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CAT 1993 — QA Question 12

Even OddEasy

Given odd positive integers x, y and z, which of the following is not necessarily true?

Answer & solution

  • A

     x2 y2 z2 is odd

  • B

    3(x2 + y3)z2 is even.

  • C

    5x + y + z4 is odd

  • z2 (x4 + y4)/2 is even

Solution

You can solve this by assuming values of x, y and z.

Let the three numbers be 1, 3 & 5. 

Option (a) is 12 32 52 = 225, which is odd. 

Option (b) is 3(12 + 33)52 = 2100, which is even. 

Option (c) is 5 + 3 + 54 = 633, which is odd. 

Option (d) is 52(14+34)2= 1025, which is not even and hence, the answer.

Hence, option (d).

CAT 1993 QA Q12: Given odd positive integers x, y and z, which of the following is not necessarily true? — Solution | TheCATExam