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Note for Members of Math Is Fun Forum: This mathematics question paper appeared in a screening test which I am forbidden to describe published by an organization which I am forbidden to describe. It is meant for 15-16 year old people. I have been told that most people who appeared for this test did not do much well. I am putting this up because I thought this up here because I thought that this is the best place to share a latex document with a few of my friends on the internet who are not (active) members over here. You may try working this out if you wish

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Maximum Marks - 50

Time - 1 hr

Instructions:-

i) Q 1 to Q 10 carry 2 marks each. Q 11 to Q 16 carry 5 marks each

ii) [comment removed by Agnishom]

iii) [comment removed by Agnishom]

1. If 15% of a number is 45, Find the number.

2. What percent is 450 m of 2.5 km?

3. Divide

by .4. If first, second and fourth terms of a proportion are 1/2,1/3,1/6 respectively, then find the third term.

5. If 8 men can do a piece of work in 15 days, then how many men are required to do the same piece of work in 10 days?

6. A man sold some items at Rs 6000, at a loss of 33.33...%. Find the cost price.

7. Divide the sum of

and by the product of and8. The HCF and LCM of two numbers are 6 and 840 respectively. If one of the numbers is 42, find the other number.

9. Find the value of tan[sup]2[/sup]60°+4 cos[sup]2[/sup]45°+3sec[sup]2[/sup]30° + 5 cos[sup]2[/sup]90°

10. What is the amount whose 24% is Rs 105?

11. If A, B, A+B, A-B are positive acute angles, find the values of A and B solving the following system:

12. If sin[sup]2[/sup] :theta + sin[sup]4[/sup] :theta = 1, then what is the value of tan[sup]4[/sup] :theta - tan [sup]2[/sup] :theta ?

13. Find the point on the line through A(-5,-4) and B(2,3) that is twice as far from A as from B

14. How many terms are identical in the two Arithmetic Progressions 2,4,6,8,... upto 100 terms and 3,6,9,12... upto 80 terms?

15. In a family, there are three children. Assuming that the chances of a child being male or female are equal, find the probability that the family has atleast one male child.

16. In a bag containing black and white balls, half the number of white balls is equal to a third of the number of black balls; and twice the whole number of balls exceeds three times the number of black balls by four. How many balls does the bag contain?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Hi;

I like 13) (- 1 / 3 , 2 / 3 )

**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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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

Yes. I am curious if the test designer intended that point or the other one. Probably the other, since it has integer coordinates. Either way, they apparently missed that there are two solutions.

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 179

1) = 300 because 45 * 4 - 180 = 60%, 180/60 = 3 = 1%

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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bobbym wrote:

Hi;

I like 13) (- 1 / 3 , 2 / 3 )

The other is (9,10)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,853

1.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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PatternMan and Phrontister, you are correct. But I do not understand PatternMan's Calculation.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,853

Neither do I, which is why I posted mine.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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Try Question 14

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

14) 33

15) 7 / 8

16) White balls = 8, black balls = 12.

**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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Are you ready to see the science paper of the same series?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

On 14, The intersection of two arithmetic series is the arithmetic series of the least common multiple. In this case, 6. Since the first series stops at 200, and the second at 240, the question becomes: how many multiples of 6 are there <= 200, which is [200/6] = 33.

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,610

Most people here can tell from where this paper is from by reading the instructions - at least those who are Indian.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

How about if you are not Indian?

**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: 3,610

Then maybe you can google it.

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ShivamS wrote:

Most people here can tell from where this paper is from by reading the instructions - at least those who are Indian.

How?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

The Rs 6000 is a giveaway.

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

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Will you buy it?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Depends on what it is.

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

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Ruby shoes?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Oh yes, they are worth a lot of money, Rs 6000 is about 100 dollars.

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

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Would you buy 100 kg onions for that amount?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

That would be a cheap price here.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Hi Agnishom

*Last edited by anonimnystefy (2014-05-04 00:22:15)*

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Thanks for putting up your efforts to do these problems

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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