Numbers and Algebra - Numbers and Algebra Section 1

21. If x+y+z=0,then x2/yx + y2/zx + z2/xy equal

  • Option : D
  • Explanation : x2/yx + y2/zx + z2/xy
                 ...(since, x+y+z=0  x3+y3+z3=3xyz)
    (x3+y3+z3) / xyz = 3xyz / xyz = 3.
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22. Average age of a committee of seven trustees is the same as it was five years ago, a younger man having been substituted for one of them. How much younger was he then trustee whose place he took?

  • Option : B
  • Explanation : Increase after 5 years should have been 7 x 5 = 35 years. But since average remains same, diference in their age is 35 years.
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23. What is the least number which must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?

  • Option : D
  • Explanation : L.C.M. of 9, 10 and 15 = 90 ∴ 1936 = 90 x 21 + 46 (Remainder). But a part of this remainder is 7. 39 should be subtracted from 1936.
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24. What is the maximum sum of the series 60, 58, 56, 54, 52, ?

  • Option : C
  • Explanation :

    Since d = -2, maximum sum of the series will be sum of all the positive terms.
    Least positive term of the series is 2 or 0 (both giving equal sum)
    Let, 2 be the nth term
    2 = 60 + (n 1) - 2 
    => n = 30
    Required sum = 30/2 (60 + 2) = 930

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25. What is the least number which on being divided by 12, 21 and 35 will leave in each case the same remainder 6?

  • Option : D
  • Explanation :

    L.C.M. of 12, 21 and 35 = 420 
    ∴ Number required = 420 + 6 = 426

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