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CAT 2002 — QA Question 16

Prime and Composite NumbersEasy

If U, V, W and m are natural numbers such that Um + Vm = Wm, then which of the following is true?

Answer & solution

  • A

    m < Min(U, V, W)

  • B

    m > Max(U, V, W)

  • m < Max(U, V, W)

  • D

    None of these

Solution

Taking m = 1, we have,

U1 + V1 = W1

The least values of U and V are 1 and 1.

∴ Least value of W = 2

Also, taking m = 2, we have,

U2 + V2 = W2

The least values of U and V are 3 and 4 (not necessarily in that order).

∴ Least value of W = 5

∴ m is always less than Max(U, V, W).

Hence, option (c).

CAT 2002 QA Q16: If U, V, W and m are natural numbers such that U m + V m = W m , then which of the following is true? — Solution | TheCATExam