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Tricky Math Problem of the Week (30 Oct)

Solution to the 30 Oct, 2006 problem ( Number Game (Division by 3))

B2 x C is definitely divisible by 3.

(I) C = P - Q where P = lmn and Q=nml ("lmn" is a three digit number having l as hundredth, m as tenth and n as unit digit.)
(II) B = √(2+ (√2+(√2 ... infinite terms)))

  • Statement (I) alone is sufficient to answer the question, but statement (II) alone is not.
  • Statement (II) alone is sufficient to answer the question, but statement (I) alone is not.
  • Statements (I) and (II) taken together are sufficient to answer the question, but neither statement alone is sufficient.
  • Each statement alone is sufficient to answer the question.
  • Statements (I) and (II) taken together are not sufficient to answer the question.

    Answer :Statement (I) alone is sufficient to answer the question, but statement (II) alone is not.

    Solution (Fast Approach)

  • Statement I => C = 100l+10m+n - 100n-10m-l = 99l -99n = 99 (l-n) .... Hence, can be divided by 3
  • Statement II => As the series is infinite. we can rewrite the equation as
    B = √(2+B)
  • Squaring both the sides
  • B2 = 2 + B
  • B2 - B -2 = 0
  • B = 2 or -1
  • We can take B as 2 only, since a square root cannot be a negative no.
  • Hence Statement II is not sufficient to answer the question

  •  

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