MCQ

MCQ 11 Mark

Mark $(\checkmark)$ against the correct answer: If $6 \times 5$ is exactly divisible by $9,$ then the least value of $x $ is

A
$1$
B
$4$
✓
$7$
D
$0$

Answer

Correct option: C.

$7$

When a number is divisible by $9,$ the sum of the digits is also divisible by $9.$
$6 + x + 5 = 11 + x$
To be divisible by $9:$
$11 + x = 18$
$\Rightarrow x = 7$

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MCQ 21 Mark

Tick $(\checkmark)$ the correct answer of following. If the $4-$digit number $x\ 27\ y$ is exactly divisible by $9,$ then the least value of $(x + y)$ is:

A
$0$
B
$3$
C
$6$
✓
$9$

Answer

Correct option: D.

$9$

If a number is divisible by $9,$ then the sum of the digits is divisible by $9.$
$x + 2 + 7 + y = (x + y) + 9$
For this to be divisible by $9,$ the least value of $(x + y)$ is $0.$
But for $x + y = 0, x$ and $y$ both will be zero.
Since $x $ is the first digit, it can never be $0.$
$\therefore x + y + 9 = 18$
Or $x + y =9$

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MCQ 31 Mark

Mark $(\checkmark)$ against the correct answer: If $x\ 48\ y$ is exactly divisible by $9$ then the least value of $(x + y)$ is:

A
$4$
B
$0$
✓
$6$
D
$7$

Answer

Correct option: C.

$6$

When a number is divisible by $9,$ the sum of digits is also divisible by $9.$
$x + 4 + 8 + y = 12 +(x + y)$
For $12 + (x + y)$ to be divisible by $9:$
$12 + (x + y) = 18$
$\Rightarrow (x + y) = 6$

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MCQ 41 Mark

Tick $(\checkmark)$ the correct answer of following. If $1\ A2\ B5$ is exactly divisible by $9,$ then the least value of $(A + B)$ is:

A
$0$
✓
$1$
C
$2$
D
$10$

Answer

Correct option: B.

$1$

For a number to be divisible by $9,$ the sum of the digits must also be divisible by $9.$
$1 + A + 2 + B + 5 = (A + B) + 8$
The number will be divisible by $9$ if $(A + B) =1(A + B) =1.$

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MCQ 51 Mark

Tick $(\checkmark)$ the correct answer of following. If $4\ xy\ 7$ is exactly divisible by $3,$ then the least value of $(x + y)$ is:

✓
$1$
B
$4$
C
$5$
D
$7$

Answer

Correct option: A.

$1$

If a number is divisible by $3,$ the sum of the digits is also divisible by $3.$
$4 + x + y + 7 = 11 + (x + y)$
For the sum to be divisible by $3:$
$11 + (x + y) = 12$
$\Rightarrow (x + y) = 1$

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MCQ 61 Mark

Tick $(\checkmark)$ the correct answer of following. If $7 \times 8$ is exactly divisible by $9,$ then the least value of $x$ is

A
$0$
B
$2$
✓
$3$
D
$5$

Answer

Correct option: C.

$3$

If a number is exactly divisible by $9,$ the sum of the digits must also be divisible by $9.$
$7 + x + 8 = 15 + x$
$18$ is divisible by $9.$
$\therefore 15 + x = 18$
$\Rightarrow x = 3$

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MCQ 71 Mark

Tick $(\checkmark)$ the correct answer of following. If $64\ y\ 8$ is exactly divisible by $3,$ then the least value of $y$ is:

✓
$0$
B
$1$
C
$2$
D
$3$

Answer

Correct option: A.

$0$

If a number is divisible by $3,$ then the sum of the digits is also divisible by $3.$
$6 + 4 + y + 8 = 18$
This is divisible by $3$ as $y$ is equal to $0.$

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MCQ 81 Mark

Tick $(\checkmark)$ the correct answer of following. If $37\ y\ 4$ is exactly divisible by $9,$ then the least value of $y$ is:

A
$2$
B
$3$
C
$1$
✓
$4$

Answer

Correct option: D.

$4$

A number is divisible by $9$ if the sum of the digits is divisible by $9.$
$3 + 7 + y + 4 = 14 + y$
For this sum to be divisible by $9:$
$14 + y = 18$
$\Rightarrow y = 4$

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MCQ 91 Mark

Mark $(\checkmark)$ against the correct answer: If $486^*7$ is divisible by $9,$ then the least value of $^*$ is:

A
$0$
B
$1$
C
$3$
✓
$2$

Answer

Correct option: D.

$2$

For a number to be divisible by $9,$ the sum of its digits must be divisible by $9.$
$4 + 8 + 6 + ^* + 7 = 25 + ^*$
Now,
$25 + ^* = 27($If $^* = 2$ and $27$ is divisible by $9)$

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MCQ 101 Mark

Tick $(\checkmark)$ the correct answer of following. If $x\ 4y\ 5z$ is exactly divisible by $9,$ then the least value of $(x + y + z)$ is:

A
$3$
B
$6$
✓
$9$
D
$0$

Answer

Correct option: C.

$9$

A number is divisible by $9$ if the sum of the digits is divisible by $9.$
$x + 4 + y + 5 + z = 9 + (x + y + z)$
The lowest value of $(x + y + z)$ is equal to $0$ is equal to $0$ for the number $x\ 4y\ 5z$ to be divisible by $9.$
In this case, all $x, y$ and $z$ will be $0.$
But $x$ is the first digit, so it cannot be $0.$
$\therefore x + 4 + y + 5 + z = 18$
$\Rightarrow x + y + z + 9 = 18$
$\Rightarrow x + y + z = 9$

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MCQ 111 Mark

Tick $(\checkmark)$ the correct answer of following. If $5\times6$ is exactly divistble by $3,$ then the least value of $x$ is$-$

A
$0$
✓
$1$
C
$2$
D
$5$

Answer

Correct option: B.

$1$

If a number is exactly divisible by $3,$ the sum of the digits must also be divisible by $3.$
$5 + x + 6 = 11 + x$ must be divisible by $3.$
The smallest value of $x$ is $1.$
$x = 1$
$\Rightarrow x + 11 = 12$ is divisible by $3.$

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