If a seven-digit number formed with distinct | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) number is divisible by $3$ if and only if the sum of its digits is divisible by $3$. Given digits are $4, 6, 9, 5, 3, x, y$. Sum of digits $= 4 +

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) number is divisible by $3$ if and only if the sum of its digits is divisible by $3$. Given digits are $4, 6, 9, 5, 3, x, y$. Sum of digits $= 4 + 6 + 9 + 5 + 3 + x + y = 27 + x + y$. For the number to be divisible by $3$,$(27 + x + y)$ must be a multiple of $3$. Since $27$ is a multiple of $3$,$(x + y)$ must be a multiple of $3$. The digits must be distinct,so $x, y \in \{0, 1, 2, 7, 8\}$. Possible pairs $(x, y)$ such that $x + y$ is a multiple of $3$ (where $x 
eq y$ and $x, y 
otin \{4, 6, 9, 5, 3\}$): If $x = 0$,$y$ can be $3$ (not allowed) or $6$ (not allowed) or $9$ (not allowed). No value. If $x = 1$,$y$ can be $2, 5$ (not allowed),$8$. Pairs: $(1, 2), (1, 8)$. If $x = 2$,$y$ can be $1, 4$ (not allowed),$7$. Pairs: $(2, 1), (2, 7)$. If $x = 7$,$y$ can be $2, 5$ (not allowed),$8$. Pairs: $(7, 2), (7, 8)$. If $x = 8$,$y$ can be $1, 4$ (not allowed),$7$. Pairs: $(8, 1), (8, 7)$. Total pairs are $(1, 2), (1, 8), (2, 1), (2, 7), (7, 2), (7, 8), (8, 1), (8, 7)$. There are $8$ such ordered pairs.

If a seven-digit number formed with distinct digits $4, 6, 9, 5, 3, x,$ and $y$ is divisible by $3$,then the number of such ordered pairs $(x, y)$ is

Similar Questions

$2^n \{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 3) \cdot (2n - 1)\} = \dots$

If all the letters of the word $COMBINATION$ are arranged in all possible ways to form $11$ letter words (with or without meaning),then the number of words among them in which $C$ and $N$ occupy the end positions and no vowel appears exactly in the middle position is

The number of all $3$-digit numbers $abc$ (in base $10$) for which $(a \times b \times c) + (a \times b) + (b \times c) + (c \times a) + a + b + c = 29$ is:

Let $m$ and $n$ $(m < n)$ be two $2$-digit numbers. Then the total number of pairs $(m, n)$ such that $\operatorname{gcd}(m, n) = 6$ is . . . . . . .

The number of $4$-digit integers in the closed interval $[2022, 4482]$ formed by using the digits $0, 2, 3, 4, 6, 7$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module