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Home Aptitude Simplification Comments

  • Question
  • 1/(1 x 4) + 1/(4 x 7) + 1/(7 x 10) + 1/(10 x 13) + 1/(13 x 16) =?


  • Options
  • A. 5/16
  • B. 3/16
  • C. 7/16
  • D. 11/16

  • Correct Answer
  • 5/16 

    Explanation

    Given expression can be written as
    = 1/(1 x 4) + 1/(4 x 7) + 1/(7 x 10) + 1/(10 x 13) + 1/(13 x 16)
    = 1/3{ 3/(1 x 4) + 3/(4 x 7) + 3/(7 x 10) + 3/(10 x 13) + 3/(13 x 16) }
    = 1/3{ (4 - 1)/(1 x 4) + (7 - 4)/(4 x 7) + (10 - 7 )/(7 x 10) + (13 - 10)/(10 x 13) + (16 - 13/(13 x 16) }
    = 1/3[(1 - 1/4) + (1/4 - 1/7) + (1/7 - 1/10) + (1/10 - 1/13) + (1/13 - 1/16)]
    = 1/3[1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16]
    = 1/3[1 - 1/16]
    = 1/3[ (16 - 1)/16]
    = 1/3[ (15)/16]
    = 1 x 15/ 3 x 16
    = 5/16


  • Simplification problems


    Search Results


    • 1. 
      If x = ( ?2 + 1 ) / ( ?2 - 1 ) and x - y = 4?2, then the value of (x2 + y2) is?

    • Options
    • A. 34
    • B. 38
    • C. 30
    • D. 32
    • Discuss
    • 2. 
      ( 8.73 x 8.73 x 8.73 + 4.27 x 4.27 x 4.27 ) / ( 8.73 x 8.73 - 8.73 x 4.27 + 4.27 x 4.27 ) is equal to?

    • Options
    • A. 11
    • B. 13
    • C. 11/7
    • D. None of these
    • Discuss
    • 3. 
      (2.247)3 + (1.730)3 + (1.023)3 - 3 x 2.247 x 1.730 x 1.023 / ( (2.247)2 + (1.730)2 + (1.023)2 - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023) )

    • Options
    • A. 1.730
    • B. 4
    • C. 5
    • D. 5.247
    • Discuss
    • 4. 
      (0.49)4 x (0.343)4 ÷ (0.2401)4 x = (70 ÷ 100)? + 3 ?

    • Options
    • A. 3
    • B. 1
    • C. 4
    • D. 7
    • Discuss
    • 5. 
      5/8 x 23/5 ÷ 4/9 =?

    • Options
    • A. 9/4
    • B. 8/4
    • C. 4/9
    • D. 6/15
    • Discuss
    • 6. 
      If x + a/x = 1, then the value of ( x2 + x + a ) / (x3 - x2) is?

    • Options
    • A. -2
    • B. -a/2
    • C. 2/a
    • D. -2/a
    • Discuss
    • 7. 
      If ?28 - 6?3 = ?3a + b, (where a, b are rationals), value of (a + b) is?

    • Options
    • A. -2
    • B. 2
    • C. 1
    • D. -1
    • Discuss
    • 8. 
      If a = ( ?2 -1)1/3, then the value of (a - a-1)3 + 3 ( a - a -1 ) is?

    • Options
    • A. -2
    • B. 2
    • C. 2?2
    • D. ?2
    • Discuss
    • 9. 
      If x = ( ? 3 + 1 ) / ( ? 3 - 1 ) and y = ( ? 3 - 1) / ( ? 3 + 1 ) , then the value of x2/y + y2/x is?

    • Options
    • A. 52
    • B. 76
    • C. 4
    • D. 64
    • Discuss
    • 10. 
      If x + a/x = b , then the value of ( x2 + bx + a) / ( bx2 - x3 ) is?

    • Options
    • A. a + b
    • B. 2b/a
    • C. b/a
    • D. ab
    • Discuss


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