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# Coins are to be put into 7 pockets so that each pocket

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Senior Manager
Joined: 31 Oct 2011
Posts: 338

Kudos [?]: 1252 [0], given: 18

Coins are to be put into 7 pockets so that each pocket [#permalink]

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04 Mar 2012, 18:36
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Difficulty:

15% (low)

Question Stats:

75% (01:12) correct 25% (01:08) wrong based on 361 sessions

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Coins are to be put into 7 pockets so that each pocket contains at least one coin. At most 3 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?

A. 7
B. 13
C. 17
D. 22
E. 28
[Reveal] Spoiler: OA

Kudos [?]: 1252 [0], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132626 [0], given: 12326

Re: Coins are to be put into 7 pockets so that each pocket [#permalink]

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04 Mar 2012, 18:48
Expert's post
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eybrj2 wrote:
Coins are to be put into 7 pockets so that each pocket contains at least one coin. At most 3 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?

A. 7
B. 13
C. 17
D. 22
E. 28

Since at most 3 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;

Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);

Total: 1+1+1+2+3+4+5=17.

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Kudos [?]: 132626 [0], given: 12326

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132626 [1], given: 12326

Re: Coins are to be put into 7 pockets so that each pocket [#permalink]

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14 Jun 2013, 05:26
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Kudos [?]: 132626 [1], given: 12326

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Joined: 03 Aug 2012
Posts: 20

Kudos [?]: 14 [0], given: 8

Location: United States (OR)
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Re: Coins are to be put into 7 pockets so that each pocket [#permalink]

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08 Mar 2014, 20:00
Here's how my brain handled this one,

Based off the question we know three out of the seven pockets can contain the same number of coins, which we will want to hold to the minimal amount because we are looking for the least amount value. The remaining have to have individual values, which will just be increments of 1 because we are talking about coins so we have to speak in integers (and not fractions/decimals).

Step 1 --> Set up the equation, A + A + A + B + C + D + E + F + G = Total
Step 2 --> Plug in our numbers, 1 + 1 + 1 + 2 + 3 + 4 + 5 = Total --> 17 = Total

Kudos [?]: 14 [0], given: 8

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Re: Coins are to be put into 7 pockets so that each pocket [#permalink]

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05 May 2015, 07:58
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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Kudos [?]: 282 [0], given: 0

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Re: Coins are to be put into 7 pockets so that each pocket [#permalink]

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17 Nov 2016, 12:21
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.
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Re: Coins are to be put into 7 pockets so that each pocket [#permalink]

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18 Dec 2016, 17:19
Great Question.
Here is what i did in this question =>

Pocket 1=>1
Pocket 2=>1
Pocket 3=>1
Pocket 4=>2
Pocket 5=>3
Pocket 6=>4
Pocket 7=>5

Hence least coins needed = 1+1+1+2+3+4+5=> 17

Hence C

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Kudos [?]: 869 [0], given: 602

Re: Coins are to be put into 7 pockets so that each pocket   [#permalink] 18 Dec 2016, 17:19
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