A multiple-choice quiz
by achernar.
Estimated time: 4 mins.

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Scroll down to the bottom for the answer key.

Quiz Answer Key and Fun Facts

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".)

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".)

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.

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

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.

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.

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.

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.

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.

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? :-)

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.

===

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

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 a good time playing it!

This quiz was reviewed by FunTrivia editor crisw before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

Most Recent Scores

Jan 16 2023
:
Guest 112: 0/10Jan 02 2023 : TERRYROYHURST: 0/10

Dec 23 2022 : Guest 76: 1/10

Dec 20 2022 : Vendetta125: 7/10

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