November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
Updated on: 13 Aug 2018, 02:11
Question Stats:
30% (03:23) correct 70% (03:18) wrong based on 963 sessions
HideShow timer Statistics
Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl are twins and Beth and Duncan are also twins. When the present ages of the four siblings are multiplied, the product is 900. If Beth is older than Abe, what is the age of Duncan? Assume the ages of all siblings to be integers. (1) The difference between Beth’s age and Abe’s age is a prime number. (2) If Carl had been born four years earlier, the difference between Duncan’s age and Carl’s age would have been a prime number. This is Ques 9 of The EGMAT Number Properties Knockout Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
Updated on: 07 Aug 2018, 02:38
Detailed SolutionStepI: Given InfoWe are told about four siblings Abe, Beth, Carl and Duncan such that Abe and Carl are twins and Beth and Duncan are also twins. We are also given that the product of the present ages of the four siblings is 900. Further we are told that Beth is older than Abe and we are asked to find the age of Duncan StepII: Interpreting the Question StatementSince Abe and Carl are twins, their ages would be same, let’s assume it to be \(x\). Similarly, since Beth and Duncan are twins, their ages would be same, let’s assume it to be \(y\). We are told that Beth is older than Abe, i.e. \(y > x\) and the product of the ages of the siblings is 900, so we can write \(x^ 2 * y^2 = 900\). We can observe here that 900 is written as product of two squares, since 900 can be prime factorized as \(900 = 2^2 * 3^2 * 5^2\), the possible set of values of (\(x, y\)) can be: • (1, 30) or • (2, 15) or • (3, 10) or • (5,6) Let’s proceed to the solutions to see if we can get a unique value of \(x\) with this understanding. StepIII: Statement IStatement tells us that \(y\) \(–\) \(x\) is a prime number. Let’s evaluate our possible cases to see if we can find a unique value for \(x\): • (1, 30) –>= 29> Prime • (2, 15) –>= 13 > Prime • (3, 10) – > = 7 > Prime • (5,6) – > = 1 > Not Prime We observe here that, there are three possible values for \(x\), hence statementI is not sufficient to arrive at the answer. StepIV: Statement IIStatementII tells us that had Carl been born four years earlier, the difference between Duncan’s age and Carl’s age would have been a prime number. Since Carl’s present age is \(x\), had he been born four years earlier, his present age would be (\(x +4\)). The Statement tells us that \(y\) \(–\) \((x +4)\) is a prime number. Let’s evaluate our possible cases to see if we can find a unique value for \(x\). • (1, 30) –>= 25> Not Prime • (2, 15) –>= 9 > Not Prime • (3, 10) – > = 3 > Prime • (5,6) – > = 3 > Prime We observe here that there are two possible values for \(x\), hence statementII is not sufficient to arrive at the answer. StepV: Combining Statements I & IIStatementI gives us the possible values of (\(x, y\)) as (1, 30), (2, 15) and (3, 10). StatementII gives us the possible values of (\(x, y\)) as (3, 10) and (5,6). Combining statementI & II give us only possible option for values of (\(x, y\)) which is (3, 10). Thus combination of StI & II is sufficient to answer the question. Hence, the correct answer is Option CKey Takeaways1. Prime factorize a number to understand the ways in which a number can be representedatom  you were right in describing why StatementII alone is not sufficient but you did not consider the combinations of statement I & II. Regards Harsh
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




Intern
Joined: 05 Apr 2014
Posts: 13

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
10 Apr 2015, 08:38
Let the ages be A,B,C & D respectively. Given A=C & B=D, A*B*C*D=900=>B^2*A^2=900=>B*A=30. Possible combinations are (30*1),(15*2),(10*3),(6*5) Statement 1: BA=P(prime) => (30*1),(15*2), & (10*3) satisfy the equation. Therefore statement 1 is insufficient. Statement 2: D(C+4)=P or B(A+4)=P or BA4=P. Now only (10*3) satisfy. Therefore B=D=10 and statement 2 is sufficient. Answer: (B)
_________________
If anything above makes any sense to you, please let me and others know by hitting the "+1 KUDOS" button



Intern
Joined: 24 Sep 2012
Posts: 19
Location: United States
WE: Project Management (Computer Software)

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
10 Apr 2015, 09:56
Shuvabrata88,
I agree with the approach which you have taken but I think the answer should be E as statement 2 simply states that diff b/w D and C is prime so it could be either DC4 or C+4D; in this case (5*6) combination also works out to be prime.
Initial ques stem mentions that B>A i.e D>C but if we add 4 to C then this statement may not hold true.
I may be over complicating the question, lets wait for OE



