January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 28 Oct 2003
Posts: 488
Location: 55405

A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
Updated on: 18 Dec 2017, 22:23
Question Stats:
52% (02:48) correct 48% (02:48) wrong based on 667 sessions
HideShow timer Statistics
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second? A. \(440 * \sqrt 2\) B. \(440 * \sqrt {2^7}\) C. \(440 * \sqrt {2^{12}}\) D. \(440 * \sqrt[12]{2^7}\) E. \(440 * \sqrt[7]{2^{12}}\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by stoolfi on 01 Jan 2004, 22:34.
Last edited by Bunuel on 18 Dec 2017, 22:23, edited 2 times in total.
Edited the question and added OA.




CEO
Joined: 15 Aug 2003
Posts: 3377

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
02 Jan 2004, 01:49
stoolfi wrote: On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
let the constant be k
F1 = 440
F2 = 440k
F3 = 440 k * k = 440 * k^2
F13= 440 * k^12
we know F13 = 2 *F1 = 2 * 440 = 880
880/440 = k^12
k = twelfth root of 2
for F7...
F7 = 440 * k^6 ( as we wrote for F2 and F3)
F7 = 440 * (twelfth root of 2) ^ 6
F7 = 440 * sqrt (2)
Answer A




Senior Manager
Joined: 19 Oct 2004
Posts: 308
Location: Missouri, USA

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Nov 2004, 10:11
Let k be the constant.
Hence, f2/f1=k. given, f1=440, f13=highest frequency=2*440=880.
Also, f13=440*k^12
therefore, 440*k^12=880 , or k^12=2, or (k^6)^2=2 or k^6=root 2.
f7=440k^6= 440*root2.
_________________
Let's get it right!!!!



Manager
Joined: 13 Oct 2004
Posts: 234

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
23 Nov 2004, 16:52
A quick gut check on this problem is that every choice but A is way more than 880. Logically the 7th note must have a smaller value(the problem also states 'lower' frequency) than than the 13th. If crunched for time, good guess would be A.



GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4163

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
23 Nov 2004, 17:54
toddmartin wrote: It took me about 3.5 minutes to get the answer, even though I did get it right. I had to think about it for a few seconds then write down what I knew in order to see the solution. How difficult is this problem in relation to the ones I'm likely to see on the test if I'm aiming for 710750?
Do not worry too much. I think this type of question does not appear unless you have 51 in quant. You can definitely break the 700 barrier without reaching 51 quant as long as you have a good verbal score also.
_________________
Best Regards,
Paul



Intern
Joined: 16 Nov 2004
Posts: 26

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
25 Nov 2004, 13:39
Took about 3 minutes.
I had no idea how to start it so I just
wrote down what I had and tried reorganizing
it.
440 * k = 2nd tone
440 * k * k = 3rd tone
.
.
440 * k ^6 = 7th tone.
At this point, I was wondering why none of
the answers had anything raised to the sixth
power, but after I wrote 440 (k^12) = 880
and started simplifying, I stumbled on the answer.
Congratulations to ruhi160184.



Senior Manager
Joined: 29 Jan 2011
Posts: 284

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
09 Nov 2011, 03:00
Praetorian wrote: stoolfi wrote: On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A The question stem says that : the ratio of frequency to next higer frequency is fixed constant ... Doesnt that mean F1/F2 = k F2/F3 = k^2 and something like that .....???and not F2/F1 = k which is F2 = kF1???



Senior Manager
Joined: 29 Jan 2011
Posts: 284

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
09 Nov 2011, 03:03
ruhi wrote: Let k be the constant.
Hence, f2/f1=k. given, f1=440, f13=highest frequency=2*440=880.
Also, f13=440*k^12
therefore, 440*k^12=880 , or k^12=2, or (k^6)^2=2 or k^6=root 2. f7=440k^6= 440*root2. The question stem says that : the ratio of frequency to next higer frequency is fixed constant ... Doesnt that mean F1/F2 = k F2/F3 = k^2 and something like that ..... ??? and not F2/F1 = k which is F2 = kF1???



Manager
Joined: 11 Sep 2009
Posts: 129

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
09 Nov 2011, 19:01
Slightly different way of approaching it...
Given
\(n_1 = 440\)
\(n_{13} = 880\)
\(n_i = 440(1+k)^{i1}\)
Solve for \(n_7\)
Given that: \(n_7 = 440(1+k)^{6}\)
\(n_{13} = 440(1+k)^{12}\)
\(880 = (440(1+k)^{6})(1+k)^{6}\)
\(440*880 = (440(1+k)^{6})(440(1+k)^{6})\)
\(2*440^2 = (n_7)^2\)
\(n_7 = \sqrt{2}(440)\)



Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 612

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
09 Nov 2011, 21:27
Siddhans, It says the ratio of a frequency to the next higher frequency is a constant. f2/f1=f3/f2=f4/f3=.....=fixed number. This is an example of a geometric progression. Here is a video explanation: http://www.gmatquantum.com/og10journal ... ition.htmlDabral



