Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65785

Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
16 Jun 2016, 04:43
Question Stats:
63% (02:09) correct 37% (02:15) wrong based on 1751 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Manager
Joined: 18 Sep 2014
Posts: 219

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
16 Jun 2016, 05:15
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.




Manager
Status: In the realms of Chaos & Night
Joined: 13 Sep 2015
Posts: 136

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
15 Jul 2016, 23:28
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)



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 515
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
17 Jul 2016, 04:33
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, SufficientCorrect Answer C



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
08 Dec 2016, 08:47
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. Answer: C
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 06 May 2015
Posts: 61
Location: India
GPA: 4

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



Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 381

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
13 Aug 2018, 23:04
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?
_________________



Manager
Joined: 06 Nov 2016
Posts: 53
Location: Viet Nam
Concentration: Strategy, International Business
GPA: 3.54

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
14 Aug 2018, 00:34
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.
_________________



SVP
Joined: 23 Feb 2015
Posts: 2004

Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
08 May 2020, 14:03
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 Hello Experts, EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, ccooley, RonPurewalIt 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..



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
09 May 2020, 13:12
Asad wrote: 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 Hello Experts, EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, ccooley, RonPurewalIt 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.. 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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



SVP
Joined: 23 Feb 2015
Posts: 2004

Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
09 May 2020, 23:29
EMPOWERgmatRichC wrote: Asad wrote: 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 Hello Experts, EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, ccooley, RonPurewalIt 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.. 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 Quote: 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 EMPOWERgmatRichCThank you so much for the explanation. 3  3  6==> 125  5  2==> 12Here, 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 exampeople would think if they face this sorta questions they may not answer those questions with 100% surety.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
10 May 2020, 14:22
Asad wrote: EMPOWERgmatRichC wrote: Asad wrote: 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 Hello Experts, EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, ccooley, RonPurewalIt 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.. 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 Quote: 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 EMPOWERgmatRichCThank you so much for the explanation. 3  3  6==> 125  5  2==> 12Here, 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 exampeople would think if they face this sorta questions they may not answer those questions with 100% surety. Hi Asad, Both of those examples match the information in Fact 2. We're told that TWO of the faceup 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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10784
Location: Pune, India

Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
Show Tags
11 May 2020, 21:25
Asad wrote: 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 Hello Experts, EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, ccooley, RonPurewalIt 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.. 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.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: Three dice, each of which has its 6 sides numbered 1 through 6, are to
[#permalink]
11 May 2020, 21:25




