GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 May 2020, 13:22 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A certain musical scale has has 13 notes, each having a different freq

Author Message
TAGS:

### Hide Tags

Senior Manager  Joined: 28 Oct 2003
Posts: 382
Location: 55405
A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

6
59 00:00

Difficulty:   95% (hard)

Question Stats: 50% (02:44) correct 50% (02:47) wrong based on 706 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. $$440 * \sqrt{2^7}$$

E. $$440 * \sqrt{2^{12}}$$

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: 3102
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

10
10
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)

##### General Discussion
Manager  Joined: 19 Oct 2004
Posts: 240
Location: Missouri, USA
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

6
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.
Manager  Joined: 13 Oct 2004
Posts: 162
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

5
1
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.
CEO  Joined: 15 Dec 2003
Posts: 3207
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

1
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 710-750?

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.
Intern  Joined: 16 Nov 2004
Posts: 18
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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
power, but after I wrote 440 (k^12) = 880
and started simplifying, I stumbled on the answer.

Congratulations to ruhi160184.
Manager  Joined: 29 Jan 2011
Posts: 227
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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)

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: 29 Jan 2011
Posts: 227
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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: 112
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

Slightly different way of approaching it...

Given

$$n_1 = 440$$

$$n_{13} = 880$$

$$n_i = 440(1+k)^{i-1}$$

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  B
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 600
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

1
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/og10-journal ... ition.html

Dabral
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

1
1
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

Intern  Joined: 21 Feb 2013
Posts: 10
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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)

Why do you multiply and not add?

Like
1. 440
2. 440 + k and so on?
Intern  Joined: 20 Feb 2013
Posts: 17
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

1
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
_________________
Pushpinder Gill
Math Expert V
Joined: 02 Sep 2009
Posts: 64242
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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)

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.
_________________
Intern  Joined: 20 Feb 2013
Posts: 17
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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)

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

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
SM - HEC Paris 2014

Intern  Joined: 20 Feb 2013
Posts: 17
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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: 8
GMAT 1: 660 Q48 V34
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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)

Intern  Joined: 17 Jun 2013
Posts: 4
Schools: ISB '14
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

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

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 V
Joined: 02 Sep 2009
Posts: 64242
Re: A certain musical scale has has 13 notes, each having a different freq  [#permalink]

### Show Tags

1
1
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

Pushpinder Ji I couldn't understand from here. Can u tell me please

1st = $$440$$
2nd = $$440k$$
3rd = $$440k^2$$
...
7th = $$440k^6$$
...
13th = $$440k^{12}=2*440=880$$ --> $$440k^{12}=880$$ --> $$k^{12}=2$$ --> $$k=\sqrt{2}$$.

Thus, 7th = $$440k^6=440(\sqrt{2})^6=440\sqrt{2}$$.

Hope it's clear.
_________________ Re: A certain musical scale has has 13 notes, each having a different freq   [#permalink] 12 Jul 2013, 23:38

Go to page    1   2    Next  [ 31 posts ]

# A certain musical scale has has 13 notes, each having a different freq  