Find that Number! Trivia Quiz

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.

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

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.

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

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.

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.

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.

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.

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.

Answer: 7

Let the number be "x".

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

Whoever said algebra was tough? :-)

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.

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I hope this quiz helped exercise your grey matter and you had a good time playing it!