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

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Coins are to be put into 7 pockets so that each pocket [#permalink] New post 04 Mar 2012, 17:36
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A
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C
D
E

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75% (02:10) correct 25% (00:59) wrong based on 146 sessions
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
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Re: Coins are to be put into 7 pockets so that each pocket [#permalink] New post 04 Mar 2012, 17:48
Expert's post
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.

Answer: C.
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Re: Coins are to be put into 7 pockets so that each pocket [#permalink] New post 14 Jun 2013, 04:26
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Re: Coins are to be put into 7 pockets so that each pocket [#permalink] New post 08 Mar 2014, 19:00
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

Answer choice is (C). :-D
Re: Coins are to be put into 7 pockets so that each pocket   [#permalink] 08 Mar 2014, 19:00
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