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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

No problem.

*Last edited by ShivamS (2014-05-25 04:28:08)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi ganesh;

That is okay.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi ShivamS and bobbym,

The solution #4990 is perfect. Marvelous!

#4991. Find the greatest number of five digits which is a perfect square.

#4992. Find the smallest number that must be added to 1780 to make it a perfect square.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solutions #4991 and #4992 are correct. Excellent!

#4993. If

, find the value of .#4994. If

and , find the value of .Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

Are we allowed to use a calculator? The only way of solving

#4991. Find the greatest number of five digits which is a perfect square.

in 10 seconds is by taking the square root of 99999 and then squaring 316.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

You could know that the square root of 10 is about 3.16, now you can easily get the square root of 100000

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym and ShivamS,

The solutions #4993 and #4994 are correct. Brilliant, bobbym!

ShivamS, the complete

#4995. Solve the following system of equations :

and#4996. Solve the following system of equations : 11x - 7y = xy and 9x - 4y = 6xy.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi ShivamS,

Solution : #4991.

The greatest number of 5 digits is 99999.

316 x 316 + x = 99999

(knowing square root of 10 = 3.16)

Required number = (99999 - 143) = 99856.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solutions #4995 and #4996 are correct. Excellent!

#4997. Find the value of

#4998. Find the value of x.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solution #4998 is perfect. Remarkable!

#4999. Find the value of x.

#5000. Find the value of x.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi ganesh;

Can you explain what you mean by 6.25 of x? I have been treating it as x.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

In the problems #4999 and #5000, the operation '6.25 of x' is to be treated as

; and is to be treated in a similar way. However, the priority is foremost on 'of' operation, followed by division, then multiplication.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Okay, thanks for the explanation, I will try the problems.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

#5001. Find the value of x.

#5002. Find the value of x.

.Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solutions #4999 and #5000 are perfect. Remarkable!

The only problems to be solved in '10 second questions' are #5001 and #5002.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solutions #5001 and #5002 are correct. Fantastic performance!

#5003. If

, find the value of.#5004. Find the difference between

and its reciprocal.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solutions #5003 and #5004 are correct. Marvelous!

#5005. When a ball bounces, it rises to

of the height from which it fell. If the ball is dropped from a height of 32 meters, how high will it rise at the third bounce?#5006. A person travels 3.5 kilometers from place A to B. Out of this distance, he travels

kilometer on bicycle, kilometer on motorbike and the rest on foot. What portion of the whole distance does he cover on foot?Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,367

Hi bobbym,

The solution #5005 is correct. Excellent!

The solution #5006 is also correct; The required distance on foot =

kilometer.The required fraction = .

#5007. Simplify :

.Character is who you are when no one is looking.

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