Introduction to Number Systems: MCQ test, Set 6

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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.

Counting numbers $1, 2, 3, 4, \ldots$ are called
A odd numbers B whole numbers C even numbers D natural numbers

Answer and solution

Answer: (D) natural numbers

Natural numbers are the counting numbers $1, 2, 3, 4, \ldots$ .
Numbers which give $0$ as remainder when divided by $2$ are called
A odd numbers B natural numbers C whole numbers D even numbers

Answer and solution

Answer: (D) even numbers

Even numbers give remainder $0$ when divided by $2$ : $0, 2, 4, 6, \ldots$
How many multiples of $8$ are there between $30$ and $70$ ?
A $6$ B $4$ C $5$ D $8$

Answer and solution

Answer: (C) $5$

$8 \times 4 = 32$ , $8 \times 5 = 40$ , $8 \times 6 = 48$ , $8 \times 7 = 56$ , $8 \times 8 = 64$

There are $5$ .
Which of the following is a factor of $119$ ?
A $11$ B $3$ C $9$ D $7$

Answer and solution

Answer: (D) $7$

$119 = 7 \times 17$ , so $7$ divides $119$ without remainder.

$3$ , $9$ , $11$ leave a remainder.
The factors of $65$ are
A $1, 5, 13$ B $1, 5, 13, 65$ C $1, 65$ D $5, 13$

Answer and solution

Answer: (B) $1, 5, 13, 65$

$65 = 1 \times 65$

$= 5 \times 13$

Factors of $65$ : $1, 5, 13, 65$
In $11t$ , the variable is
A $1$ B $11t$ C $t$ D $11$

Answer and solution

Answer: (C) $t$

$11t = 11 \times t$ ; $t$ takes various values.
Which of the following equals $-n$ ?
A $-1 + n$ B $1 \times n$ C $-n \times n$ D $-1 \times n$

Answer and solution

Answer: (D) $-1 \times n$

As $-1 \times a = -a$ , $-1 \times n = -n$ .
$r + r + r + r + r =$
A $r^{5}$ B $4r$ C $5r$ D $5 + r$

Answer and solution

Answer: (C) $5r$

$r + r + r + r + r$ is $r$ added $5$ times.

$r + r + r + r + r = 5r$
$5x + 2x + 10x =$
A $16x$ B $17x^{3}$ C $100x$ D $17x$

Answer and solution

Answer: (D) $17x$

$5x + 2x + 10x = (5 + 2 + 10)x = 17x$
$z^{4}$ is equal to
A $z \times z \times z \times z$ B $4 \times z$ C $z + 4$ D $z \times z \times z$

Answer and solution

Answer: (A) $z \times z \times z \times z$

$z^{4}$ is $z$ multiplied $4$ times.
The square of $86$ is
A $7396$ B $6436$ C $172$ D $1204$

Answer and solution

Answer: (A) $7396$

$86^{2} = 86 \times 86$

$86 \times 6 = 516$

$86 \times 8 = 688$ , written one place to the left: $6880$

$516 + 6880 = 7396$
$35 \times 35 =$
A $280$ B $925$ C $1225$ D $70$

Answer and solution

Answer: (C) $1225$

$35^{2} = 35 \times 35$

$35 \times 5 = 175$

$35 \times 3 = 105$ , written one place to the left: $1050$

$175 + 1050 = 1225$
$22^{3} =$
A $484$ B $10648$ C $234256$ D $66$

Answer and solution

Answer: (B) $10648$

$22^{3} = 22 \times 22 \times 22$

$22 \times 22 = 484$ , $484 \times 22 = 10648$

$= 10648$
$32^{3}$ is read as
A $32$ cubed B $32$ squared C $3$ times $32$ D $3$ power $32$

Answer and solution

Answer: (A) $32$ cubed

$32^{3} = 32 \times 32 \times 32$ is read as '32 cubed'.
If $20^{\square} = 8000$ , the number in the box is
A $2$ B $4$ C $3$ D $400$

Answer and solution

Answer: (C) $3$

Divide by $20$ again and again:

$8000 \div 20 = 400$ , $400 \div 20 = 20$

$8000 = 20 \times 20 \times 20 = 20^{3}$
A number is divisible by $2$ if the digit at its unit place is
A $1, 3, 5, 7$ or $9$ B $0$ or $5$ C $2$ only D $0, 2, 4, 6$ or $8$

Answer and solution

Answer: (D) $0, 2, 4, 6$ or $8$

A number is divisible by $2$ if the digit at its unit place is $0, 2, 4, 6$ or $8$ .
Which of the following numbers between $8000$ and $9000$ is NOT divisible by $3$ ?
A $8186$ B $8997$ C $8607$ D $8427$

Answer and solution

Answer: (A) $8186$

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

Sum of the digits of $8186$ : $8 + 1 + 8 + 6 = 23$

$23$ is not divisible by $3$ ( $23 = 3 \times 7 + 2$ ), so $8186$ is not divisible by $3$ .

Each of the others passes the test.
The largest number less than $4001$ that is divisible by $3$ is
A $3998$ B $3999$ C $4000$ D $3996$

Answer and solution

Answer: (B) $3999$

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

$4000$ : digit sum $4$ , not divisible by $3$

$3999$ : digit sum $30$ , divisible by $3$
Which of the following numbers between $70000$ and $80000$ is NOT divisible by $4$ ?
A $77292$ B $75740$ C $75618$ D $71680$

Answer and solution

Answer: (C) $75618$

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

Last two digits of $75618$ together: $18$ ; $18 = 4 \times 4 + 2$ , so $75618$ is not divisible by $4$ .

Each of the others passes the test.
Which of the following numbers between $9000$ and $10000$ is divisible by $5$ ?
A $9353$ B $9335$ C $9601$ D $9151$

Answer and solution

Answer: (B) $9335$

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

The digit at the unit place of $9335$ is $5$ , so $9335$ is divisible by $5$ .

The other three are not divisible.
Which of the following numbers between $20000$ and $30000$ is divisible by $6$ ?
A $26172$ B $26342$ C $26217$ D $25556$

Answer and solution

Answer: (A) $26172$

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

The digit at the unit place of $26172$ is $2$ , so $26172$ is divisible by $2$ .

Sum of the digits of $26172$ : $2 + 6 + 1 + 7 + 2 = 18$

$18$ is divisible by $3$ ( $18 = 3 \times 6$ ), so $26172$ is divisible by $3$ .

$\therefore$ $26172$ is divisible by $6$ .

Each of the others fails the test.
Which of the following numbers between $30000$ and $40000$ is NOT divisible by $6$ ?
A $37143$ B $30366$ C $30546$ D $37314$

Answer and solution

Answer: (A) $37143$

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

The digit at the unit place of $37143$ is $3$ , so $37143$ is not divisible by $2$ .

Sum of the digits of $37143$ : $3 + 7 + 1 + 4 + 3 = 18$

$18$ is divisible by $3$ ( $18 = 3 \times 6$ ), so $37143$ is divisible by $3$ .

$\therefore$ $37143$ is not divisible by $6$ .

Each of the others passes the test.
Which of the following numbers between $600$ and $700$ is NOT divisible by $7$ ?
A $623$ B $632$ C $658$ D $616$

Answer and solution

Answer: (B) $632$

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

$632$ : $63 - 2(2) = 63 - 4 = 59$ ; $59 = 7 \times 8 + 3$ , not a multiple of $7$ , so $632$ is not divisible by $7$ .

Each of the others passes the test.
To test $738$ for divisibility by $7$ , twice the unit digit is subtracted from the remaining part. The result is
A $65$ B $57$ C $722$ D $89$

Answer and solution

Answer: (B) $57$

Remaining part $= 73$ , unit digit $= 8$

$73 - 8(2) = 73 - 16 = 57$
Which of the following numbers between $60000$ and $70000$ is divisible by all of $2, 3, 4, 5$ and $6$ ?
A $60090$ B $66204$ C $68620$ D $63540$

Answer and solution

Answer: (D) $63540$

$63540$ : unit digit $0$ (by $2$ and $5$ ); digit sum $18$ (by $3$ , so by $6$ ); last two digits $40$ (by $4$ )

$68620$ fails the rule for $3$ , $60090$ fails the rule for $4$ , $66204$ fails the rule for $5$ .

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MCQ test, Set 6