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 $a^{3}+b^{3}+c^{3}=3abc$.

The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :

Answer:

Explanation:

Let the numbers be $x$ and $y$. Then,
$\frac{x+y}{x-y}=\frac{40}{4}=10$
$\Leftrightarrow (x+y)=10(x-y)$
$\Leftrightarrow 9x = 11y \Leftrightarrow \frac{x}{y} = \frac {11}{9}$

The sum of two numbers is 25 and their difference is 13. B'ind their product.

Answer:

Explanation:

Let the numbers be $x$ and $y$. Then,
$x+y=25$ and $x-y=13$.
$4xy=(x+y)^{2}-(x-y)^{2}$
$=(25)^{2}-(13)^{2}=625-139=456$
$\Rightarrow xy = 114$.

The sum of three numbers is 264. If, the first number be twice the second and third number be one-third of the first, then the second number is :

Answer:

Explanation:

Let the numbers be $x$. Then, first number $= 2x$ and third number $=\frac{2x}{3}$.
$\therefore 2x+x+\frac{2x}{3}=264$.
$\Leftrightarrow x = \left(\frac{264 \times 3}{11}\right)=72$.

Three numbers are in the ratio of 3 : 4 : 6 and their product is 1944. The largest of these numbers is :

Answer:

Explanation:

Let the numbers be $3x$, $4x$ and $6x$.
Then, $3x \times 4x \times 6x = 1944$
$\Leftrightarrow x^{3}=27 \Leftrightarrow x = 3$
$\therefore$ Largest number $=6x=18$.

Three numbers are in the ratio 4:5:6 and their average is 25. The largest number is :

Answer:

Explanation:

Let the numbers be $4x$, $5x$ and $6x$.
Then, $\frac{4x+5x+6x}{3}=25$
$\Leftrightarrow 5x = 25 \Leftrightarrow x = 25$.
$\therefore Largest number = 6x = 30$.

• Problems on Numbers - General Questions