Simplification


  1. If x is a perfect square integer such that 7 < (2x – 3) < 17, then the value of x is :









  1. View Hint View Answer Discuss in Forum

    Check through options When x = 9,
    2x – 3 = 2 × 9 – 3 = 15 < 17

    Correct Option: C

    Check through options When x = 9,
    2x – 3 = 2 × 9 – 3 = 15 < 17


  1. The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is :









  1. View Hint View Answer Discuss in Forum

    Let the numbers be x and y.
    Then,
    x2 + y2 = 100      ...(i)
    x2 – y2 = 28      ...(ii)
    On adding,
    2x2 = 128
    ⇒  x2 = 64 ⇒ x = 8
    From equation (i),
    64 + y2 = 100
    ⇒  y2 = 36 ⇒ y = 6
    ∴  Required sum
    = 8 + 6 = 14

    Correct Option: C

    Let the numbers be x and y.
    Then,
    x2 + y2 = 100      ...(i)
    x2 – y2 = 28      ...(ii)
    On adding,
    2x2 = 128
    ⇒  x2 = 64 ⇒ x = 8
    From equation (i),
    64 + y2 = 100
    ⇒  y2 = 36 ⇒ y = 6
    ∴  Required sum
    = 8 + 6 = 14



  1. If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their squares is :









  1. View Hint View Answer Discuss in Forum

    Let x + y = 20 and
    x – y = 8
    ∴  (x + y) (x – y) = 20 × 8
    ⇒  x2 – y2 = 160

    Correct Option: D

    Let x + y = 20 and
    x – y = 8
    ∴  (x + y) (x – y) = 20 × 8
    ⇒  x2 – y2 = 160


  1. The number, whose square is equal to the difference between the squares of 975 and 585, is :









  1. View Hint View Answer Discuss in Forum

    Let the required number be x.
    As per given information,
    x2 = (975)2 – (585)2
    ⇒  x2 = (975 + 585) (975 – 585)
    ⇒  x2 = 1560 × 390
    ⇒  x = √1560 × 390
    = √13 × 12 × 3 × 13 × 10 × 10
    = 780

    Correct Option: A

    Let the required number be x.
    As per given information,
    x2 = (975)2 – (585)2
    ⇒  x2 = (975 + 585) (975 – 585)
    ⇒  x2 = 1560 × 390
    ⇒  x = √1560 × 390
    = √13 × 12 × 3 × 13 × 10 × 10
    = 780



  1. The sum of the squares of two numbers is 386. If one of the number is 5, the other will be :









  1. View Hint View Answer Discuss in Forum

    Let the required number be x. Then,
    x2 + 52 = 386
    ⇒  x2 = 386 – 25
    ⇒  x2 = 361
    ⇒  x = √361 =19

    Correct Option: B

    Let the required number be x. Then,
    x2 + 52 = 386
    ⇒  x2 = 386 – 25
    ⇒  x2 = 361
    ⇒  x = √361 =19