Rows and Columns

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ifairo: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sun Nov 30, 2008 1:44 pm; Thanked: 2 times

by ifairo » Fri Dec 19, 2008 8:20 pm

There are 100 soldiers. In how many different rows and columns these soldiers can be arranged?

Some ways:
1) 1, 100 => 1 row, 100 columns.
2) 2, 50 => 2 rows, 50 columns.
...
...
n-1) 50, 2 => 50 rows, 2 columns
n) 100, 1 => 100 rows, 1 column

Best answer can be applied to any number of soldiers - say, 955, 15555, 20000, etc.

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Source: Beat The GMAT — Problem Solving | Fri Dec 19, 2008 8:20 pm

720dreaming: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon Dec 08, 2008 9:55 pm; Thanked: 4 times

by 720dreaming » Fri Dec 19, 2008 8:27 pm

I am getting 10. Two numbers must multiple to make 100.

1*100
2*50
4*25
5*20
10*10.

You can also reverse the rows/columns, so have

100*1, 50*2, etc.

Is this a question from an outside source?

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ifairo: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sun Nov 30, 2008 1:44 pm; Thanked: 2 times

Rows and Columns

by ifairo » Fri Dec 19, 2008 8:32 pm

I don't know the source of this question.

It would be good if we can form an approach to handle any kind of number - say a value which is larger than 100.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: Rows and Columns

by logitech » Fri Dec 19, 2008 8:35 pm

ifairo wrote:There are 100 soldiers. In how many different rows and columns these soldiers can be arranged?

Some ways:
1) 1, 100 => 1 row, 100 columns.
2) 2, 50 => 2 rows, 50 columns.
...
...
n-1) 50, 2 => 50 rows, 2 columns
n) 100, 1 => 100 rows, 1 column

Best answer can be applied to any number of soldiers - say, 955, 15555, 20000, etc.

Let's work with a small number to understand the logic behind the solution. How about 10 soldiers:

10x1
5x2
2x5
1x10

so 4 ways! If you look closely, you will see that 10,5,2 and 1 are factors of 10. So actually we are being asked to find the number of factors

for 100 soldiers:

100 = 2x2x5x5 = 2^2 x 5 ^2

# factors = (2+1) x (2+1) = 9

100x1
50x2
25x4
20x5

10x10

5x20
4x25
2x50
1x100

P.S. for perfect squares, the # factors will always be ODD number!

n....1.....n = 2n+1

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Fri Dec 19, 2008 8:37 pm

720dreaming wrote:I am getting 10. Two numbers must multiple to make 100.

1*100
2*50
4*25
5*20
10*10.

You can also reverse the rows/columns, so have

100*1, 50*2, etc.

Is this a question from an outside source?

you counted 10x10 two times!

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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ifairo: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sun Nov 30, 2008 1:44 pm; Thanked: 2 times

Rows and Columns

by ifairo » Fri Dec 19, 2008 8:47 pm

Factors of 100 = 2 * 2 * 5 * 5

# factors = (2+1) x (2+1) = 9

Can you please help me how you got this (2+1) * (2+1)? I see there are two 2s, and two 5s. But, why do you add 1 and multiply. Please clarify.

I think, you answer seems to be working for many numbers, but since the part I am asking here is not clear to me, I am not confident that this will work for every possible number. Please help.

Thanks.

[/quote]

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: Rows and Columns

by logitech » Fri Dec 19, 2008 9:00 pm

ifairo wrote:Factors of 100 = 2 * 2 * 5 * 5

# factors = (2+1) x (2+1) = 9

Can you please help me how you got this (2+1) * (2+1)? I see there are two 2s, and two 5s. But, why do you add 1 and multiply. Please clarify.

I think, you answer seems to be working for many numbers, but since the part I am asking here is not clear to me, I am not confident that this will work for every possible number. Please help.

Thanks.

[/quote]

Lets just say it is a rule...just add 1 and multiply. The derivation of the formula is out of scope in GMAT land.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Sat Dec 20, 2008 1:04 am

so 4 ways! If you look closely, you will see that 10,5,2 and 1 are factors of 10. So actually we are being asked to find the number of factors

PERFECT catch wizard!!!!

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