Introduction to Number Systems: MCQ test, Set 1

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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.

How many whole numbers are less than $9$ ?
A $10$ B $7$ C $9$ D $8$

Answer and solution

Answer: (C) $9$

Whole numbers are the natural numbers along with $0$ : $0, 1, 2, 3, \ldots$

Less than $9$ : $0, 1, 2, \ldots, 8$ . Counting $0$ also, there are $9$ .
Which of the following is an odd number?
A $7290$ B $538$ C $4651$ D $1004$

Answer and solution

Answer: (C) $4651$

$4651 = 2 \times 2325 + 1$

Remainder is $1$ , so $4651$ is an odd number.
Which of the following is a multiple of $7$ ?
A $75$ B $107$ C $57$ D $91$

Answer and solution

Answer: (D) $91$

$7 \times 13 = 91$ , so $91$ is a multiple of $7$ .

$75$ , $57$ and $107$ leave a remainder when divided by $7$ .
The factors of $46$ are
A $1, 2, 23$ B $1, 46$ C $2, 23$ D $1, 2, 23, 46$

Answer and solution

Answer: (D) $1, 2, 23, 46$

$46 = 1 \times 46$

$= 2 \times 23$

Factors of $46$ : $1, 2, 23, 46$
How many divisors does $64$ have?
A $8$ B $7$ C $6$ D $5$

Answer and solution

Answer: (B) $7$

$64 = 1 \times 64$

$= 2 \times 32$

$= 4 \times 16$

$= 8 \times 8$

$8 \times 8$ gives the divisor $8$ only once.

Divisors: $1, 2, 4, 8, 16, 32, 64$ , so there are $7$ .
Which of the following is a constant?
A $b$ B $x$ C $15$ D $z$

Answer and solution

Answer: (C) $15$

A symbol which has a fixed value is called a constant.

$15$ has a fixed value.
$-1 \times q =$
A $-1$ B $q$ C $-q$ D $-1 + q$

Answer and solution

Answer: (C) $-q$

As $-1 \times a = -a$ , $-1 \times q = -q$ .
$7x + 6x =$
A $13x$ B $42x$ C $13$ D $13x^{2}$

Answer and solution

Answer: (A) $13x$

$7x + 6x = (7 + 6)x = 13x$
$11n - 4n =$
A $7$ B $7n$ C $7n^{2}$ D $15n$

Answer and solution

Answer: (B) $7n$

$11n - 4n = (11 - 4)n = 7n$
$x \times x \times x \times x =$
A $x^{4}$ B $x + 4$ C $4x$ D $x^{3}$

Answer and solution

Answer: (A) $x^{4}$

$x$ is multiplied $4$ times, so it is $x^{4}$ .
$38^{2} =$
A $418$ B $76$ C $1444$ D $964$

Answer and solution

Answer: (C) $1444$

$38^{2} = 38 \times 38$

$38 \times 8 = 304$

$38 \times 3 = 114$ , written one place to the left: $1140$

$304 + 1140 = 1444$
The square of $67$ is
A $4489$ B $134$ C $871$ D $3649$

Answer and solution

Answer: (A) $4489$

$67^{2} = 67 \times 67$

$67 \times 7 = 469$

$67 \times 6 = 402$ , written one place to the left: $4020$

$469 + 4020 = 4489$
$17^{3} =$
A $51$ B $83521$ C $4913$ D $289$

Answer and solution

Answer: (C) $4913$

$17^{3} = 17 \times 17 \times 17$

$17 \times 17 = 289$ , $289 \times 17 = 4913$

$= 4913$
Write $7 \times 7 \times 7 \times 7 \times 7 \times 7$ in exponential form.
A $7 \times 6$ B $7^{6}$ C $6^{7}$ D $7^{5}$

Answer and solution

Answer: (B) $7^{6}$

$7$ is multiplied by itself $6$ times, so it is $7^{6}$ .
The exponential form of $128$ with base $2$ is
A $2^{6}$ B $7^{2}$ C $2^{8}$ D $2^{7}$

Answer and solution

Answer: (D) $2^{7}$

Divide by $2$ again and again:

$128 \div 2 = 64$ , $64 \div 2 = 32$ , $32 \div 2 = 16$

$16 \div 2 = 8$ , $8 \div 2 = 4$ , $4 \div 2 = 2$

$128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{7}$
Which of the following numbers between $2000$ and $3000$ is divisible by $2$ ?
A $2332$ B $2303$ C $2907$ D $2525$

Answer and solution

Answer: (A) $2332$

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 $2332$ is $2$ , so $2332$ is divisible by $2$ .

