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CAT 2006 — QA Question 24

LogarithmsEasy
Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

If logyx = a × logzy = b × logxz = ab, then which of the following pairs of values for (a, b) is not possible?

Answer & solution

  • A

    -2, 12

  • B

    1, 1

  • C

    0.4, 2.5

  • D

    π, 1π

  • 2, 2

Solution

If logyx = a × logzy = b × logxz = ab

⇒ logyx = ab   ...(1)

⇒ a × logzy = ab ⇒ logzy = b   ...(2)

⇒ b × logxz = ab ⇒ logxz = a   ...(3)

From (1), (2) and (3), we get
logyx = logxz × logzy

∴  log xlog y = log zlog x×log ylog z = log ylog x

∴ (log x)2 = (log y)2

∴ log x = ± log y

∴ log x = log y or log x = - log y

∴  x = y or x = 1y

∴ ab = logy x = 1 or -1

Only option (e) does not satisfy this.

Hence, option (e).

CAT 2006 QA Q24: If log y x = a × log z y = b × log x z = ab, then which of the following pairs of values for (a, b — Solution | TheCATExam