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# A certain office supply store stocks 2 sizes of self-stick notepads

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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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anilnandyala wrote:
bunuel can you make me more clear, how it is 4 books of same colour

thank u

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.

Hope it's clear.
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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bunuel can you make me more clear, how it is 4 books of same colour

thank u
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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msand wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A. 6
B. 8
C. 16
D. 24
E. 32

First scenario 2C1 * 4C3 = 8
Second scenario 2C1*4C1 = 8

Total 16

Hope it helps
Cheers!
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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Hi All,

The question is essentially about the Combination Formula and following instructions. However, if you don't realize that, then you can always "brute force" the solution - you just have to draw it all out.

We're told that there are 2 sizes of notepads and 4 colors (Blue, Green, Yellow, Prink) of notepads. For organizational purposes, I'm going to refer to the 8 types of pads as:

Etc.

Now, we just need to figure out how many options fit each description:

1st: 3 notepads of the SAME SIZE and SAME COLOR….

BBB
bbb
GGG
ggg
YYY
yyy
PPP
ppp

8 options

2nd: 3 notepads of the SAME SIZE and 3 DIFFERENT COLORS

BGY
BGP
BYP
GYP
bgy
bgp
byp
gyp

8 options

Total options = 8 + 8 = 16

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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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msand wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A. 6
B. 8
C. 16
D. 24
E. 32

we have 2 types of notebooks.
we can select either 3 colors or 1 color
to select 3 colors: 4C3 = 4
to select 1 color: 4C1 = 4
so for each type of notebook, we have 8 possible arrangements
8x2 = 16

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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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msand wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A. 6
B. 8
C. 16
D. 24
E. 32

1. Ordering is not important, so this is a combination problem
2. Is there a constraint? There are two cases each with a constraint
3. In the first case ,Constraint is 3 notebooks of the same color . So there are 2 ways of selecting a size and 4C1 ways of selecting a color. So a total of 2*4= 8 ways
4. In the second case, constraint is 3 notebooks of the same size but 3 different colors. There are 2 ways of selecting a size and 4C3 ways of selecting colors, for a total of 2*4=8 ways
5. Total number of combinations is (3) + (4) = 16
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
msand wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A. 6
B. 8
C. 16
D. 24
E. 32

Let’s say the 2 sizes of notepads are small and large. Then, for the small notepads, there are 4 packages of notepads of all the same color (one package for each color) and 4C3 = 4 packages of notepads of three different colors. Thus, for the small notepads, there are a total of 4 + 4 = 8 different packages. Similarly, there are 8 different packages for the large notepads. Thus, there are a total of 8 + 8 = 16 different packages for the 2 sizes of notepads.

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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
Bunuel wrote:
anilnandyala wrote:
bunuel can you make me more clear, how it is 4 books of same colour

thank u

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.

Hope it's clear.

Hi Bunuel,

Sorry but I don't follow this..

When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple

Pls explain..what am I missing here?

Regards
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
zanaik89 wrote:
Bunuel wrote:
anilnandyala wrote:
bunuel can you make me more clear, how it is 4 books of same colour

thank u

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.

Hope it's clear.

Hi Bunuel,

Sorry but I don't follow this..

When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple

Pls explain..what am I missing here?

Regards

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have:

4 BLUE
4 GREEN
4 YELLOW
4 PINK

4 blue
4 green
4 yellow
4 pink
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
Hello,

What if there where 5 colours total.
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
Hi andresan,

Even if there were 5 colors (instead of 4), the approaches would not change - you can either use the Combination formula or 'brute force' the list of options. Have you attempted either approach (and what answer did you get?)?

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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have:

4 BLUE
4 GREEN
4 YELLOW
4 PINK

4 blue
4 green
4 yellow
4 pink[/quote]

Shouldn't this be:

For large size..
3 Blue
3 Green
3 Yellow
3 Pink

For small size..
3 Blue
3 Green
3 Yellow
3 Pink
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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Hi ishaan100,

The numbers "4" and "3" have specific meanings in the context of this question - and do NOT refer to the total number of notepads in the store.

1) There are 4 different colors of pad: Blue, Green, Yellow and Pink - and each color appears in 2 different sizes.
2) Each package contains 3 types of pads: either all the same size & color OR the same size & 3 different colors.

Most of the posts in this thread define how there are 16 POSSIBLE packages of notepads - but again, that has nothing to do with the actual number of notepads in the store.

GMAT assassins aren't born, they're made,
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A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
Hi Gmat700Knight, chetan2u

I am just starting on P&C so I too struggle with it. Therefore, I want to ask something about this question. I have gone through all the solutions provided on this thread but I am not being able to clear my head about something. How did we take into account that fact that we have to make 3 notepads.

We have to make either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors right?
3 notepads of the same size and the same color + 3 notepads of the same size and of 3 different colors right
Choose 1 size out of 2 and Choose 1 color out of 4 + Choose 1 size out of 2 and Choose 1 color out of 4
2C1 * 4C1 + 2C1 * 4C3 = 16
I understood this but how did me make 3 notepads though ?

Thank you,
Dablu

Originally posted by gurudabl on 08 Mar 2020, 22:43.
Last edited by gurudabl on 15 May 2020, 23:17, edited 2 times in total.
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A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
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msand wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

A. 6
B. 8
C. 16
D. 24
E. 32

There are two different cases to consider:
1) All 3 pads the same color
2) The 3 pads are 3 different colors

Case 1: All 3 pads the same color

Stage 1: Select a size
There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 1 color (to be applied to all 3 pads)
There are 4 possible colors from which to choose, so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)

Case 2: The 3 pads are 3 different colors

Stage 1: Select a size
There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 3 different colors
There are 4 possible colors, and we must choose 3 of them.
Since the order of the selected colors does not matter, we can use combinations.
We can select 3 colors from 4 colors in 4C3 ways (4 ways), so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)

So, both cases can be completed in a total of 8 + 8 ways = 16

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
Hi Bunuel,

I can't understand this question or any of the solutions one bit, can you please help me..

Bunuel wrote:
anilnandyala wrote:
bunuel can you make me more clear, how it is 4 books of same colour

thank u

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.

Hope it's clear.
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Re: A certain office supply store stocks 2 sizes of self-stick notepads [#permalink]
AKhannaLko wrote:
Hi Bunuel,

I can't understand this question or any of the solutions one bit, can you please help me..

Bunuel wrote:
anilnandyala wrote:
bunuel can you make me more clear, how it is 4 books of same colour

thank u

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.