Mathematical Number Quiz

apocalypticdreaming · 11:40 PM

Based on information provided to you about a number, you have to say what that number is. Though a pencil and paper might be helpful, they aren't strictly necessary.

Total 10 Questions. For each correct answer you will get 10 points. Anyone can give the answer anytime within 1 week. Everyone will pm the answer to the quiz master.
Quiz master will post the result. If more than one participate get same maximum points, quiz master will arrange one more quiz for them. This time it will be 5 questions quiz, and difficult then before. Winner will be the next quiz master. He/she will arrange the next quiz.

Now see, if I get any respond.

February 6, 08 6.25 PM GMT

1. A natural number is doubled when added to its reciprocal. Find that number!
a) 1/2
b) 2
c) 1
d) 0

2. The logarithm (base ten) of five hundred times an integer is three. Find that number!
a) 450
b) 8
c) 1500
d) 2

3. A natural number is halved when reduced by thirteen. Find that number!
a) 123
b) 57
c) 26
d) 523

4. Twice a negative integer is eight less than its square. Find that number!
a) 16
b) 8
c) -2
d) -64

5. A positive integer is equal to 4 times its reciprocal. Find that number!
a) 9
b) -4
c) 2
d) 3

6. The sum of the square of a negative integer and itself is zero. Find that number!
a) 0
b) -1
c) -2
d) -1/2

7. The product of a positive integer and the integer that succeeds it is twelve. Find that number!
a) 27
b) 5
c) 3
d) 26

8. The digit in the units place of a two-digit number exceeds that in the tens place by one. If the number is equal to four times the sum of its digits, find that number!
a) 19
b) 91
c) 392
d) 12

9. A number added to twice itself gives twenty-one. Find that number!
a) 9
b) 36
c) 7
d) 42

10. The fourth power of a positive integer is equal to four times its square. Find that number!
a) 4
b) 0
c) 2
d) 1

Deadline: February 13, 2008

**mina** · February 6th, 2008, 10:53 PM

eishob ki tumi feb 6 deadline dile ki hobe naki...khelbona...time barao

apocalypticdreaming · February 6th, 2008, 11:45 PM

Well.
I announced the quiz in 6 February.
Deadline: 13 February.

**mina** · February 27th, 2008, 10:33 PM

eije results koi???

Vor · February 27th, 2008, 11:25 PM

let me try

1 - c
2 - d
3 - c
4 - c
5 - c
6 - b
7 - c
8 - d
9 - c
10 - c

apocalypticdreaming · February 27th, 2008, 11:35 PM

1. A natural number is doubled when added to its reciprocal. Find that number!

The correct answer: 1.

Let the number be "x". This gives:

x + 1/x = 2x
=> 1/x = 2x - x
=> 1/x = x
=> x^2 = 1
=> x = [plus or minus] 1

Since x is a natural number, it has to be positive; therefore x = 1.

(In case you didn't know, the carat ( ^ ) sign is used before exponential powers, e.g., "seven cubed" is written as "7^3".)

2. The logarithm (base ten) of five hundred times an integer is three. Find that number!

The correct answer: 2

Let the unknown number be "x".

log(500x) = 3

Notice that 3 can be written as "log(1000)", because 10^3 = 1000. Substituting "3" with "log(1000)",

log(500x) = log(1000)

Cancelling log from both sides,

500x = 1000
=> x = 2

And so the value of the integer is 2.

3. A natural number is halved when reduced by thirteen. Find that number!

The correct answer: 26.

Let the number be "x". (Pardon me for using "x" each time to represent the unknown quantity, just don't want to deviate from tradition.)

x - 13 = (1/2)x
=> x - (1/2)x = 13
=> (2x - x)/2 = 13
=> x/2 = 13
=> x = 26

4. Twice a negative integer is eight less than its square. Find that number!

The correct answer: -2

Let the number be "x". According to the given data:

2x = x^2 - 8
=> x^2 - 2x - 8 = 0
=> x^2 - 4x + 2x - 8 = 0
=> x(x - 4) + 2(x - 4) = 0
=> (x + 2)(x - 4) = 0

This gives x = -2 or x = 4. However, as it's a negative integer we're looking for, 4 cannot be the answer, which means it is -2.

