Introduction to Number Systems: MCQ test, Set 7

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

The three whole numbers just before $300$ are
A $301, 302, 303$ B $297, 298, 299$ C $298, 299, 300$ D $296, 297, 298$

Answer and solution

Answer: (B) $297, 298, 299$

Just before $300$ : $299$ , then $298$ , then $297$ .
Which of the following is NOT an even number?
A $312$ B $4005$ C $0$ D $86$

Answer and solution

Answer: (B) $4005$

$4005 = 2 \times 2002 + 1$

Remainder is $1$ , so $4005$ is an odd number.

$0$ , $86$ and $312$ leave remainder $0$ , so they are even.
The products obtained when a number is multiplied by $1, 2, 3, \ldots$ are called its
A powers B divisors C factors D multiples

Answer and solution

Answer: (D) multiples

Multiples of a number are the products of that number with $1, 2, 3, \ldots$ .
Which of the following is NOT a factor of $98$ ?
A $7$ B $14$ C $2$ D $21$

Answer and solution

Answer: (D) $21$

$98 = 2 \times 49$ , $98 = 7 \times 14$ , $98 = 14 \times 7$

$98 = 21 \times 4 + 14$ leaves remainder $14$ , so $21$ is not a factor of $98$ .
How many divisors does $30$ have?
A $7$ B $6$ C $8$ D $10$

Answer and solution

Answer: (C) $8$

$30 = 1 \times 30$

$= 2 \times 15$

$= 3 \times 10$

$= 5 \times 6$

Divisors: $1, 2, 3, 5, 6, 10, 15, 30$ , so there are $8$ .
Another name for a variable is
A power B factor C literal D constant

Answer and solution

Answer: (C) literal

A symbol which takes various numerical values is called a variable (or) literal.
$-12 \times p =$
A $-12 + p$ B $-12p$ C $-12 - p$ D $12p$

Answer and solution

Answer: (B) $-12p$

A number times a letter: write the number (with its sign) before the letter.

$-12 \times p = -12p$
$10b + 13b =$
A $130b$ B $23b$ C $23b^{2}$ D $23$

Answer and solution

Answer: (B) $23b$

$10b + 13b = (10 + 13)b = 23b$
$21t - 12t =$
A $33t$ B $9$ C $9t^{2}$ D $9t$

Answer and solution

Answer: (D) $9t$

$21t - 12t = (21 - 12)t = 9t$
The exponential form of $b \times b \times b \times b \times b \times b$ is
A $b^{6}$ B $b^{5}$ C $6^{b}$ D $6b$

Answer and solution

Answer: (A) $b^{6}$

$b$ is multiplied $6$ times, so it is $b^{6}$ .
$69^{2} =$
A $3681$ B $1035$ C $138$ D $4761$

Answer and solution

Answer: (D) $4761$

$69^{2} = 69 \times 69$

$69 \times 9 = 621$

$69 \times 6 = 414$ , written one place to the left: $4140$

$621 + 4140 = 4761$
The square of $26$ is
A $676$ B $52$ C $208$ D $436$

Answer and solution

Answer: (A) $676$

$26^{2} = 26 \times 26$

$26 \times 6 = 156$

$26 \times 2 = 52$ , written one place to the left: $520$

$156 + 520 = 676$
$18^{3} =$
A $104976$ B $5832$ C $324$ D $54$

Answer and solution

Answer: (B) $5832$

$18^{3} = 18 \times 18 \times 18$

$18 \times 18 = 324$ , $324 \times 18 = 5832$

$= 5832$
Write $12 \times 12 \times 12 \times 12 \times 12$ in exponential form.
A $12^{5}$ B $5^{12}$ C $12 \times 5$ D $12^{4}$

Answer and solution

Answer: (A) $12^{5}$

$12$ is multiplied by itself $5$ times, so it is $12^{5}$ .
The exponential form of $100000$ with base $10$ is
A $5^{10}$ B $10^{5}$ C $10^{4}$ D $10^{6}$

Answer and solution

Answer: (B) $10^{5}$

$100000$ is $1$ followed by $5$ zeros.

$100000 = 10 \times 10 \times 10 \times 10 \times 10 = 10^{5}$
Which of the following numbers between $8000$ and $9000$ is divisible by $2$ ?
A $8225$ B $8523$ C $8808$ D $8649$

Answer and solution

Answer: (C) $8808$

A number is divisible by $2$ if the digit at its unit place is $0, 2, 4, 6$ or $8$ .

The digit at the unit place of $8808$ is $8$ , so $8808$ is divisible by $2$ .

The other three are not divisible.
Which of the following numbers between $9000$ and $10000$ is divisible by $3$ ?
A $9653$ B $9943$ C $9141$ D $9256$

Answer and solution

Answer: (C) $9141$

A number is divisible by $3$ if the sum of all its digits is divisible by $3$ .

