Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43787

The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
28 Jan 2015, 06:58
Question Stats:
58% (01:49) correct 42% (01:44) wrong based on 119 sessions
HideShow timer Statistics



Intern
Joined: 18 Jul 2012
Posts: 7
Location: United States
Concentration: Finance, International Business
GPA: 3.87
WE: Consulting (Consulting)

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
28 Jan 2015, 08:23
1
This post received KUDOS
Is the answer C?
Below is my solution
a4 = sq(a3*a1) option 1 gives us a1 value.(1) a6 = sq(a5*a3) and a5 =sq(a4*a2)..option 2 gives us a2 value..combining (1)+(2) gives a6 .. a2 value is given in option2 hence using



Intern
Joined: 18 Jul 2012
Posts: 7
Location: United States
Concentration: Finance, International Business
GPA: 3.87
WE: Consulting (Consulting)

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
28 Jan 2015, 08:23
1
This post received KUDOS
Is the answer C? Below is my solution a4 = sq(a3*a1) option 1 gives us a1 value.(1) a6 = sq(a5*a3) and a5 =sq(a4*a2)..option 2 gives us a2 value..combining (1)+(2) gives a6 .. a2 value is given in option2 hence using



Senior Manager
Joined: 27 Dec 2013
Posts: 298

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
28 Jan 2015, 11:16
IMO Answer should be C. Please post OA. Bunuel wrote: The sequence a1, a2, …, an, … is such that \(a_n=\sqrt{a_{n1}*a_{n3}}\) for all integers n≥4. If \(a_4=16\), what is the value of a6?
(1) a1=2 (2) a2=4
Kudos for a correct solution.
_________________
Kudos to you, for helping me with some KUDOS.



Manager
Joined: 27 Aug 2014
Posts: 98
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
28 Jan 2015, 13:52
1
This post received KUDOS
Bunuel wrote: The sequence a1, a2, …, an, … is such that \(a_n=\sqrt{a_{n1}*a_{n3}}\) for all integers n≥4. If \(a_4=16\), what is the value of a6?
(1) a1=2 (2) a2=4
Kudos for a correct solution. Answer is C: from stem: a4 =16 from 1: a1 = 2, from stem a4 = sqrt(2*a3) ==> 16 = sqrt(2*a3), so a3 = 128, we just know the sequence as 2,a2,126,15,a5..., we need a5 to find a6, so NSF from 2: a2 = 4, as a1 is not known, this statement itslef is insufficient NSF combined 1+2: a5 = sqrt(a4*a2) = 8, sequence is like 2,4,128,16,8,..we have all values to find a6 so C



Manager
Joined: 14 Jul 2014
Posts: 96

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
02 Feb 2015, 02:17
To Find a6 , we need to know the values of a5 & a3
Stmnt 1  gives value of a3  Not Suff Stmtn 2  gives value of a5  Not suff
Combined  Suff
Ans  C



Math Expert
Joined: 02 Sep 2009
Posts: 43787

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
02 Feb 2015, 02:35
Bunuel wrote: The sequence a1, a2, …, an, … is such that \(a_n=\sqrt{a_{n1}*a_{n3}}\) for all integers n≥4. If \(a_4=16\), what is the value of a6?
(1) a1=2 (2) a2=4
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:One key for this problem, which looks worse than it actually is, is to avoid actually solving for the values. We only need to answer the question of whether a certain value can be solved for, not the more difficult question of what value would actually result. The sequence rule gives that \(a_6=\sqrt{(a_5)(a_3)}\). In order to obtain the value of a6, we will need to obtain the values of both a5 and a3. Standing alone, a4 cannot produce either. Adding statement (1) to the mix, we have the values of a1 and a4. Using the sequence rule with n=4 gives \(a_4=\sqrt{(a_3)(a_1)}\). Since we have both a4 and a1, this equation will allow us to solve for a3. From there, however, we can go no further. The values of a1,a3, and a4 do not collectively produce any of the other terms, and, in particular, we cannot solve for a5 with this information. Statement (1) alone is insufficient. Taking statement (2) alone, we have the values of a2 and a4. Using the sequence rule with n = 5 gives \(a_5=\sqrt{(a_4)(a_2)}\). We have both a4 and a2, so we can get a5. Again, though, we reach a dead end. The values of a2,a4, and a5 do not collectively produce any of the other terms, and, in particular, we cannot solve for a3 with this information. Statement (2) alone is insufficient. Combining the two statements, we are able to obtain all values from a1 through a5 (and beyond). In particular, statement (1) allows us to solve for a3, and statement (2) allows us to solve for a5. Recalling that \(a_6=\sqrt{(a_5)(a_3)}\), we know that we will be able to obtain a6. The two statements taken together are sufficient.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Oct 2016
Posts: 30
Location: India
WE: Sales (Energy and Utilities)

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]
Show Tags
12 Sep 2017, 13:28
Bunuel, Is this approach right. √(ab)=√a√b , So a4= √a3*√a1 a5= √a4*√a2 a6= √a5*√a3 Weare given a4=16 a4= √a3*√a1 STMT 1: a1=2 . 16=√a3*√2 so √a3= 16/√2 = 8√2 STM2: a2=4 a5= √a4*√a2 a5=√16*√4 a5= 8 a6= √a5*√a3 From above we can find the value of a6
_________________
Abhimanyu




Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for
[#permalink]
12 Sep 2017, 13:28






