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Aptitude miscellaneous
  1. The sum of three consecutive natural numbers each divisible by 5, is 225. The largest among them is








  1. View Hint View Answer Discuss in Forum

    Let the required largest number be x.
    According to the question,
    x + x – 5 + x – 10 = 225
    ⇒  3x – 15 = 225
    ⇒  3x = 225 + 15 = 240

    ⇒  x =
    240
    		 = 80
    3

    Correct Option: D

    Let the required largest number be x.
    According to the question,
    x + x – 5 + x – 10 = 225
    ⇒  3x – 15 = 225
    ⇒  3x = 225 + 15 = 240

    ⇒  x =
    240
    		 = 80
    3

  1. The sum of three consecutive natural numbers divisible by 3 is 45. The smallest number is :








  1. View Hint View Answer Discuss in Forum

    Let the numbers be : 3x, 3x + 3 and 3x + 6
    According to the question,
    3x + 3x + 3 + 3x + 6 = 45
    ⇒  9x + 9 = 45
    ⇒  9x = 45 – 9 = 36

    ⇒  x =
    36
    		 = 4
    9

    ∴  The smallest number
    = 3x = 3 × 4 = 12

    Correct Option: C

    Let the numbers be : 3x, 3x + 3 and 3x + 6
    According to the question,
    3x + 3x + 3 + 3x + 6 = 45
    ⇒  9x + 9 = 45
    ⇒  9x = 45 – 9 = 36

    ⇒  x =
    36
    		 = 4
    9

    ∴  The smallest number
    = 3x = 3 × 4 = 12

  1. Two positive whole numbers are such that the sum of the first number and twice the second number is 8 and their difference is 2. The numbers are :








  1. View Hint View Answer Discuss in Forum

    Let the numbers be x and y.
    According to the question,
    x + 2y = 8 .... (i)
    x – y = 2 ....... (ii)
    By equation (i) – (ii),
    2y + y = 8 – 2
    ⇒  3y = 6 ⇒ y = 2
    From equation (ii),
    x – 2 = 2 ⇒ x = 4

    Correct Option: C

    Let the numbers be x and y.
    According to the question,
    x + 2y = 8 .... (i)
    x – y = 2 ....... (ii)
    By equation (i) – (ii),
    2y + y = 8 – 2
    ⇒  3y = 6 ⇒ y = 2
    From equation (ii),
    x – 2 = 2 ⇒ x = 4

  1. What is the arithmetic mean of first 20 odd natural numbers ?








  1. View Hint View Answer Discuss in Forum

    Sum of first n odd natural numbers = n2 = (20)2 = 400

    Correct Option: D

    Sum of first n odd natural numbers = n2 = (20)2 = 400

    ∴  Required average =
    400
    		 = 20
    20

  1. Find the sum of all positive multiples of 3 less than 50








  1. View Hint View Answer Discuss in Forum

    Sum of all multiples of 3 upto 50
    = 3 + 6 + ..... + 48
    = 3 (1 + 2 + 3 + .... + 16)

    =
    3 × 16(16 + 1)
    		 = 3 × 8 × 17
    2

    = 408
    ∵  1 + 2 + 3 + .....+ n =
    n(n + 1)
    2

    Correct Option: C

    Sum of all multiples of 3 upto 50
    = 3 + 6 + ..... + 48
    = 3 (1 + 2 + 3 + .... + 16)

    =
    3 × 16(16 + 1)
    		 = 3 × 8 × 17
    2

    = 408
    ∵  1 + 2 + 3 + .....+ n =
    n(n + 1)
    2