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# In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side

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Joined: 02 Sep 2009
Posts: 58103
In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side  [#permalink]

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15 Mar 2015, 23:22
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:40) correct 47% (02:46) wrong based on 48 sessions

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In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?

(A) 61
(B) 106
(C) 424
(D) 840
(E) 960

Kudos for a correct solution.

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Re: In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side  [#permalink]

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16 Mar 2015, 00:11
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Hi

Now here the language of the question is the key to the answer. It asks to find the no of different totals of the 4 rolled dices can be there.
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Re: In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side  [#permalink]

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16 Mar 2015, 22:48
1
Hi All,

As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:

1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.

With 4 dice, we could end up with any SUM between:

4 (if we rolled 1s on all 4 dice)

to

64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).

Thus, there are only 61 possible sums.

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Re: In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side  [#permalink]

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23 Mar 2015, 03:52
Bunuel wrote:
In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?

(A) 61
(B) 106
(C) 424
(D) 840
(E) 960

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This is not really a counting question, in that it doesn’t involves any of the standard counting techniques. We just have think about this logically. No matter what four dice we pick, the lowest roll we could get is a “1” on each of the four dice, for a total of 4. We could get any integer value from 4 up to the highest value. The highest value would occur if we picked the two 20-sided dice and two of the 12-sided dice, and got the highest value on each die: 20 + 20 + 12 + 12 = 64. We could get any integer from 4 to 64, inclusive. For this, we simply need inclusive counting. 64 – 4 + 1 = 61.

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Re: In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side  [#permalink]

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10 Aug 2018, 03:28
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: In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side   [#permalink] 10 Aug 2018, 03:28
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