The sum of the 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: C
Let the second number be \(x\). Then, first number \(= 2x\) and third number \(= \dfrac{2x}{3}\)
\(2x + x + \dfrac{2x}{3} = 264\\
\Rightarrow \dfrac{11x}{3} = 264\\
\Rightarrow x = 72\)
Please log in or register to report this question.
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
Answer: D
Let the ten's digit be \(x\) and unit's digit be \(y\)
Then, number \(10x + y\)
Number obtained by interchanging the digits \(= 10y + x\)
\((10x + y) + (10y + x) = 11(x + y)\)
which is divisible by 11
Please log in or register to report this question.
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Answer: B
Let the ten's digit be \(x\) and unit's digit be \(y\)
Then,
\((10x + y) - (10y + x) = 36\\
\Rightarrow 9(x - y) = 36\\
\Rightarrow x - y = 4\)
Please log in or register to report this question.
Sum of a rational number and its reciprocal is \(\dfrac {13}{6}\). Find the number.
Answer: B
Let,
\(x + \dfrac{1}{x} = \dfrac{13}{6}\\
\Rightarrow \dfrac{x^2+1}{x} = \dfrac{13}{6}\\
\Rightarrow 6x^2-13x+6 = 0\\
\Rightarrow 6x^2-9x-4x+6 = 0\\
\Rightarrow (3x-2)(2x-3)\\
\Rightarrow x = \dfrac{2}{3} \text{ or } \dfrac{3}{2}\)
Please log in or register to report this question.
The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
Answer: B
Let the numbers be \(a\), \(b\) and \(c\).
Then,
\(a^2 + b^2 + c^2 = 138\\
\text{and}\\
ab+bc+ca = 138\\
(a + b + c)^2\\
= a^2 + b^2 + c^2 + 2(ab + bc + ca)\\
=138 + 2 \times 131\\
= 400\\
\therefore (a + b + c) = \sqrt{400} = 20\)
Please log in or register to report this question.
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
Answer: D
If the number is \(x\)
Then,
\(x + 17 = \dfrac{60}{x}\\
x^2 + 17x - 60 = 0\\
(x + 20)(x - 3) = 0\\
x = 3, -20\\
\text{so } x = 3 (\because 3 \text{ is positive})\)
Please log in or register to report this question.
The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?
Answer: B
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let the ten's and unit's digits be \(2x\) and \(x\) respectively.
Then, \((10 \times 2x + x) - (10x + 2x) = 36\)
\(9x = 36\\
x = 4\)
Required difference
\(= (2x + x) - (2x - x)\\ = 2x\\ = 8\)
Please log in or register to report this question.
