Number Puzzle - Involving Triangles


 
 
Concept Explanation
 

Number Puzzle - Involving Triangles

Number Puzzle : Problems involving Triangles:

  • In these types of problems, three triangles will be given numbers outside and inside.
  • The number inside will be obtained by operating some arithmetic rule on the numbers outside the triangle.
  • Generally, the numbers outside the triangle are the three vertices.
  • The number inside the third triangle also follows the same rule as that of the first two triangles.
  • Various Types of Relationships

    (i) n (a + b + c) = d, where n is a number

    (ii) frac{(a+b+c)}{n}=d

    (iii) (frac{abc}{n})=d

    (iv) sqrt{a^{2}+b^{2}+c^{2}}=d

    (v) sqrt[3]{a}+sqrt[3]{b}+sqrt[3]{c}=d

    Example : Find the missing number:

    A. 34               B. 27                 C. 28                D. 29

    Answer : 29

    Explanation : The product of the two largest numbers minus the square of the smallest. It can be explained as :

    Triangle 1 : Product of Two Largest numbers = 7 X 5 = 35

    Square of third smalled number = large 3^2 = 9 . So answer will be 35 - 9 = 26.

    Applying this rule in the forth triangle : Product of largest two numbers = 5 X 9 = 45. Subtracting the square of smallest third number = large 4^2 16

    , So the missing number is 45 -16 = 29

    Example : Find the missing number

    A.  9            B.  10                   C.  11               D.  12

    Answer : 9

    Explanation : In each triangle, multiply the lower two numbers together and add the upper number to give the value in the centre.

    In triangle 1 : Multiply lower two numbers (numbers at the base) = 6 X 2 = 12

    Add the third number = 12 + 7 = 19

    Similarly in triangle 3 : Multiply lower two numbers = 2 x y (let the unknown be y)

    Add the third number = 2y + 5 = 23

    Subtracting 5 from both sides : 2y + 5 - 5 = 23 - 5

    2y = 18

    y = 9. Hence answer is 9.

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Which number replaces the question mark (?)

    Right Option : B
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    Explanation
    Question : 2

    Which number replaces the question mark (?)

    Right Option : B
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    Explanation
    Question : 3

    Which number replaces the question mark (?)

    Right Option : A
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    Explanation
     
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