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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A magician holds one six-sided die in his left hand... tagged by: swerve ##### This topic has 1 expert reply and 1 member reply ### Top Member ## A magician holds one six-sided die in his left hand... A magician holds one six-sided die in his left hand and two in his right. What is the probability the number of the dice in his left hand is greater than the sum of the dice in his right? A. 7/108 B. 5/54 C. 1/9 D. 2/17 E. 1/4 The OA is B. Please, can any expert explain this PS question for me? I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply swerve wrote: A magician holds one six-sided die in his left hand and two in his right. What is the probability the number of the dice in his left hand is greater than the sum of the dice in his right? A. 7/108 B. 5/54 C. 1/9 D. 2/17 E. 1/4 The OA is B. Please, can any expert explain this PS question for me? I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks. P(x) = # Desired Outcomes/# Total possible outcomes # Total possible outcomes when rolling 3 dice = 6^3 = 216. Notice that for the single die to be greater than the sum of the other two, the single die must be at least 3. Single die: 3; Two other dice sum to less than 3: [1,1] --> 1 desired outcome Single die: 4; Two other dice sum to less than 4: [1,1; 2,1; 1,2] --> 3 desired outcomes Single die: 5; Two other dice sum to less than 5:[1,1; 2,1; 1,2, 3,1; 1,3; 2,2] --> 6 desired outcomes Single die: 6; Two other dice sum to less than 6: [1,1; 2,1; 1,2, 3,1; 1,3; 2,2; 2,3; 3,2; 1,4; 4,1} --> 10 desired outcomes # Desired outcomes: 1 + 3 + 6 + 10 = 20 20/216 = 5/54. the answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Newbie | Next Rank: 10 Posts
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DavidG@VeritasPrep wrote:
swerve wrote:
A magician holds one six-sided die in his left hand and two in his right. What is the probability the number of the dice in his left hand is greater than the sum of the dice in his right?

A. 7/108
B. 5/54
C. 1/9
D. 2/17
E. 1/4

The OA is B.

Please, can any expert explain this PS question for me? I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
P(x) = # Desired Outcomes/# Total possible outcomes

# Total possible outcomes when rolling 3 dice = 6^3 = 216.

Notice that for the single die to be greater than the sum of the other two, the single die must be at least 3.

Single die: 3; Two other dice sum to less than 3: [1,1] --> 1 desired outcome
Single die: 4; Two other dice sum to less than 4: [1,1; 2,1; 1,2] --> 3 desired outcomes
Single die: 5; Two other dice sum to less than 5:[1,1; 2,1; 1,2, 3,1; 1,3; 2,2] --> 6 desired outcomes
Single die: 6; Two other dice sum to less than 6: [1,1; 2,1; 1,2, 3,1; 1,3; 2,2; 2,3; 3,2; 1,4; 4,1} --> 10 desired outcomes

# Desired outcomes: 1 + 3 + 6 + 10 = 20

20/216 = 5/54. the answer is B
is there any other possible solution rather than counting manually

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