Problems on Numbers Questions Answers

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

  1. 20
  2. 23
  3. 27
  4. 150

  Answer And Explanation

  Answer: Option 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}

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

  1. 12
  2. 13
  3. 15
  4. 17

  Answer And Explanation

  Answer: Option 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

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• 10. Find the number which when multiplied by 15 is increased by 196

  1. 10
  2. 12
  3. 14
  4. 16

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let the number be x.
  Then, 15x = x + 196
  =› 14 x= 196
  =› x = 14.

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• 11. if the sum of \begin{aligned} \frac{1}{2} \end{aligned} and \begin{aligned} \frac{1}{5} \end{aligned} of a number exceeds \begin{aligned} \frac{1}{3} \end{aligned} of the number by \begin{aligned} 7\frac {1}{3} \end{aligned}, then number is

  1. 15
  2. 20
  3. 25
  4. 30

  Answer And Explanation

  Answer: Option B

  Explanation:

  Seems a bit complicated, isnt'it, but trust me if we think on this question with a cool mind then it is quite simple...
  Let the number is x,
  then, \begin{aligned} (\frac{1}{2}x + \frac{1}{5}x) - \frac{1}{3}x = \frac{22}{3} \end{aligned}
  
  \begin{aligned}
  => \frac{11x}{30} = \frac{22}{3}
  \end{aligned}
  
  \begin{aligned}
  => x = 20
  \end{aligned}

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• 12. find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.

  1. 214
  2. 216
  3. 114
  4. 116

  Answer And Explanation

  Answer: Option B

  Explanation:

  Let the number is x,
  \begin{aligned}
  => \frac{2}{3}x-50 = \frac{1}{4}x + 40
  \end{aligned}
  
  \begin{aligned}
  <=> \frac{2}{3}x-\frac{1}{4}x = 90
  \end{aligned}
  \begin{aligned}
  <=> \frac{5x}{12} = 90
  \end{aligned}
  \begin{aligned}
  <=> x = 216
  \end{aligned}

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• 13. Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

  1. \begin{aligned} \frac{290}{289} \end{aligned}
  2. \begin{aligned} \frac{1}{289} \end{aligned}
  3. \begin{aligned} \frac{290}{90} \end{aligned}
  4. \begin{aligned} \frac{290}{19} \end{aligned}

  Answer And Explanation

  Answer: Option A

  Explanation:

  If the numbers are a, b, then ab = 17,
  as 17 is a prime number, so a = 1, b = 17.
  
  \begin{aligned} \frac{1}{a^2} + \frac{1}{b^2} =
  \frac{1}{1^2} + \frac{1}{17^2}
  \end{aligned}
  \begin{aligned} = \frac{290}{289}
  \end{aligned}

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• 14. Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is

  1. 70
  2. 71
  3. 72
  4. 73

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let the second number is x, then first is 2x, and third is 1/3(2x)
  \begin{aligned}
  =>2x + x + \frac{2x}{3} = 264 <=> \frac{11x}{3} = 264
  \end{aligned}
  
  \begin{aligned}
  => x = 72
  \end{aligned}

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