The other three are not divisible.
Which of the following numbers between $1000$ and $2000$ is divisible by $3$ ?
A $1379$ B $1191$ C $1403$ D $1249$

Answer and solution

Answer: (B) $1191$

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

Sum of the digits of $1191$ : $1 + 1 + 9 + 1 = 12$

$12$ is divisible by $3$ ( $12 = 3 \times 4$ ), so $1191$ is divisible by $3$ .

Each of the others fails the test.
The smallest number greater than $720$ that is divisible by $3$ is
A $726$ B $722$ C $721$ D $723$

Answer and solution

Answer: (D) $723$

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

$721$ : digit sum $10$ , not divisible by $3$

$722$ : digit sum $11$ , not divisible by $3$

$723$ : digit sum $12$ , divisible by $3$
Which of the following numbers between $20000$ and $30000$ is divisible by $4$ ?
A $25298$ B $29856$ C $24402$ D $28834$

Answer and solution

Answer: (B) $29856$

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

Last two digits of $29856$ together: $56$ ; $56 = 4 \times 14$ , so $29856$ is divisible by $4$ .

Each of the others fails the test.
Which of the following numbers between $3000$ and $4000$ is divisible by $5$ ?
A $3770$ B $3701$ C $3907$ D $3802$

Answer and solution

Answer: (A) $3770$

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

The digit at the unit place of $3770$ is $0$ , so $3770$ is divisible by $5$ .

The other three are not divisible.
A number is divisible by $6$ if it is divisible by
A $2$ or $3$ B both $2$ and $4$ C both $2$ and $3$ D $3$ only

Answer and solution

Answer: (C) both $2$ and $3$

A number is divisible by $6$ if it is divisible by both $2$ and $3$ .
Which of the following numbers between $2000$ and $3000$ is divisible by $6$ ?
A $2904$ B $2181$ C $2354$ D $2516$

Answer and solution

Answer: (A) $2904$

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

The digit at the unit place of $2904$ is $4$ , so $2904$ is divisible by $2$ .

Sum of the digits of $2904$ : $2 + 9 + 0 + 4 = 15$

$15$ is divisible by $3$ ( $15 = 3 \times 5$ ), so $2904$ is divisible by $3$ .

$\therefore$ $2904$ is divisible by $6$ .

Each of the others fails the test.
Which of the following numbers between $100$ and $200$ is divisible by $7$ ?
A $121$ B $104$ C $103$ D $161$

Answer and solution

Answer: (D) $161$

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

$161$ : $16 - 1(2) = 16 - 2 = 14$ ; $14 = 7 \times 2$ , a multiple of $7$ , so $161$ is divisible by $7$ .

Each of the others fails the test.
To test $309$ for divisibility by $7$ , twice the unit digit is subtracted from the remaining part. The result is
A $21$ B $12$ C $291$ D $48$

Answer and solution

Answer: (B) $12$

Remaining part $= 30$ , unit digit $= 9$

$30 - 9(2) = 30 - 18 = 12$
Among $2, 3, 4, 5$ and $6$ , the number $17538$ is divisible by
A $2, 3, 4$ and $6$ only B $2$ and $3$ only C $2$ and $6$ only D $2, 3$ and $6$ only

Answer and solution

Answer: (D) $2, 3$ and $6$ only

The digit at the unit place of $17538$ is $8$ , so $17538$ is divisible by $2$ .

Sum of the digits of $17538$ : $1 + 7 + 5 + 3 + 8 = 24$

$24$ is divisible by $3$ ( $24 = 3 \times 8$ ), so $17538$ is divisible by $3$ .

Last two digits of $17538$ together: $38$ ; $38 = 4 \times 9 + 2$ , so $17538$ is not divisible by $4$ .

The digit at the unit place of $17538$ is $8$ , so $17538$ is not divisible by $5$ .

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

So $17538$ is divisible by $2, 3$ and $6$ .

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MCQ test, Set 1