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Byju's Answer

Standard VII

Mathematics

Integers

If x,y and ...

Question

If $x, y$ and $z$ are consecutive integers. Is $x + y + z$ divisible by $3$ $ ?

Yes

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Solution

The correct option is C Yes
Yes: For any odd number of consecutive integers, the sum of those integers is divisible by the number of integers. There are three consecutive integers $(x, y$ , and $z)$ , so the rule applies in this case.

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Similar questions

Q. Let,

x, y

and

z

are the natural numbers. Which of the following statements is true?
I) If

x

is divisible by

y

and

y

is divisible by

z

, then

x

must be divisible by

z

.
II) If

x

is a factor of

y

and

z

, then

x

must be a factor of

y + z

.
III) If

x

is a factor of

y

and

z

, then

x

must be a factor of

\frac{y}{z}

Q. If

x, y, z

are three consecutive positive integer, then

log (1 + z x)

is equal to

Q. If

x^{3} + y^{3} + z^{3} = 6 x y z

, where x, y, z are non-zero integers,

x + y + z \neq 0

and

x y z = x + y + z

, then the value of

(x - y)^{2} + (y - z)^{2} + (z - x)^{2}

is equal to

Q. If

x, y, z

are non-negative integers such that

2 (x^{3} + y^{3} + z^{3}) = 3 (x + y + z)^{2}

, then maximum value of

x + y + z

Show that $x^{2} + x y + y^{2}, z^{2} + z x + x^{2}$ and $y^{2} + y z + z^{2}$ are consecutive terms of an A.P., if $x, y$ and $z$ are in A.P.

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If x,y and z are consecutive integers. Is x+y+z divisible by 3$ ?

The correct option is C YesYes: For any odd number of consecutive integers, the sum of those integers is divisible by the number of integers. There are three consecutive integers (x,y, and z), so the rule applies in this case.

If $x, y$ and $z$ are consecutive integers. Is $x + y + z$ divisible by $3$ $ ?

The correct option is C Yes
Yes: For any odd number of consecutive integers, the sum of those integers is divisible by the number of integers. There are three consecutive integers $(x, y$ , and $z)$ , so the rule applies in this case.