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8792
Location: Pune, India

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
10 Nov 2011, 21:32
siddhans wrote: ruhi wrote: Let k be the constant.
Hence, f2/f1=k. given, f1=440, f13=highest frequency=2*440=880.
Also, f13=440*k^12
therefore, 440*k^12=880 , or k^12=2, or (k^6)^2=2 or k^6=root 2. f7=440k^6= 440*root2. The question stem says that : the ratio of frequency to next higer frequency is fixed constant ... Doesnt that mean F1/F2 = k F2/F3 = k^2 and something like that ..... ??? and not F2/F1 = k which is F2 = kF1??? Responding to a pm: The statement, "the ratio of a frequency to the next higher frequency is a fixed constant." means that the ratio of two consecutive frequencies is always the same. It doesn't matter how you write it. You can say F1/F2 = F2/F3 = F3/F4 = ... = F12/F13 = k You can also say F2/F1 = F3/F2 = F4/F3 = ... = F13/F12 = k The two constants are different. Your k will be reciprocal of each other in the two cases. You can follow any approach. You will get the value of k accordingly. Mind you, F2/F3 is also k, not k^2. The ratio remains constant. It is a geometric progression. The ratio between any two consecutive values is always the same.
_________________
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 >



Intern
Joined: 21 Feb 2013
Posts: 11

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Feb 2013, 03:38
Praetorian wrote: stoolfi wrote: On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A Why do you multiply and not add? Like 1. 440 2. 440 + k and so on?



Intern
Joined: 20 Feb 2013
Posts: 20

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Feb 2013, 04:48
Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2  1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A
_________________
Pushpinder Gill



Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Feb 2013, 05:12
karmapatell wrote: Praetorian wrote: stoolfi wrote: On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A Why do you multiply and not add? Like 1. 440 2. 440 + k and so on? Because we are given that the ratio of a frequency to the next higher frequency is a fixed constant: F2/F1=k.
_________________
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: 20 Feb 2013
Posts: 20

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Feb 2013, 09:29
karmapatell wrote: Praetorian wrote: stoolfi wrote: On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A Why do you multiply and not add? Like 1. 440 2. 440 + k and so on? "For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant" The question says that the ratio of two consecutive frequencies is constant. Hence we multiply.
_________________
Pushpinder Gill



Intern
Joined: 17 Oct 2011
Posts: 24
Location: France
Concentration: Strategy
GPA: 4

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Feb 2013, 12:59
Shoudln't "the ratio of a frequency to the next higher frequency is a fixed constant" be interpreted as f1/f2 = k instead of f2/f1=k?
_________________
Alejandro LC MMT  EGADE Business School 2013 SM  HEC Paris 2014
Starting your journey towards business school? My experience can help you...



Intern
Joined: 20 Feb 2013
Posts: 20

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
22 Feb 2013, 21:51
Let's take a simple example Series : 2 4 6 8 Now going forward the multiplying factor is 2 and backward the factor is 1/2 Hence if you go backwards in the question the factor will be 1/2 and still you will get the same answer. Posted from my mobile device
_________________
Pushpinder Gill



Intern
Joined: 06 May 2013
Posts: 9

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
23 Jun 2013, 14:04
Since the ratio is constant it is a geometric progression
7th term is the middle term of the series
mean of the geometric series given by sqrt(a*b)
a= first term of the series = 440 b= last term of the series = 2*440
Mean = 7th term = sqrt(2*440*440) = 440*sqrt(2)
Answer A



Intern
Joined: 17 Jun 2013
Posts: 4

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
Updated on: 12 Jul 2013, 23:28
Pushpinder wrote: Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2  1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A Pushpinder Ji I couldn't understand from here. Can u tell me please
Originally posted by dasikasuneel on 12 Jul 2013, 21:40.
Last edited by Bunuel on 12 Jul 2013, 23:28, edited 2 times in total.
Edited.



Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A certain musical scale has has 13 notes, each having a different freq
[#permalink]
Show Tags
12 Jul 2013, 23:38
dasikasuneel wrote: Pushpinder wrote: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2  1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A Pushpinder Ji I couldn't understand from here. Can u tell me please 1st = \(440\) 2nd = \(440k\) 3rd = \(440k^2\) ... 7th = \(440k^6\) ... 13th = \(440k^{12}=2*440=880\) > \(440k^{12}=880\) > \(k^{12}=2\) > \(k=\sqrt[12]{2}\). Thus, 7th = \(440k^6=440(\sqrt[12]{2})^6=440\sqrt{2}\). Answer: A. Hope it's clear.
_________________
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




Re: A certain musical scale has has 13 notes, each having a different freq &nbs
[#permalink]
12 Jul 2013, 23:38



Go to page
1 2
Next
[ 27 posts ]



