Number System


  1. 64329 is divided by a certain number. While dividing, the numbers, 175, 114 and 213 appear as three successive remainders. The divisor is









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    According to question ,

    Number at (i) = 643 – 175 = 468
    Number at (ii) = 1752 – 114 = 1638
    Number at (iii) = 1149 – 213 = 936

    Correct Option: C

    According to question ,

    Number at (i) = 643 – 175 = 468
    Number at (ii) = 1752 – 114 = 1638
    Number at (iii) = 1149 – 213 = 936
    Clearly, 468, 1638 and 936 are multiples of 234 and 234 > 213.
    ∴  Divisor = 234


  1. Which of the following number is NOT divisible by 18 ?









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    As we know that A number will be exactly divisible by 18 if it is divisible by 2 and 9 both. Clearly option ( d ) , 65043 is not divisible by 2.

    Correct Option: D

    As we know that A number will be exactly divisible by 18 if it is divisible by 2 and 9 both. Clearly option ( d ) , 65043 is not divisible by 2.
    ∴  Required number = 65043



  1. A number divided by 13 leaves a remainder 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65 ?









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    Let the least number be x.

    Correct Option: D

    Let the least number be x.

    y = 5 × 1 + 3 = 8
    x = 13 × 8 + 1 = 105
    On dividing 105 by 65,
    ⇒ 105 = ( 65 × 1 ) + 40
    Hence required remainder = 40


  1. When a number is divided by 893, the remainder is 193. What will be the remainder when it is divided by 47 ?









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    As per the given above question ,
    Here, 893 is exactly divisible by 47.
    Hence, the required remainder is obtained on dividing 193 by 47.

    Correct Option: B

    As per the given above question ,
    Here, 893 is exactly divisible by 47.
    Hence, the required remainder is obtained on dividing 193 by 47.
    ⇒ 193 = ( 47 × 4 ) + 5
    ∴  Remainder = 5



  1. A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is :









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    According to question ,
    The remainder will be same. On dividing 9 by 6, remainder = 3
    ∴ ( Number )2 = 92 = 81

    Correct Option: D

    According to question ,
    The remainder will be same. On dividing 9 by 6, remainder = 3
    ∴ ( Number )2 = 92 = 81
    On dividing 81 by 6
    ⇒ 81 = ( 6 × 13 ) + 3
    Hence , Required remainder = 3