BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

What is the probability that a three-digit integer corresponding with the three numbers thrown on three different d

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

What is the probability that a three-digit integer corresponding with the three numbers thrown on three different d

by Max@Math Revolution » Mon Jan 27, 2020 6:20 pm
[GMAT math practice question]

What is the probability that a three-digit integer corresponding with the three numbers thrown on three different dice is a multiple of 11?

A. 1/3
B. 2/27
C. 4/27
D. 5/27
E. 2/9
Top
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: What is the probability that a three-digit integer corresponding with the three numbers thrown on three different d

by Max@Math Revolution » Mon Jan 27, 2020 6:20 pm
=>

In order for a three-digit integer abc to be a multiple of 11, a – b + c must be a multiple of 11 since we have 100a + 10b + c = 99a + a + 11b – b + c = (99a + 11b) + a – b + c = 11(9a+b) + a – b +c.

If a – b + c = 0, then the possible cases for (a, b, c) are
(1, 2, 1), (1, 3, 2), (1, 4, 3), (1, 5, 4), (1, 6, 5), (2, 3, 1), (2, 4, 2), (2, 5, 3), (2, 6, 4), (3, 4, 1), (3, 5, 2), (3, 6, 3), (4, 5, 1), (4, 6, 2) and (5, 6, 1), and we have 15 cases.

If a – b + c = 11, then we have only the case (a, b, c) = (6, 1, 6).

Thus the probability is 16/(6^3) = 16/216 = 2/27.

Therefore, the answer is B.
Answer: B
Top
Post new topic Post Reply
• Page 1 of 1