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Aptitude miscellaneous
  1. When 231 is divided by 5 the remainder is








  1. View Hint View Answer Discuss in Forum

    We can write ,

    231 = (28)4 ÷ 2 = (256)4 ÷ 2 =  
    ......6
    		 = ......3
    2

    Correct Option: B

    We can write ,

    231 = (28)4 ÷ 2 = (256)4 ÷ 2 =  
    ......6
    		 = ......3
    2

    Clearly, the remainder will be 3 when divided by 5.
    Illustration :
    23 ÷ 5 gives remainder = 3
    83 ÷ 5 gives remainder = 3
    Hence required remainder is 3 .

  1. If 17200 is divided by 18, the remainder is—








  1. View Hint View Answer Discuss in Forum

    (17)200 = (18 – 1)200
    With the help of binomial theorem we solve this question ,

    (x + a)n =  xn + nxn–1.a +
    n (n − 1)
    		xn − 2a 2 +
    n (n − 1) (n − 2)
    		xn − 3a3 + .....+ an
    1 × 21 × 2 × 3

    Correct Option: C

    (17)200 = (18 – 1)200
    With the help of binomial theorem we solve this question ,

    (x + a)n =  xn + nxn–1.a +
    n (n − 1)
    		xn − 2a2 +
    n (n − 1) (n − 2)
    		xn − 3a3 + .....+ an
    1 × 21 × 2 × 3

    We see that all the terms on the R.H.S. except an has x as one of its factor and hence are divisible by x. So, (x + a)n is divisible by x or not will be decided by an.
    Let x = 18, a = – 1 and n = 200
    ∴  (18 – 1)200 is divisible by 18 or not will depend on (–1)200 as all other terms in its expansion will be divisible by 18 because each of them will have 18 as one of their factors.
    (–1)200 = 1 (∵ 200 is even)
    1 is not divisible by 18 and is also less than 18.
    ∴ 1 is the remainder.

  1. 96 – 11 when divided by 8 would leave a remainder of :










  1. View Hint View Answer Discuss in Forum

    If (p ± 1)n is divided by
    p, the remainder is (±1)n,

    Correct Option: E

    If (p ± 1)n is divided by
    p, the remainder is (±1)n,
    Now, 96 – 11 = (8 + 1)6 –11
    When it is divided by 8, remainder = + 1 – 11 = – 10
    When – 10 is divided by 8, remainder = – 2
    ⇒ – 2 + 8 = 6
    Therefore required remainder is 6 .

  1. When a number is divided by 36, the remainder is 19. What will be the remainder when the number is divided by 12 ?








  1. View Hint View Answer Discuss in Forum

    Here, the first divisor (36) is exactly divisible by the second divisor (12).

    Correct Option: A

    Here, the first divisor (36) is exactly divisible by the second divisor (12).
    ∴ Required remainder = Remainder obtained after 19 is divided by 12 ⇒ Required remainder = ( 19 × 1 ) + 7 , Where 7 is remainder .
    Hence Required remainder = 7

  1. A number when divided by 49 leaves 32 as remainder. This number when divided by 7 will have the remainder as








  1. View Hint View Answer Discuss in Forum

    Here, the first divisor ( 49 ) is multiple of second divisor ( 7 ).

    Correct Option: A

    Here, the first divisor ( 49 ) is multiple of second divisor ( 7 ).
    ∴ Required remainder = Remainder obtained on dividing 32 by 7 = 4
    Hence Required remainder = 4