Intern
Joined: 17 Jan 2014
Posts: 6

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
10 Apr 2015, 11:26
EgmatQuantExpertHad a happy time solving, please provide the OA asap



Intern
Joined: 24 Sep 2012
Posts: 19
Location: United States
WE: Project Management (Computer Software)

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
11 Apr 2015, 11:40
Oh yes Harsh, my bad ; thanks for the detailed solution



Intern
Joined: 29 Dec 2014
Posts: 24
Concentration: Operations, Strategy
GMAT 1: 690 Q48 V35 GMAT 2: 710 Q48 V39

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
12 Apr 2015, 08:37
egmat representative i am sorry but i disagree with your evaluation of statement two. following are my points of dispute: It is given that beth ( & hence duncan, since they are twins) is older than abe ( & correspondingly carl). That is a fact and cannot be challenged, right ? Also, fact 2: clearly states difference between Duncan's age and Carl's age..makes sense because we would want to end up with negetive number which would occur if the reverse ( C  D) were to happen..so far so good. now consider the possible age value sets (keeping in mind the logical validity of the statement ) " Since Carl’s present age is x, had he been born four years earlier, his present age would be (x +4). The Statement tells us that y – (x +4) is a prime number. " this is your explanation..totally with you till this point. HOWEVER, y – (x +4) when applied to the set (5,6) yields 3 (which is not positive first of all forget being prime) and not 3 as you said..absolutely illogical and hence not a valid set i feel. the other sets (resultantprime or otherwise) at least yield a positive number since x and x+4 are both lesser than y. And if we were to take this into account, the only valid set is (3,10) from stmnt 2..sufficient ans: B WOULD REQUEST your thoughts on this and would kindly appreciate if A MATH EXPERT would care to enlighten or clarify. regards



Intern
Joined: 24 Sep 2012
Posts: 19
Location: United States
WE: Project Management (Computer Software)

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
12 Apr 2015, 11:12
smashbiker84,
I agree that D>C is given in the question, but how would you know D>C+4?? we can have C+4>D right? Hence we must need to consider DC4 and C+4D; in this case 5,6 gives you the prime output
Hope it helps
Cheers AT



Intern
Joined: 24 Oct 2014
Posts: 40
Location: United States
GMAT 1: 710 Q49 V38 GMAT 2: 760 Q48 V47

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
12 Apr 2015, 20:04
This is my question. Well we can come up with the following pairs (A,B) or (D, C) = (15, 2), (6, 5), (10, 3), or (30, 1). From statement 2 we get that had Carl been born four years earlier, the difference would have been a prime number. So from the given information we know that Carl's age is either 2,5,3,1. So if he was born 4 years earlier then his age could have been (2, 1, 1, 3). Well obviously only 1 is possible, so the difference between 6 and 1 be a prime number.
But clearly that is not the way to approach this problem, nor is this approach taken by anyone. I just want to know what am I missing here.
Thanks!



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
Updated on: 07 Aug 2018, 02:39
Hi smashbiker84 We are not challenging any facts here. StatementII presents a 'What If' scenario which gives another relation between the ages of the siblings. The question statement talks about the present situation, while statementII talks about an alternate situation. For example, assume a situation where you are 3 years elder to your sister. If your sister were to be born 4 years earlier, she would become a year elder to you. This is not contradicting the present situation, but building upon the present situation. To answer your 2nd question, please note that difference between two things is positive in real world scenarios. For example, difference between a son's age and his father's age is 30 years and the difference between the father’s and his son’s age is also 30 years. We do not say that the difference between son’s age and father’s age is 30 years. The "" is only an indication that you have subtracted the larger item from the smaller item. Hence, when we are talking about difference between two things, it would mean the absolute difference or the magnitude of the difference. . Hi nphatak, if a person is born earlier, his age would increase, so instead of subtracting 4 from the present age, you would need to add 4 in the present age. For ex: If a person is born in 2004, his present age would be 11, but if he is born four years earlier i.e. in 2000, his present age would be (11 + 4) = 15. So, in this case Carl's age would be (6,9,7,5) instead of (2, 1, 1, 3). Hope its clear! Regards Harsh



Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
20 Apr 2017, 02:25
Option CIn terms of age, A = C & B = D. Also, A*B*C*D = 900 =A^2*B^2 = C^2*D^2 A*B = C*D = 30 Which means, (A,B) or (B,A) could possibly be (1,30) ; (2,15) ; (3,10) ; (5,6). I: B  A = Prime number. Let us look at the possible options: B  A = 30 1 = 29 or 15  2 = 13 or 10  3 = 7 or 6  5 = 1. Except for the last combination (6,5), rest satisfy the condition of being Prime number, so there is NO unique solution. Hence, I is Insufficient. II: Carl's age today, had he born four years ago, would be C +4. So, D  (C + 4) = B  (A+4) = Prime number. Now again looking at the possible combinations, we can see: 30  (1+4) = 25 Not a Prime 15  (2+4) = 9 Not a Prime 10  (3+4) = 3 Prime Again, no Unique solution. Insufficient. Now, if we combine both I + II: I:BA = Prime Number Also, II:B  (A+4) = Prime Number From possible solutions, only one combination B = 10 & A = 3 satisfy both the conditions. As, BA = 10 3 = 7 Prime B  (A+4) = 10  (3+4) = 3 Prime Hence, Sufficient.
_________________
Press Kudos if you liked the post!
Rules for posting  PLEASE READ BEFORE YOU POST



Intern
Joined: 17 Oct 2017
Posts: 7

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
31 Oct 2017, 14:38
EgmatQuantExpert wrote: Detailed Solution
StepI: Given Info
We are told about four siblings Abe, Beth, Carl and Duncan such that Abe and Carl are twins and Beth and Duncan are also twins. We are also given that the product of the present ages of the four siblings is 900. Further we are told that Beth is older than Abe and we are asked to find the age of Duncan
StepII: Interpreting the Question Statement
Since Abe and Carl are twins, their ages would be same, let’s assume it to be \(x\). Similarly, since Beth and Duncan are twins, their ages would be same, let’s assume it to be \(y\).
We are told that Beth is older than Abe, i.e. \(y > x\) and the product of the ages of the siblings is 900, so we can write \(x^ 2 * y^2 = 900\).
We can observe here that 900 is written as product of two squares, since 900 can be prime factorized as \(900 = 2^2 * 3^2 * 5^2\), the possible set of values of (\(x, y\)) can be:
• (1, 30) or • (2, 15) or • (3, 10) or • (5,6)
Let’s proceed to the solutions to see if we can get a unique value of \(x\) with this understanding.
StepIII: Statement I
Statement tells us that \(y\) \(–\) \(x\) is a prime number. Let’s evaluate our possible cases to see if we can find a unique value for \(x\):
• (1, 30) –>= 29> Prime • (2, 15) –>= 13 > Prime • (3, 10) – > = 7 > Prime • (5,6) – > = 1 > Not Prime
We observe here that, there are three possible values for \(x\), hence statementI is not sufficient to arrive at the answer.
StepIV: Statement II
StatementII tells us that had Carl been born four years earlier, the difference between Duncan’s age and Carl’s age would have been a prime number. Since Carl’s present age is \(x\), had he been born four years earlier, his present age would be (\(x +4\)). The Statement tells us that \(y\) \(–\) \((x +4)\) is a prime number. Let’s evaluate our possible cases to see if we can find a unique value for \(x\).
• (1, 30) –>= 25> Not Prime • (2, 15) –>= 9 > Not Prime • (3, 10) – > = 3 > Prime • (5,6) – > = 3 > Prime
We observe here that there are two possible values for \(x\), hence statementII is not sufficient to arrive at the answer.
StepV: Combining Statements I & II
StatementI gives us the possible values of (\(x, y\)) as (1, 30), (2, 15) and (3, 10). StatementII gives us the possible values of (\(x, y\)) as (3, 10) and (5,6).
Combining statementI & II give us only possible option for values of (\(x, y\)) which is (3, 10). Thus combination of StI & II is sufficient to answer the question. Hence, the correct answer is Option C
Key Takeaways
1. Prime factorize a number to understand the ways in which a number can be represented
Regards Harsh This interpretation of between of in the problem seems to go against what is used on GMAT"difference between x and y" is interpreted as "xy"this is also shown in GMAT club math book; am I missing something here because the difference has a direction associated with it (+/) so (5 and 6) would actually result in (6(5+4)) [representing Duncan  Carl Born Four Years Ealier] is actually negative and thus cannot be a prime so statement II alone should be sufficient and the right answer should be B...



Intern
Joined: 29 Sep 2017
Posts: 5

Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl
[#permalink]
Show Tags
11 Aug 2018, 09:35
i too am getting statement B as sufficient.




Re: Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl &nbs
[#permalink]
11 Aug 2018, 09:35






