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

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.

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)

Answer C)

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

Correct Answer C

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.

Answer: C
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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

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.

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, ccooley, RonPurewal

It seems that the ordering of statement 2 is totally confusing and does not make sense, at least to me! Suppose, 2 is the number that is facing up. So, how this 2 is equal to itself? Shouldn't the version be something like below?

(2) Of the numbers that are facing up, 2, but not all 3, are equal
Possible version:
(2) Of the numbers that are facing up, two's, but not all three's, are equal.

or something like that ^^

Thanks for giving me your precious time..
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Hi Asad,

The wording in Fact 2 is a bit 'quirky', but the 'intent' isn't too difficult to determine.

From the prompt, we know that there are three dice - and each of the dice could end up showing any one of the numbers 1, 2, 3, 4, 5 or 6 on the "face up" side. Fact 2 tells us that TWO of the THREE "face up" sides are the SAME number. In simple terms, this means that when we throw the three dice, two of the numbers are the SAME and the third number is DIFFERENT.

If there was no other information to work with, then we could have a number of different options. For example:
1 - 1 - 5
3 - 3 - 2
6 - 6 - 4
Etc.

However, the prompt ALSO tells us that the SUM of the three dice is 12. This significantly limits the number of possibilities for Fact 2. The only ones are:
3 - 3 - 6
5 - 5 - 2

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

EMPOWERgmatRichC
Thank you so much for the explanation.
3 - 3 - 6==>12
5 - 5 - 2==>12
Here, blue part goes with prompt, but red part does not go with statement 2 for sure!

If it is considered as "quirky", it will be hard for us to adjust ourselves to the real exam. From the one side someone may think it as "quirky", but from the other side, other people (GMAT takers') may consider statement 2 as "serious fault", which makes the people scared to take the real exam-people would think if they face this sorta questions they may not answer those questions with 100% surety.
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Hi Asad,

Both of those examples match the information in Fact 2. We're told that TWO of the face-up numbers are EQUAL (to one another) while the third number is not (meaning that the third number is NOT equal to the other two.

3 - 3 - 6 means that there are two 3s and one 6. The two 3s are equal to one another and the third number (the 6) is not.
5 - 5 - 2 means that there are two 5s and one 2. The two 5s are equal to one another and the third number (the 2) is not.

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

Asad, I am fine with the wording on stmnt 2. It is quite clear.

The question stem already talks about "3 numbers that are facing up" so we know that they are talking about the numbers you see when you roll the dice.
Stmnt 2 says "of the numbers facing up.... 2 are equal (but not all 3)"
So 2 of the numbers facing up are equal. All 3 numbers facing up are not equal.

The statement clearly says "of the numbers facing up..." so we know it means "2 of the numbers ..." though they could have written it this way.
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The sum of the 3 numbers of the three dices are facing up is 12, is at least one of the number 5?

(1) 5, 5, 2, and 4, 4, 4 Two possibilities. Yes/No; Insufficient.

(2) 6, 4, 2 and 5, 5, 2 or , 6, 5, 1 Yes/No; Insufficient.

Considering both options.
5, 5, 2 Yes
Ans. C

Answer: Option C

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Nice one !

let x, y, and z are the three number that shows up --- > given, x+y+z= 12

(1) None of the 3 numbers that are facing up is divisible by 3 -- we're left with (1,2,4,5)

we can get 12 both ways, with or without 5, e.g. : \(4+4+4 = 12 \)(none of 'em is divisible by 3 and sum =12 )
OR
\(5+5+2 = 12\) (again none divisible by 3, but this time we have 5)

this statement alone is N.S

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

again, two possibilities.\( 3+3+6 = 12\)

\(5+5+2 = 12 \)

we get 5 in one of the possibilities.

this statement alone is N.S

1+2
Only way,\( x+y+z = 12\) when a number is repeated twice and none of the numbers are divisible by 3.

\(5+5+2 = 12\)

we did get 5, finally (:

C is the Answer.

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