Playing with Numbers Test

Result

Playing with Numbers Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers is divisible by $9$ ?

A
$8576901$

B
$96345210$

C
$67594310$

D
none of these

Solution

We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Since sum of its digits $= 8 + 5 + 7 + 6 + 9 + 0 + 1 = 36$
$36$ is divisible by $9$
Option (a) is the correct answer

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Question 2
1 / -0

The expanded form of the number $9578$ is

A
$9\times 10000+5\times 1000+7\times 10+8\times 1$

B
$9\times 1000+5\times 100+7\times 10+8\times 1$

C
$9\times 1000+57\times 10+8\times 1$

D
$9\times 100+5\times 100+7\times 10+8\times 1$

Solution

Expanded form of $9578$
$=9\times 1000+5\times 100+7\times 10+8\times 1$
Hence, B is the correct answer.

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Question 3
1 / -0

By using dot $(.)$ patterns, which of the following numbers can be arranged in all the three ways namely a line, a triangle and a rectangle ?

A
$9$

B
$10$

C
$11$

D
$12$

Solution

Option $B$ is right
As we know that every number can be arranged as a line.
The number $10$ can be shown as
$..........$
Also, it can show a triangle Given below
And, the number cam show as a rectangle. Given below

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Question 4
1 / -0

Evaluate: $3\times 10000+7\times 1000+9\times 100+0\times 10+4$

A
$3794$

B
$37940$

C
$37904$

D
$379409$

Solution

Consider, $3\times 10000+7\times 1000+9\times 100+0\times 10+4$
$=30000+7000+900+0+4$
$=37904$
Hence, option C is right.

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Question 5
1 / -0

Which of the following numbers is divisible by $9$ ?

A
$972063$

B
$730542$

C
$785423$

D
$561284$

Solution

We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Sum of digits $= 9 + 7 + 2 + 0 + 3 = 27$ which is divisible by $9$

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Question 6
1 / -0

Which of the following numbers is divisible by $3$ ?

A
$50762$

B
$42063$

C
$52871$

D
$37036$

Solution

We use a rule to check whether the number is divisible by 3 or not.
A number is divisible by 3 if the sum of the digits is evenly divisible by 3.
Sum of digits is $= 4 + 2 + 0 + 6 + 3 = 15$ which is divisible by $3$

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Question 7
1 / -0

A four-digit number $aabb$ is divisible by $55$ . Then possible value(s) of $b$ is/are

A
$0$ and $2$

B
$2$ and $5$

C
$0$ and $5$

D
$7$

Solution

If the number is divisible by $55$ ,
It must also be divisible by $5$ .
Therefore the number ends with $0$ or $5$ .

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Question 8
1 / -0

If $5A\times A=399$ , then the value of $A$ is

A
$3$

B
$6$

C
$7$

D
$9$

Solution

Given,
$$\ \ \ \ 5\ A$$
$$\times\ \ \ \ A$$
$\overline{ \ \ 3\ 9\ 9\ \ }$

Here,
$A\times A=$ a number whose unit digit is $9$
The number from $0$ to $9$ whose product with itself is a number having its unit's digit $9$ is $7$ .

Hence, $A=7$
And the option (C) is correct.

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Question 9
1 / -0

Let $abc$ be a three digit number. Then $abc+bca+cab$ is not divisible by

A
$a+b+c$

B
$3$

C
$37$

D
$9$

Solution

We have,
$abc+bca+cab=(100a+10b+c)+(100b+10c+a)+(100c+10a+b)$
$=111a+111b+111c$
$=111(a+b+c)$
$=3\times 37(a+b+c)$
Therefore the number $abc+bca+cab$ is divisible by $3,37$ and $(a+b+c)$ but not by $9$ .

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Question 10
1 / -0

A six-digit number is formed by repeating a three-digit number. For example $256256, 678678$ , etc. Any number of this form is always divisible by

A
$7$ only

B
$11$ only

C
$13$ only

D
$1001$

Solution

Let
A six-digit number formed by repeating a three-digit number be $abcabc$
Then,
$abcabc=100000a+10000b+1000c+100a+10b+c$
$=a(100000+100)+b(10000+10)+c(1000+1)$
$=(100100)a+(10010)b+(1001)c$
$=1001(100a+10b+c)$

Therefore, the six-digit number formed by repeating a three-digit number is always divisible by $1001$ .

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 18

Result

Playing with Numbers Test - 18

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Rank

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SHARING IS CARING

Question 1

857690185769018576901

963452109634521096345210

675943106759431067594310

none of these

Solution

Question 2

9×10000+5×1000+7×10+8×19\times 10000+5\times 1000+7\times 10+8\times 19×10000+5×1000+7×10+8×1

9×1000+5×100+7×10+8×19\times 1000+5\times 100+7\times 10+8\times 19×1000+5×100+7×10+8×1

9×1000+57×10+8×19\times 1000+57\times 10+8\times 19×1000+57×10+8×1

9×100+5×100+7×10+8×19\times 100+5\times 100+7\times 10+8\times 19×100+5×100+7×10+8×1

Solution

Question 3

999

101010

111111

121212

Solution

Question 4

379437943794

379403794037940

379043790437904

379409379409379409

Solution

Question 5

972063 972063 972063

730542 730542 730542

785423 785423 785423

561284 561284 561284

Solution

Question 6

50762 50762 50762

42063 42063 42063

52871 52871 52871

37036 37036 37036

Solution

Question 7

000 and 222

222 and 555

000 and 555

777

Solution

Question 8

333

666

777

999

Solution

Question 9

a+b+ca+b+ca+b+c

333

373737

999

Solution

Question 10

777 only

111111 only

131313 only

100110011001

Solution

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Question Analysis

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$8576901$

$96345210$

$67594310$

$9\times 10000+5\times 1000+7\times 10+8\times 1$

$9\times 1000+5\times 100+7\times 10+8\times 1$

$9\times 1000+57\times 10+8\times 1$

$9\times 100+5\times 100+7\times 10+8\times 1$

$9$

$10$

$11$

$12$

$3794$

$37940$

$37904$

$379409$

$972063$

$730542$

$785423$

$561284$

$50762$

$42063$

$52871$

$37036$

$0$ and $2$

$2$ and $5$

$0$ and $5$

$7$

$3$

$6$

$7$

$9$

$a+b+c$

$3$

$37$

$9$

$7$ only

$11$ only

$13$ only

$1001$