Sum of the digits of $9141$ : $9 + 1 + 4 + 1 = 15$

$15$ is divisible by $3$ ( $15 = 3 \times 5$ ), so $9141$ is divisible by $3$ .

Each of the others fails the test.
Which of the following numbers between $10000$ and $20000$ is NOT divisible by $3$ ?
A $15315$ B $16666$ C $13182$ D $11670$

Answer and solution

Answer: (B) $16666$

A number is divisible by $3$ if the sum of all its digits is divisible by $3$ .

Sum of the digits of $16666$ : $1 + 6 + 6 + 6 + 6 = 25$

$25$ is not divisible by $3$ ( $25 = 3 \times 8 + 1$ ), so $16666$ is not divisible by $3$ .

Each of the others passes the test.
Which of the following numbers between $80000$ and $90000$ is divisible by $4$ ?
A $81876$ B $83662$ C $86098$ D $86474$

Answer and solution

Answer: (A) $81876$

A number is divisible by $4$ if its last two digits together are divisible by $4$ .

Last two digits of $81876$ together: $76$ ; $76 = 4 \times 19$ , so $81876$ is divisible by $4$ .

Each of the others fails the test.
Which of the following numbers between $20000$ and $30000$ is divisible by $5$ ?
A $29107$ B $26551$ C $20606$ D $21510$

Answer and solution

Answer: (D) $21510$

A number is divisible by $5$ if the digit at its unit place is $0$ or $5$ .

The digit at the unit place of $21510$ is $0$ , so $21510$ is divisible by $5$ .

The other three are not divisible.
Which of the following numbers between $40000$ and $50000$ is NOT divisible by $6$ ?
A $47304$ B $44982$ C $46776$ D $48134$

Answer and solution

Answer: (D) $48134$

A number is divisible by $6$ if it is divisible by both $2$ and $3$ .

The digit at the unit place of $48134$ is $4$ , so $48134$ is divisible by $2$ .

Sum of the digits of $48134$ : $4 + 8 + 1 + 3 + 4 = 20$

$20$ is not divisible by $3$ ( $20 = 3 \times 6 + 2$ ), so $48134$ is not divisible by $3$ .

$\therefore$ $48134$ is not divisible by $6$ .

Each of the others passes the test.
Which of the following numbers between $50000$ and $60000$ is divisible by $6$ ?
A $54336$ B $54536$ C $58737$ D $56758$

Answer and solution

Answer: (A) $54336$

A number is divisible by $6$ if it is divisible by both $2$ and $3$ .

The digit at the unit place of $54336$ is $6$ , so $54336$ is divisible by $2$ .

Sum of the digits of $54336$ : $5 + 4 + 3 + 3 + 6 = 21$

$21$ is divisible by $3$ ( $21 = 3 \times 7$ ), so $54336$ is divisible by $3$ .

$\therefore$ $54336$ is divisible by $6$ .

Each of the others fails the test.
Which of the following numbers between $700$ and $800$ is divisible by $7$ ?
A $708$ B $747$ C $735$ D $713$

Answer and solution

Answer: (C) $735$

A number is divisible by $7$ if the remaining part minus twice the unit digit is a multiple of $7$ (or $0$ ).

$735$ : $73 - 5(2) = 73 - 10 = 63$ ; $63 = 7 \times 9$ , a multiple of $7$ , so $735$ is divisible by $7$ .

Each of the others fails the test.
To test $887$ for divisibility by $7$ , twice the unit digit is subtracted from the remaining part. The result is
A $81$ B $873$ C $74$ D $102$

Answer and solution

Answer: (C) $74$

Remaining part $= 88$ , unit digit $= 7$

$88 - 7(2) = 88 - 14 = 74$
Among $2, 3, 4, 5$ and $6$ , the number $70668$ is divisible by
A $2, 3, 4$ and $6$ only B $2, 3$ and $4$ only C $2, 3$ and $6$ only D $2, 4$ and $6$ only

Answer and solution

Answer: (A) $2, 3, 4$ and $6$ only

The digit at the unit place of $70668$ is $8$ , so $70668$ is divisible by $2$ .

Sum of the digits of $70668$ : $7 + 0 + 6 + 6 + 8 = 27$

$27$ is divisible by $3$ ( $27 = 3 \times 9$ ), so $70668$ is divisible by $3$ .

Last two digits of $70668$ together: $68$ ; $68 = 4 \times 17$ , so $70668$ is divisible by $4$ .

The digit at the unit place of $70668$ is $8$ , so $70668$ is not divisible by $5$ .

Divisible by both $2$ and $3$ means divisible by $6$ .

So $70668$ is divisible by $2, 3, 4$ and $6$ .

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MCQ test, Set 7