Number System


  1. The sum of 5 consecutive numbers is equal to 170. what is the product of largest and smallest numbers ?









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    Let smallest number = x.
    Then, x + x + 1 + x + 2 + x + 3 + x + 4 = 170

    Correct Option: C

    Let smallest number = x.
    Then, x + x + 1 + x + 2 + x + 3 + x + 4 = 170
    ⇒ 5x + 10 = 170
    ⇒ x = 160 / 5
    ⇒ x = 32

    ∴ product of smallest and largest number = 32 x 36
    = 1152


  1. Which of the following number always divides the difference between the square of two consecutive odd numbers ?









  1. View Hint View Answer Discuss in Forum

    Let the two consecutive odd numbers be 2x+1 and 2x + 3 .

    Correct Option: C

    Let the two consecutive odd numbers be 2x+1 and 2x + 3 .
    ∴ Difference = ( 2x + 3 )2 - ( 2x + 1 )2
    = ( 2x + 3 + 2x + 1 )( 2x + 3 - 2x - 1 )
    =( 4x + 4 ) x 2
    = 8 (x + 1)
    whis is exactly divisible by 8.



  1. 9856 x 156 + 9856 x 844 = ?









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    156 + 844 = 1000

    Correct Option: A

    9856 x 156 + 9856 x 844 = 9856 x (156 + 844)
    = 9856 x 1000
    = 9856000


  1. 6674 x 625 =?









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    6674 x 625 = 6674 x (5)4

    Correct Option: D

    6674 x 625 = 6674 x (5)4
    = 6674 x (104/24
    = 66740000/16 = 4171250



  1. 9998 x 999 = ?









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    999 = 1000 -1

    Correct Option: B

    Exp.= 9998 x 999
    = 9998 x (1000-1)
    = 9998 x 1000 - 9998 x 1
    = 9998000 - 9998 = 9988002