Even Odd — CAT Previous-Year Questions

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

Each of the numbers x₁, x₂...., x_n, n > 4, is equal to 1 or –1. Suppose,

x₁x₂x₃x₄ + x₂x₃x₄x₅ + x₃x₄x₅x₆ + ... + x_n–3x_n–2x_n–1x_n + x_n–2x_n–1x_nx₁+ x_n–1x_nx₁x₂ + x_nx₁x₂x₃ = 0, then,

n³ is odd. Which of the following statement(s) is(are) true?

I. n is odd.
II. n² is odd.
III. n² is even.

The maximum number of coins collected by any one of them cannot exceed

If A collected 54 coins, then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least

If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be

Number of students who have opted for subjects A, B and C are 60, 84 and 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each  room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions?

You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth?

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