Arithmetic aptitude :: Problems on Numbers :: General Questions

• Problems on Numbers - General Questions
• Problems on Numbers - Important Formulas and Facts

Basic Formulae:
1). $(a+b)(a-b)=(a^{2}-b^{2})$.
2). $(a+b)^{2}=(a^{2}+b^{2}+2ab)$.
3). $(a-b)^{2}=(a^2+b^{2}-2ab)$.
4). $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$.
5). $(a^{3}+b^{3})=(a+b)(a^{2}-ab+b^{2})$.
6). $(a^{3}-b^{3})= (a-b)(a^{2}+ab+b^{2})$.
7). $(a^{3}+b^{3}+c^{3}-3abc)=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ac)$.
8). When $a+b+c = 0$, then $a^{3}+b^{3}+c^{3}=3abc$.

A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is :

Answer:

Explanation:

Let the numbers be $x$.
Then, $x-4=\frac{21}{x}$
$\Leftrightarrow x^{2}-4x-21=0$
$\Leftrightarrow (x+7)(x+3)=0$
$\Leftrightarrow x =7$.

The sum of a number and its reciprocal is one-eighth of 34. What is the product of the number and its square root ?

Answer:

Explanation:

Let the numbers be $x$.
Then, $x+\frac{1}{x}=\frac{34}{8}$
$\Leftrightarrow 8x^{2}-34x+8=0$
$\Leftrightarrow 4x^{2}-17x+4 = 0$
$\Leftrightarrow (4x-1)(x-4) = 0$
$\Leftrightarrow x =4$.
neglecting $x=\frac{1}{4},$ as x is a natural number.
$\therefore$ Required Number $=4 \times \sqrt{4}= 4 \times 2 = 8$.

Twenty times a positive integer is less than its square by 96. What is the integer ?

Answer:

Explanation:

Let the integer be $x$.
Then, $x^{2}-20x-96=0$
$\Leftrightarrow (x+4)(x-24)=0$
$\Leftrightarrow x = 24$.

If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is :

Answer:

Explanation:

Let the number be $x$.
Then, $2x+20=8x-4$
$\Leftrightarrow 6x = 24$
$\Leftrightarrow x = 4$.

If one-seventh of a number exceeds its eleventh part by 100, then the number is :

Answer:

Explanation:

Let the number be $x$.
Then, $\frac{1}{7}x-\frac{1}{11}x=100$
$\Leftrightarrow \frac{4x}{77} = 100$
$\Leftrightarrow x = \frac{7700}{4}=1925$.

• Problems on Numbers - General Questions