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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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: 105,682

Hi ganesh;

That is okay.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

Hi bobbym,

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

#4993. If

, find the value of .#4994. If

and , find the value of .It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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: 105,682

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

Hi bobbym,

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

#4997. Find the value of

#4998. Find the value of x.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

Hi bobbym,

The solution #4998 is perfect. Remarkable!

#4999. Find the value of x.

#5000. Find the value of x.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi ganesh;

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

Hi bobbym,

#5001. Find the value of x.

#5002. Find the value of x.

.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

Hi bobbym,

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

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi ganesh;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,682

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,470

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 :

.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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