$n^2$$ deposited > After month 5: +$$n^2$$ deposited > After month 6: +$$n^2$$ deposited ** Here, 1/4 of people leave and you are left with $$\frac{3}{4}n$$ people, each depositing $$\frac{3}{4}n$$ dollars ** > After month 7: +($$\frac{3}{4}n$$) x ($$\frac{3}{4}n$$) deposited = $$\frac{9}{16}n^2$$ > After month 8: +$$\frac{9}{16}n^2$$ deposited > After month 9: +$$\frac{9}{16}n^2$$ deposited ** Here, 1/3 of the remaining people leave and you are left with $$(\frac{2}{3})(\frac{3}{4}n)$$ people, each depositing $$(\frac{2}{3})(\frac{3}{4}n)$$ dollars ** > After month 10: + ($$\frac{2}{3})(\frac{3}{4}n$$) x $$(\frac{2}{3})(\frac{3}{4}n)$$ = $$\frac{1}{4}n^2$$ > After month 11: +$$\frac{1}{4}n^2$$ > After month 12: +$$\frac{1}{4}n^2$$ Put it all together and for the 12-month period, you get: $$6(n^2) + 3(\frac{9}{16}n^2) + 3 (\frac{1}{4})n^2 = 4860$$ Finally, solve to get: $$n=24$$ Answer: B GMAT Club Legend Joined: 09 Sep 2013 Posts: 13461 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: Some people form a joint account for one year with the condi [#permalink] ### Show Tags 22 Jun 2016, 10:39 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Some people form a joint account for one year with the condi [#permalink] 22 Jun 2016, 10:39 Similar topics Replies Last post Similar Topics: 12 This year, x people won an Olympic medal for water competitions. One 7 16 Sep 2015, 06:16 5 In a joint family there are 3 couples. The ages (all in years) of the 3 06 Nov 2014, 19:56 20 At the end of year X, automobile installment credit accounte 7 11 Nov 2013, 12:31 1 John deposits$5000 in a savings account for 5 years 3 12 Jan 2012, 17:41
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