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

Question

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.

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

iamdp · Accepted Answer

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.

EMPOWERgmatRichC · Answer

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.

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

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)

warriortx · Answer

No need to use complicated statistics at all.

The dice are numbered in 1-unit increments; thus, all the values ranging from the minimum value to the maximum value will be possible.

Minimum value: 4 dice; the four of them have a "1" facing upwards. Sum: 4.
Maximum value: 2 dice with 20 sides, whose numbers are both "20"; and 2 dice of 12 sides, with two "12". Sum: 64.

Number of different values in between: 64 - 4 + 1 (we add one because the range is "both inclusive").

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards