Introduction to Number Systems: MCQ test, Set 10

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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 there from $0$ to $50$ ?
A $49$ B $50$ C $52$ D $51$

Answer and solution

Answer: (D) $51$

From $0$ to $50$ : $0, 1, 2, \ldots, 50$ .

$50$ natural numbers and $0$ : $51$ whole numbers.
A number gives remainder $1$ when it is divided by $2$ . The number is
A an even number B a multiple of $2$ C an odd number D divisible by $2$

Answer and solution

Answer: (C) an odd number

Odd numbers give remainder $1$ when divided by $2$ : $1, 3, 5, 7, \ldots$
The multiples of $5$ that are less than $30$ are
A $5, 15, 25$ B $10, 15, 20, 25$ C $5, 10, 15, 20, 25, 30$ D $5, 10, 15, 20, 25$

Answer and solution

Answer: (D) $5, 10, 15, 20, 25$

$5 \times 1 = 5$ , $5 \times 2 = 10$ , $5 \times 3 = 15$ , $5 \times 4 = 20$ , $5 \times 5 = 25$

$5 \times 6 = 30$ is not less than $30$ .
How many divisors does $45$ have?
A $8$ B $4$ C $5$ D $6$

Answer and solution

Answer: (D) $6$

$45 = 1 \times 45$

$= 3 \times 15$

$= 5 \times 9$

Divisors: $1, 3, 5, 9, 15, 45$ , so there are $6$ .
In $128 = 4 \times \square$ , the number in the box is
A $34$ B $124$ C $32$ D $30$

Answer and solution

Answer: (C) $32$

$128 \div 4 = 32$

$128 = 4 \times 32$
$x, y, z, a, b, c$ are examples of
A multiples B variables C natural numbers D constants

Answer and solution

Answer: (B) variables

A symbol which takes various numerical values is called a variable (or) literal.
In $-t$ , the number multiplying $t$ is
A $t$ B $-1$ C $0$ D $1$

Answer and solution

Answer: (B) $-1$

As $-1 \times a = -a$ , $-t = -1 \times t$ .
$q + q + q + q + q + q =$
A $6 + q$ B $q^{6}$ C $6q$ D $5q$

Answer and solution

Answer: (C) $6q$

$q + q + q + q + q + q$ is $q$ added $6$ times.

$q + q + q + q + q + q = 6q$
$9b + 4b + 11b =$
A $24b$ B $396b$ C $24b^{3}$ D $23b$

Answer and solution

Answer: (A) $24b$

$9b + 4b + 11b = (9 + 4 + 11)b = 24b$
If $y \times y \times y \times y = y^{\square}$ , the number in the box is
A $5$ B $2$ C $4$ D $3$

Answer and solution

Answer: (C) $4$

$y$ is multiplied $4$ times, so it is $y^{4}$ .
$39^{2} =$
A $1521$ B $468$ C $78$ D $981$

Answer and solution

Answer: (A) $1521$

$39^{2} = 39 \times 39$

$39 \times 9 = 351$

$39 \times 3 = 117$ , written one place to the left: $1170$

$351 + 1170 = 1521$
The square of $62$ is
A $3844$ B $364$ C $496$ D $124$

Answer and solution

Answer: (A) $3844$

$62^{2} = 62 \times 62$

$62 \times 2 = 124$

$62 \times 6 = 372$ , written one place to the left: $3720$

$124 + 3720 = 3844$
$21^{3} =$
A $441$ B $9261$ C $63$ D $194481$

Answer and solution

Answer: (B) $9261$

$21^{3} = 21 \times 21 \times 21$

$21 \times 21 = 441$ , $441 \times 21 = 9261$

$= 9261$
Write $20 \times 20 \times 20 \times 20 \times 20 \times 20$ in exponential form.
A $20 \times 6$ B $20^{6}$ C $6^{20}$ D $20^{5}$

Answer and solution

Answer: (B) $20^{6}$

$20$ is multiplied by itself $6$ times, so it is $20^{6}$ .
If $21^{\square} = 441$ , the number in the box is
A $2$ B $21$ C $1$ D $3$

Answer and solution

Answer: (A) $2$

Divide by $21$ again and again:

$441 \div 21 = 21$

$441 = 21 \times 21 = 21^{2}$
Which of the following numbers between $1000$ and $2000$ is NOT divisible by $2$ ?
A $1646$ B $1709$ C $1842$ D $1848$

Answer and solution

Answer: (B) $1709$

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 $1709$ is $9$ , so $1709$ is not divisible by $2$ .

The other three are divisible.
Which of the following numbers between $50000$ and $60000$ is NOT divisible by $3$ ?
A $57945$ B $57210$ C $55611$ D $52496$

Answer and solution

Answer: (D) $52496$

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

Sum of the digits of $52496$ : $5 + 2 + 4 + 9 + 6 = 26$

$26$ is not divisible by $3$ ( $26 = 3 \times 8 + 2$ ), so $52496$ is not divisible by $3$ .

Each of the others passes the test.
The largest number less than $8000$ that is divisible by $3$ is
A $7997$ B $7995$ C $7999$ D $7998$

Answer and solution

Answer: (D) $7998$

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

$7999$ : digit sum $34$ , not divisible by $3$

$7998$ : digit sum $33$ , divisible by $3$
Which of the following numbers between $1000$ and $2000$ is divisible by $4$ ?
A $1022$ B $1238$ C $1736$ D $1494$

Answer and solution

Answer: (C) $1736$

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

Last two digits of $1736$ together: $36$ ; $36 = 4 \times 9$ , so $1736$ is divisible by $4$ .

Each of the others fails the test.
Which of the following numbers between $60000$ and $70000$ is divisible by $5$ ?
A $62509$ B $63801$ C $63025$ D $67851$

Answer and solution

Answer: (C) $63025$

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

The digit at the unit place of $63025$ is $5$ , so $63025$ is divisible by $5$ .

The other three are not divisible.
Which of the following numbers between $100000$ and $200000$ is divisible by $6$ ?
A $103041$ B $182394$ C $194818$ D $100226$

Answer and solution

Answer: (B) $182394$

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

The digit at the unit place of $182394$ is $4$ , so $182394$ is divisible by $2$ .

Sum of the digits of $182394$ : $1 + 8 + 2 + 3 + 9 + 4 = 27$

$27$ is divisible by $3$ ( $27 = 3 \times 9$ ), so $182394$ is divisible by $3$ .

$\therefore$ $182394$ is divisible by $6$ .

Each of the others fails the test.
Which of the following numbers between $200000$ and $300000$ is NOT divisible by $6$ ?
A $282063$ B $284208$ C $206004$ D $220800$

Answer and solution

Answer: (A) $282063$

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

The digit at the unit place of $282063$ is $3$ , so $282063$ is not divisible by $2$ .

Sum of the digits of $282063$ : $2 + 8 + 2 + 0 + 6 + 3 = 21$

$21$ is divisible by $3$ ( $21 = 3 \times 7$ ), so $282063$ is divisible by $3$ .

$\therefore$ $282063$ is not divisible by $6$ .

Each of the others passes the test.
Which of the following numbers between $1000$ and $2000$ is NOT divisible by $7$ ?
A $1002$ B $1127$ C $1043$ D $1064$

Answer and solution

Answer: (A) $1002$

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

$1002$ : $100 - 2(2) = 100 - 4 = 96$ ; $96 = 7 \times 13 + 5$ , not a multiple of $7$ , so $1002$ is not divisible by $7$ .

Each of the others passes the test.
To test $343$ for divisibility by $7$ , twice the unit digit is subtracted from the remaining part. The result is
A $337$ B $28$ C $40$ D $31$

Answer and solution

Answer: (B) $28$

Remaining part $= 34$ , unit digit $= 3$

$34 - 3(2) = 34 - 6 = 28$
Which of the following numbers between $1000$ and $2000$ is divisible by all of $2, 3, 4, 5$ and $6$ ?
A $1296$ B $1650$ C $1040$ D $1080$

Answer and solution

Answer: (D) $1080$

$1080$ : unit digit $0$ (by $2$ and $5$ ); digit sum $9$ (by $3$ , so by $6$ ); last two digits $80$ (by $4$ )

$1040$ fails the rule for $3$ , $1650$ fails the rule for $4$ , $1296$ fails the rule for $5$ .

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MCQ test, Set 10