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

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

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New post 15 Mar 2015, 22:22
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Question Stats:

53% (02:39) correct 47% (02:57) wrong based on 39 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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New post 15 Mar 2015, 23:11
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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.
please see the picture attached.
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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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New post 16 Mar 2015, 21:48
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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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New post 23 Mar 2015, 02:52
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.

Answer = (A)
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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Re: In a bag, there are five 6-sided dice (numbered 1 to 6), three 12-side &nbs [#permalink] 10 Aug 2018, 02:28
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