Register

CAT 2000 | Question: 65

• edited by
1,883 views
1 1 vote

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

  1. $xyz^2$ is odd.
  2. $(x − y)^2 z$ is even.
  3. $(x + y − z)^2 (x + y)$ is even.
  4. $(x − y) (y + z) (x + y − z)$ is odd

1 Answer

Best answer
2 2 votes

​​​​​​The difference of two odd integers is always an even number.

The multiplication of even integer with any(even/odd) integer is always an even integer.

Hence 4th option is not possible.

• selected by
Voting & Accepting an answer helps improve the community
← Previous · CAT 2000 | Question:...Next → · CAT 2000 | Question:...
← Previous in category · CAT 2000 | Question:...Next in category → · CAT 2000 | Question:...
Position:
Show:
Answer:

Related questions

0 0 votes
0 0 answers
2.5k
2.5k views
go_editor asked May 1, 2016
2,478 views
CAT 2000 | Question: 74
$\text{A, B, C}$ are three numbers. Let $@ \text{(A, B)} =$ average of $\text{A}$ and $\text{B}$, $/ \text{(A, B)} = $ product of $\text{A}$ and $\text{B}$, and $\text{X...
2 2 votes
2 2 answers
3.5k
3.5k views
go_editor asked Mar 28, 2016
3,501 views
CAT 2000 | Question: 73
$\text{A, B, C}$ are three numbers. Let $@ \text{(A, B)} =$ average of $\text{A}$ and $\text{B}$, $/ \text{(A, B)} = $ product of $\text{A}$ and $\text{B}$, and $\text{X...
0 0 votes
0 0 answers
1.2k
1.2k views
go_editor asked Mar 28, 2016
1,171 views
CAT 2000 | Question: 70
Each of the numbers $x_1, x_2,\dots, x_n, n 4,$ is equal to $1$ or $–1.$ Suppose, $x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + \dots + x_{n–3}x_{n–2}x_{n–1}x_n + x_{n–2...
0 0 votes
1 1 answer
1.9k
1.9k views
go_editor asked Mar 26, 2016
1,862 views
CAT 2000 | Question: 57
$\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y & 4 & 8 & 14 & 22 & 32 & 44 \\\hline \end{array}$In the above table, for suitably chosen con...
0 0 votes
0 0 answers
2.0k
2.0k views
go_editor asked May 1, 2016
1,973 views
CAT 2000 | Question: 76
Answer the following question based on the information given below.For real numbers $x, y,$ let$f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\...