5. A positive integer is equal to 4 times its reciprocal. Find that number!

The correct answer: 2.

Let tbe positive integer be "x". This means its reciprocal is (1/x).

x = 4(1/x)
=> x = 4/x
=> x^2 = 4
=> x = 2 or -2

Since "x" is supposed to be positive, the number is 2.

6. The sum of the square of a negative integer and itself is zero. Find that number!

The correct answer: -1.

Let the negative integer be "x".

x^2 + x = 0
=> x(x + 1) = 0
=> x = 0 or -1

As we're looking for a negative integer, -1 is the answer.

7. The product of a positive integer and the integer that succeeds it is twelve. Find that number!

The correct answer: 3.

Let the unkown number be "x". Therefore, the number that succeeds it is (x + 1). According to what's given,

x(x + 1) = 12
=> x^2 + x = 12
=> x^2 + x - 12 = 0

Factorising the left hand side of this quadratic equation,

(x - 3)(x + 4) = 0

This gives x = 3 or -4. However, since it's a positive integer we're looking for, we reject x = -4, thus leaving only x = 3 as a possible answer.

8. The digit in the units place of a two-digit number exceeds that in the tens place by one. If the number is equal to four times the sum of its digits, find that number!

The correct answer: 12

Let the digit in the tens place be "x". Since the digit in the units place exceeds that in the tens place by 1, it becomes (x + 1).

The sum of the digits = x + x + 1 = 2x + 1

Any two-digit number can be expressed in the following manner: 10*(digit in the tens place) + (digit in the units place)
e.g. 34 = 10*3 + 4; 71 = 10*7 + 1

Thus, the number we are seeking can be expressed as [10x + (x + 1)].

According to the given data,

4(2x + 1) = 10x + (x + 1)
=> 8x + 4 = 10x + x + 1
=> 3x = 3
=> x = 1

Hence, the digit in the tens place is 1. The digit in the units place is given by (x + 1) = 1 + 1 = 2.

And so the number is 12.

9. A number added to twice itself gives twenty-one. Find that number!

The correct answer: 7.

Let the number be "x".

x + 2x = 21
=> 3x = 21
=> x = 7

Whoever said algebra was tough? :-)

10. The fourth power of a positive integer is equal to four times its square. Find that number!

The correct answer: 2.

Let the number be "x". This gives:

x^4 = 4x^2
=> (x^2)^2 = 4(x^2)

To make things simple, let x^2 = y.

=> y^2 = 4y
=> y^2 - 4y = 0
=> y(y - 4) = 0
=> y = 0 or 4

If y = 0 then x = 0 and if y = 4 then x = 2 (because two squared equals four). Since it is given that x is a positive integer (which 0 isn't), the number is 2.

I hope this quiz helped exercise your grey matter and you had some good minutes to playing it, Mina Aapu. Yes you are the winner. People did not get any interest with it. So I totally forgot about this. Anyway thanks to you. As now you are the Quiz Master, now you decide, what you wanna do, if you want you can start a new quiz. But I do not think people has any interest here.

**mina** · February 28th, 2008, 12:16 AM

Ofcourse we do....next time when you open something like this quiz type...let me know i will make this as a sticky....so we all will notice. cuz this thread was in 3rd page. even you forgot right...

YAY me winnnerrrrrrrrrrrrrrr

what do i get?

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The Following User Says Thank You to apocalypticdreaming For This Useful Post:
mina (February 6th, 2008)

The Following User Says Thank You to apocalypticdreaming For This Useful Post:
mina (February 7th, 2008)