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A secretary differentiates files by a variety of color combinations.

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A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post Updated on: 16 May 2017, 07:53
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A secretary differentiates files by a variety of color combinations. If she uses 4 different colors, and marks each file with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24

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Originally posted by Kritesh on 16 May 2017, 07:48.
Last edited by Bunuel on 16 May 2017, 07:53, edited 1 time in total.
Renamed the topic and edited the question.
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A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 16 May 2017, 07:55
Kritesh wrote:
A secretary differentiates files by a variety of color combinations. If she uses 4 different colors, and marks each file with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24


If she marks by only one color then total possible combinations = 4C1 = 4

If she marks by only two colors then total possible combinations = 4C2 = 6

If she marks by only three colors then total possible combinations = 4C3 = 4

Total possible combinations = 4+6+4 = 14

Answer: Option C
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Re: A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 16 May 2017, 08:39
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Kritesh wrote:
A secretary differentiates files by a variety of color combinations. If she uses 4 different colors, and marks each file with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24


What's the source of this question?
I ask because it doesn't specify whether the order of the colors matters.
For example, is the color combination RED-BLUE-YELLOW different from BLUE-YELLOW-RED?
Based on the official answer, it seems that the above combinations are the same, but how do we know this?

ASIDE: es, I know that some people will feel that the word "combination" in the question basically tells us that order does not matter. However, I'll argue that using the word "combination" does not necessarily imply that order does not matter....... unless we want to then conclude that it doesn't matter which order we enter the code numbers a combination lock :-D

Cheers,
Brent
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A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 27 Jan 2019, 18:19
GMATPrepNow wrote:
What's the source of this question?
I ask because it doesn't specify whether the order of the colors matters.
For example, is the color combination RED-BLUE-YELLOW different from BLUE-YELLOW-RED?
Based on the official answer, it seems that the above combinations are the same, but how do we know this?

ASIDE: es, I know that some people will feel that the word "combination" in the question basically tells us that order does not matter. However, I'll argue that using the word "combination" does not necessarily imply that order does not matter....... unless we want to then conclude that it doesn't matter which order we enter the code numbers a combination lock :-D

Cheers,
Brent


Source is GMAT Hacks, going through it now (a lower quality, poor man's version of MGMAT, imo... although more concise in its explanations). Would an actual GMAT problem always state that colors are not ordered or something, rather just use the word combined or arranged?
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Re: A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 28 Jan 2019, 08:14
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energetics wrote:
GMATPrepNow wrote:
What's the source of this question?
I ask because it doesn't specify whether the order of the colors matters.
For example, is the color combination RED-BLUE-YELLOW different from BLUE-YELLOW-RED?
Based on the official answer, it seems that the above combinations are the same, but how do we know this?

ASIDE: es, I know that some people will feel that the word "combination" in the question basically tells us that order does not matter. However, I'll argue that using the word "combination" does not necessarily imply that order does not matter....... unless we want to then conclude that it doesn't matter which order we enter the code numbers a combination lock :-D

Cheers,
Brent


Source is GMAT Hacks, going through it now (a lower quality, poor man's version of MGMAT, imo... although more concise in its explanations). Would an actual GMAT problem always state that colors are not ordered or something, rather just use the word combined or arranged?


The test-makers don't have one particular way to let test-takers know whether order matters. Sometimes the context of the question let's you know. Other times, there is clear wording (and sometimes even an example) that indicates whether order matters.

The important thing to keep in mind is that the test-makers take every precaution to minimize/eliminate any ambiguity.

Cheers,
Brent
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Re: A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 03 Aug 2019, 00:15
GMATinsight wrote:
Kritesh wrote:
A secretary differentiates files by a variety of color combinations. If she uses 4 different colors, and marks each file with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24


If she marks by only one color then total possible combinations = 4C1 = 4

If she marks by only two colors then total possible combinations = 4C2 = 6

If she marks by only three colors then total possible combinations = 4C3 = 4

Total possible combinations = 4+6+4 = 14

Answer: Option C


We usually multiply the combinations when combining the result, why did we add here?

Please help chetan2u, Gladiator59, VeritasKarishma, Bunuel, generis
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Re: A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 04 Aug 2019, 04:06
DarkHorse2019 wrote:
GMATinsight wrote:
Kritesh wrote:
A secretary differentiates files by a variety of color combinations. If she uses 4 different colors, and marks each file with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24


If she marks by only one color then total possible combinations = 4C1 = 4

If she marks by only two colors then total possible combinations = 4C2 = 6

If she marks by only three colors then total possible combinations = 4C3 = 4

Total possible combinations = 4+6+4 = 14

Answer: Option C


We usually multiply the combinations when combining the result, why did we add here?

Please help chetan2u, Gladiator59, VeritasKarishma, Bunuel, generis


Since this is an OR statement. She has three choices to mark the files i.e by one color or two or three colors.
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Re: A secretary differentiates files by a variety of color combinations.  [#permalink]

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New post 05 Aug 2019, 21:47
DarkHorse2019 wrote:
GMATinsight wrote:
Kritesh wrote:
A secretary differentiates files by a variety of color combinations. If she uses 4 different colors, and marks each file with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24


If she marks by only one color then total possible combinations = 4C1 = 4

If she marks by only two colors then total possible combinations = 4C2 = 6

If she marks by only three colors then total possible combinations = 4C3 = 4

Total possible combinations = 4+6+4 = 14

Answer: Option C


We usually multiply the combinations when combining the result, why did we add here?

Please help chetan2u, Gladiator59, VeritasKarishma, Bunuel, generis


Partial solutions are multiplied (A AND B AND C) and complete solutions are added (X OR Y).

Let's understand this with an example:

Say there is a fast food joint which serves meals consisting of a burger/pizza slice, a side and a drink.
There are 3 different kids of burgers, 4 different kinds of pizza, 2 different sides and 5 different drinks available.
In how many different ways can you make a meal?

Let's make burger meals first. We can choose a burger in 3 ways, sides in 2 ways and drinks in 5 ways.
You need to choose a burger AND a side AND a drink.
So total burger meals = 3*2*5 = 30 burger meals

Now let's make pizza meals. We can choose a pizza slice in 4 ways, sides in 2 ways and drinks in 5 ways.
You need to choose a pizza AND a side AND a drink.
So total pizza meals = 4*2*5 = 40 pizza meals

Now, to choose a meal, you pick either a burger meal OR a pizza meal. The 30 burger meals are complete in themselves and 40 pizza meals are complete in themselves too.
So you ADD them to get 30 + 40 = 70 meals. You can pick a meal in 70 ways.


In the original question, she can mark a file using 1 colour only. So the 4 colours give us 4 different complete solutions.
OR she can mark a file using 2 colours 4C2 = 6 ways of marking a file using 2 colours (complete solutions).
Or she can mark a file using 3 colours in 4C3 = 4 ways. Again complete solutions

So we add them to get 4 + 6 + 4 = 14 solutions.
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Re: A secretary differentiates files by a variety of color combinations.   [#permalink] 05 Aug 2019, 21:47
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