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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

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: 90,663

Hi ganesh;

That is okay.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 90,663

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

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: 90,663

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.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 90,663

Hi;

**In mathematics, you don't understand things. You just get used to them.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 15,164

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: 90,663

Hi;

**In mathematics, you don't understand things. You just get used to them.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 90,663

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.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 90,663

Hi;

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

**In mathematics, you don't understand things. You just get used to them.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 15,164

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: 90,663

Hi ganesh;

**In mathematics, you don't understand things. You just get used to them.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 90,663

Hi;

**In mathematics, you don't understand things. You just get used to them.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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: 90,663

Hi;

**In mathematics, you don't understand things. You just get used to them.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,164

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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