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Aptitude miscellaneous
  1. The sum of four consecutive even numbers is 748. The smallest among them is








  1. View Hint View Answer Discuss in Forum

    x + x + 2 + x + 4 + x + 6 = 748
    ⇒  4x + 12 = 748
    ⇒  4x = 748 – 12 = 736

    ⇒  x =
    736
    		 = 184
    4

    Correct Option: C

    x + x + 2 + x + 4 + x + 6 = 748
    ⇒  4x + 12 = 748
    ⇒  4x = 748 – 12 = 736

    ⇒  x =
    736
    		 = 184
    4

  1. The sum of all even numbers between 21 and 51 is








  1. View Hint View Answer Discuss in Forum

    22 + 24 + 26 + ... + 50
    = 2 (11 + 12 + 13 + .... + 25)
    = 2 [(1 + 2 + 3 + ... + 25) – (1 + 2 + 3 ... + 10)]

    = 2
    25 × 26
    		 −
    10 × 11
    22

    = 2 (325 – 55) = 2 × 270 = 540
    Method 2 :

    Sum of first n even numbers = n (n + 1)
    ∴  Required sum = Sum of 25
    even numbers from 1 to 50 – sum
    of 10 even numbers from 1 to 20
    = 25×26 – 10 × 11 = 650 – 110
    = 540

    Correct Option: B

    22 + 24 + 26 + ... + 50
    = 2 (11 + 12 + 13 + .... + 25)
    = 2 [(1 + 2 + 3 + ... + 25) – (1 + 2 + 3 ... + 10)]

    = 2
    25 × 26
    		 −
    10 × 11
    22

    = 2 (325 – 55) = 2 × 270 = 540
    Method 2 :

    Sum of first n even numbers = n (n + 1)
    ∴  Required sum = Sum of 25
    even numbers from 1 to 50 – sum
    of 10 even numbers from 1 to 20
    = 25×26 – 10 × 11 = 650 – 110
    = 540

  1. Which one of the following is a factor of the sum of first twentyfive natural numbers ?








  1. View Hint View Answer Discuss in Forum

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

    ∴  1 + 2 + 3 + .. + 25
    =
    25(25 + 1)
    		 = 25 × 13
    2

    Hence, 13 is a factor of required sum.

    Correct Option: C

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

    ∴  1 + 2 + 3 + .. + 25
    =
    25(25 + 1)
    		 = 25 × 13
    2

    Hence, 13 is a factor of required sum.

  1. Out of six consecutive natural numbers, if the sum of first three is 27, what is the sum of the other three ?








  1. View Hint View Answer Discuss in Forum

    x + x + 1 + x + 2 = 27
    3x + 3 = 27
    3x = 24
    x = 8
    ∴  Three consecutive no's whose sum is 27 are 8, 9,10. Hence, next 3 consecutive no's having 36 as sum are 11, 12 and 13

    Correct Option: A

    x + x + 1 + x + 2 = 27
    3x + 3 = 27
    3x = 24
    x = 8
    ∴  Three consecutive no's whose sum is 27 are 8, 9,10. Hence, next 3 consecutive no's having 36 as sum are 11, 12 and 13

  1. The sum of all the 3-digit numbers is








  1. View Hint View Answer Discuss in Forum

    First 3 – digit number = 100
    Last 3 – digit number = 999
    Number of terms = 900

    ∴  S =
    n
    		(a + 1)
    2

    =
    900
    		[100 + 999]
    2

    = 450 × 1099 = 494550

    Correct Option: B

    First 3 – digit number = 100
    Last 3 – digit number = 999
    Number of terms = 900

    ∴  S =
    n
    		(a + 1)
    2

    =
    900
    		[100 + 999]
    2

    = 450 × 1099 = 494550