Quantitative Aptitude

Number System and Digits

380 Questions

Number system and digits questions test the ability to manipulate numbers, identify significant digits, and form specific values. These problems often require finding missing digits or determining the properties of large sums. They form a vital component of the quantitative aptitude section.

Number formationMissing digitsSignificant digitsLargest and smallest numbersDigit sum properties

Number System and Digits Questions

Multiple choice maths numbers and place value face value of digit large numbers general form of number

A number consists of two digits whose sum is $11$. If $27$ is added to the number, then the digits change their places. What is the number?

  1. $47$
  2. $65$
  3. $83$
  4. $92$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the ten's digit be $x$. Then, unit's digit $= \left(11 - x\right)$.
So, number $= 10x + \left(11 - x\right) = 9x + 11$.
Therefore $\left(9x + 11\right) + 27 = 10 \left(11 - x\right) + x  \Leftrightarrow  9x + 38 = 110 - 9x \Leftrightarrow   18x = 72 \Leftrightarrow   x = 4$.
Thus, ten's digit $= 4$ and unit's digit $= 7$.
Hence, required number $= 47$.

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

A $3$ digit id a $3$ digit number (not starting with zero) which reads the same backwards as forwards. For example $171$. The sum of all even $3$ digit palindromes, is 

  1. $22380$
  2. $25700$
  3. $22000$
  4. $22400$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A 3-digit palindrome is of the form ABA. For it to be even, A must be 2, 4, 6, or 8. B can be 0-9. For each A, there are 10 possibilities for B. Summing these values: 202+212+...+292, 404+414+...+494, etc. The sum is 22380.

Multiple choice statistics information processing fundamental principle of addition fundamental principles of counting principles of counting

The number of $n$ digit numbers which consists of the digits $1$ & $2$ only if each digits is to be used atleast once, is equal to $510$  then $n$ is equal to

  1. $7$
  2. $8$
  3. $9$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total number of n-digit numbers using digits 1 and 2 is 2^n. Subtracting the cases where either 1 or 2 is never used gives 2^n - 2 numbers where both digits appear at least once. Setting 2^n - 2 = 510 gives 2^n = 512, which means n = 9.

Multiple choice maths number work indian place value chart place value of digit largest and smallest numbers

If number read " Ten thousand eight hundred six." Find missing digit.
$1\ \ _,806$

  1. $1$
  2. $10$
  3. $2$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Number reads Ten thousand eight hundred six.

$1$ is at ten thousand's place, $0$ at thousand's place, $8$ at hundred's place, $0$ at ten's place and $6$ at one's place.

This written in numeral is $10,806$

Missing digit is $0$ in thousands place

Multiple choice maths number work indian place value chart place value of digit largest and smallest numbers

If number reads "Forty five lakh sixty one thousand two hundred thirty four"
the sum of digits in the number is

  1. $45$
  2. $25$
  3. $15$
  4. $65$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let us convert the given number in words into numerals as follows:


Forty five lakh$=45,00,000$
Sixty one thousand$=61,000$
Two hunderd$=200$
Thirty$=30$
Four$=4$

Now, add the numerals as shown below:

$4500000+61000+200+30+4=4561234$

Therefore, the required number is $45,61,234$.

Now let us find the sum of the digits of the number $45,61,234$:

$4+5+6+1+2+3+4=25$

Hence, the sum of the digits is $25$.

Multiple choice maths number work indian place value chart place value of digit largest and smallest numbers

If number reads "Eleven lakh seventy thousand six hundred seven" Find missing digits.
$11,70,\ _07$

  1. $3$
  2. $6$
  3. $2$
  4. $5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let us convert the given number in words into numerals as follows:


Eleven lakh$=11,00,000$
Seventy thousand$=70,000$
Six hunderd$=600$
Seven$=7$

Now, add the numerals as shown below:

$1100000+70000+600+7=1170607$

Therefore, the required number is $11,70,607$.

Hence, the missing digit in $11,70,07$ is $6$.

Multiple choice physics electronic devices boolean algebra digital electronics and logic gates logic gates

In the binary number system, the number $100$ represents

  1. one

  2. three

  3. four

  4. hundred
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In binary number system only $0$'s and $1$'s are used to built the whole number system.
Hence,
$0 = 0$
$1 = 1$
Start back at $0$ again, but add $1$ on the left,
$2 = 10$
$3 = 11$
Start back at $0$ again, and add one to the number on the left, but that number is already at $1$, so it also goes back to $0$ and $1$ is added to the next position on the left. Hence,
$4 = 100$ .... and so on.