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# Three dice, each of which has its 6 sides numbered 1 through 6, are to

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Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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16 Jun 2016, 04:43
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62% (02:09) correct 38% (02:12) wrong based on 992 sessions

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Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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16 Jun 2016, 05:15
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Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

Stmt 1 says that it can 1,2,4,5 then we can have 4,4,4 or 5,5,2 not suff.
Stmt 2 says 2 are year equal not three, it can mean 3,3,6 or 5,5,2. not suff

Hence C is the answer. as we rule out none of the numbers are divisible by 3.
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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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15 Jul 2016, 23:28
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Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
3's & 6's are out - The result can be achieved with (5,2,5)/ (4,4,4) -Insufficient

(2) Of the numbers that are facing up, 2, but not all 3, are equal
Possibilities for the condition are (5,5,2)/ (3,3,6) - Insufficient

Combining Statements 1) & 2) Only possible was of getting the sum is (5,5,2)

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Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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17 Jul 2016, 04:33
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Bunuel wrote:
Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

Sides of the dices are 1,2,3,4,5,and 6

(1)Among the above dice sides,sides divisible by 3 are 3 and 6,so facing up numbers must be among 1,2,4,and 5,so to get sum the three dice sides could be 4,4,and 4 or 5,5,2 .......>Not Sufficient
(2)Sum of the at most 2 two equal sides that are facing up and another 1 side may happen with many combination of dice numbers,example-(3,3,6)(5,5,2), .........>Not sufficient

(1)+(2) only combination of 5,5,and 2 sides on top of the dice sum up to 12,Sufficient

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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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08 Dec 2016, 08:47
1
Bunuel wrote:
Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

We are given that three dice (numbered 1 to 6) are tossed and that the sum of the three numbers facing up is 12. We need to determine whether one of these numbers is 5.

Statement One Alone:

None of the 3 numbers that are facing up is divisible by 3.

The information in statement one is not sufficient to answer the question. The numbers facing up could be 4, 4, and 4, and none of these numbers are 5. However, the numbers facing up could be 5, 5, and 2, and at least one of these numbers is 5. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Of the numbers that are facing up, 2, but not all 3, are equal.

The information in statement two is not sufficient to answer the question. The numbers facing up could be 3, 3, and 6, and none of these numbers are 5. However, the numbers facing up could be 5, 5, and 2, and at least one of these numbers is 5. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we can determine that the only way to obtain a sum of 12, when none of the numbers are divisible by 3 and when exactly two of the numbers are equal, is if the numbers facing up are 5, 5, and 2. Thus, at least one of the numbers is 5.

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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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11 Aug 2017, 02:19
Bunuel wrote:
Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

Stmt 1 Alone - Not Sufficient:
(5+5+2)=12 (Is at least 1 of these numbers 5? --> YES)
(4+4+4)=12 (Is at least 1 of these numbers 5? --> NO)
Stmt 2 Alone - Not Sufficient:
(3+3+6)=12 ((Is at least 1 of these numbers 5? --> NO)
(5+5+2)=12 ((Is at least 1 of these numbers 5? --> YES)
Stmt 1 & 2 together (Sufficient)
(6,6,x) not possible combo
(5,5,2) Possible - (Is at least 1 of these numbers 5? --> YES)
(4,4,4) not possible combo (stmt2 violated)
(3,3,6) not possible combo (stmt1 violated)
(2,2,x) not possible combo
(1,1,x) not possible combo.

OA: C
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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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13 Aug 2018, 23:04
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FightToSurvive wrote:
Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

Stmt 1 says that it can 1,2,4,5 then we can have 4,4,4 or 5,5,2 not suff.
Stmt 2 says 2 are year equal not three, it can mean 3,3,6 or 5,5,2. not suff

Hence C is the answer. as we rule out none of the numbers are divisible by 3.

Can't it be 2, 4 and 6, Which satisfies option C?
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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to  [#permalink]

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14 Aug 2018, 00:34
1
Baten80 wrote:
FightToSurvive wrote:
Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

Stmt 1 says that it can 1,2,4,5 then we can have 4,4,4 or 5,5,2 not suff.
Stmt 2 says 2 are year equal not three, it can mean 3,3,6 or 5,5,2. not suff

Hence C is the answer. as we rule out none of the numbers are divisible by 3.

Can't it be 2, 4 and 6, Which satisfies option C?

6 is divisible by 3 --> (2,4,6) doesn't satisfy Statement 1.
$$2 \neq 4 \neq 6$$ --> (2,4,6) doesn't satisfy Statement 2.

When combining 2 statements, only (5,5,2) satisfies.

Hope it helps.
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Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to &nbs [#permalink] 14 Aug 2018, 00:34
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