# Problems on Numbers Questions Answers

Problems on Numbers Questions Answers (MCQ) listings with explanations which includes questions on simplification of numbers, simplify questions, evaluation questions and other important types which are useful in competitive exams.

1) Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the numb

• 1) 5
• 2) 15
• 3) 7.5
• 4) 4
Ans.   A
Explanation :
Let the number be x. 7x -15 = 2x + 10 => 5x = 25 => x = 5

2) Sum of a rational number and its reciprocal is 13/6. Find the numb

• 1) 2
• 2) 3/2
• 3) 4/2
• 4) 5/2
Ans.   B
Explanation :
\begin{aligned} => x + \frac{1}{x} = \frac{13}{6} \end{aligned} \begin{aligned} => \frac{x^2+1}{x} = \frac{13}{6} \end{aligned} \begin{aligned} => 6x^2-13x+6 = 0 \end{aligned} \begin{aligned} => 6x^2-9x-4x+6 = 0 \end{aligned} \begin{aligned} => (3x-2)(2x-3) \end{aligned} \begin{aligned} => x = 2/3 or 3/2 \end{aligned}

3) find the number, difference between number and its 3/5 is 5

• 1) 120
• 2) 123
• 3) 124
• 4) 125
Ans.   D
Explanation :
Let the number = x, Then, x-(3/5)x = 50, => (2/5)x = 50 => 2x = 50*5, => x = 125

4) 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

• 1) 15
• 2) 20
• 3) 25
• 4) 35
Ans.   B
Explanation :
Let the numbers be a, b and c. Then, \begin{aligned} a^2 + b^2 + c^2 = 138 \end{aligned} and (ab + bc + ca) = 131 \begin{aligned} (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) \end{aligned} = 138 + 2 x 131 = 400 \begin{aligned} => (a + b + c) = \sqrt{400} = 20. \end{aligned}

5) If one third of one fourth of number is 15, then three tenth of number

• 1) 34
• 2) 44
• 3) 54
• 4) 64
Ans.   C
Explanation :
Let the number is x, \begin{aligned} \frac{1}{3} of\frac{1}{4} * x = 15 \end{aligned} \begin{aligned} => x = 15\times 12 = 180 \end{aligned} \begin{aligned} => so \frac{3}{10} \times x = \frac{3}{10} \times 180 = 54 \end{aligned}

6) A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that numb

• 1) 8
• 2) 10
• 3) 12
• 4) 14
Ans.   A
Explanation :
=> 3(2x+9) = 75 => 2x+9 = 25 => x = 8

7) Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the numb

• 1) 17
• 2) 15
• 3) 8
• 4) 3
Ans.   D
Explanation :
If the number is x, Then, x + 17 = 60/x x2 + 17x - 60 = 0 (x + 20)(x - 3) = 0 x = 3, -20, so x = 3 (as 3 is positive)

8) The product of two numbers is 120 and the sum of their squares is 289. The sum of the number

• 1) 20
• 2) 23
• 3) 27
• 4) 150
Ans.   B
Explanation :
We know \begin{aligned} (x + y)^2 = x^2 + y^2 + 2xy \end{aligned} \begin{aligned} => (x + y)^2 = 289 + 2(120) \end{aligned} \begin{aligned} => (x + y) = \sqrt{529} = 23 \end{aligned}

9) Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer

• 1) 12
• 2) 13
• 3) 15
• 4) 17
Ans.   C
Explanation :
Let the three integers be x, x+2 and x+4. Then, 3x = 2(x+4)+3, x= 11 Therefore, third integer x+4 = 15

10) Find the number which when multiplied by 15 is increased by

• 1) 10
• 2) 12
• 3) 14
• 4) 16