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 in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

Identify the place value for the underlined digit of the number below. 

$8,52\underline 3,615$

  1. Millions

  2. Thousands

  3. Hundreds

  4. Tens
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mlns     hth tthous thous     hund tens ones
8            5    2        3             6       1       5

So, the place value of 3 is thousands

Multiple choice maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

In a two digit number, the digit at unit place is $x$ at the digit at tens place is $5$, then the new number obtained by interchanging the digits of that number is

  1. $50x+5$
  2. $10x+5$
  3. $x+50$
  4. $5x+4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The digit in units place is $x$


The digit in tens place is $5$

So the number is $50+x$

If the number is reversed,

The units digit is $5$

The tens digit is $x$

So the number is $10x+5$

Multiple choice maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

If the digit $1$ is placed after a two digit number whose ten's digit is $t$ and unit's digit is $u$, then the new number is: 

  1. $\displaystyle 10t+u+1$
  2. $\displaystyle 100t+10u+1$
  3. $\displaystyle 1000t+10u+1$
  4. $\displaystyle t+u+1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, ten's place digit $= t$ and one's place digit $= u$
Two digit number $= 10\times$ten's place digit+one's place digit
                             $= 10t+u = tu$

If the digit 1 is placed after a two digit number, the new number is $tu1$, 
which now becomes a three digit number. 

The hundreds place digit $= t$, ten's place digit $= u$ and one's place digit $= 1$

$\therefore$ Number $=100\times$hundred's place digit + $10\times$ten's place digit + one's place digit
                   $=100t+10u+1$

So, Option B is correct.

Multiple choice maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

If the digit $1$ is placed after a two digit number whose tens digit is $'t' $and units digit is $'u',$  the new number is:

  1. $l0t + u + 1$
  2. $100t + 10u + 1$
  3. $t + u + 1$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Placing 1 after two digit number is the indication that,

shift the given digit towards left, so that $t$ is now hundred's digit and $u$ is now tens digit so the value becomes $100t+10u+1$
So $100t+10u+1$ is correct answer

Multiple choice maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

Unit's digit of the number ${36^{1001}} \times$ ${7^{1002}} \times$${13^{1003}}$ is 

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

Unit's digit of $36^{1001}$ will be $6$

$7^{1002}=(7^2)^{501}=(49^4)^{125}\times 49$
Unit's digit of $(49^4)$ is $1$. So, unit's digit of $(49^4)^{125}$ will be $1$ and thus, unit's digit of $7^{1002}$ will be $9$.
$13^{1003}=(13^2)^{501}\times 13=(169^4)^{125}\times 169\times 13$
Unit's digit of $169^4$ is $1$. So, unit's digit of $13^{1003}$ will be $7$.
Hence, unit's digit of $36^{1001}\times 7^{1002}\times 13^{1003}$ will be $8$.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

A number consists of two digits whose sum is $9$. If $27$ is added to the number, its digits are interchanged. Are the given steps to find the number true?
Step $1$: Let the unit's digit be x
Step $2$: Then, ten's digit $=(9-x)$
$\therefore$ number $=10\times (9-x)+x\Rightarrow 90-10x+x=(90-9x)$
Step $3$: Adding $27$ to the number $90-9x$ we get $117-9x$
Step $4$: Number with digits interchanged is $10x+(9-x)=9x+9$
Step $5$: $117-9x=9x+9$ 
Step $6$: Therefore unit's digit$=6$ and ten's digit $=3$
Step $7$: Hence the number $=36$.

  1. Yes

  2. No

  3. Cannot say
  4. Only step $1$ and $2$ are correct
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

All the given steps to find that unknown number are True.
Hence the option A is the correct answer.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. Find the number, if the difference between its digits is $3$. 

  1. $14$
  2. $25$
  3. $36$
  4. $47$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let one's digit be $x$ and the tens be $x-3$


Number = $10(x-3) +x$ 

Reversed no. = $10x +x-3$ 

$ 7(10(x-3) +x) = 4(x-3 +10x)\ 70x -210 + 7x = 4x -12 +40x\ 33x = 198\ x = 6$ 

Number = $36$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The sum of a $2$ digit number and the number obtained by reversing its digits is $154$. If the digits differ by $4$, find the number.

  1. $95$
  2. $73$
  3. $84$
  4. $62$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let two digit number $=ab=10a+b$
Sum of number and reversed number $=154$
$(10a+b)+(10b+a)=154$
$a+b=14$
difference between digits$=\left|a-b\right|=4$
$a-b=\pm 4$
$(a+b=14)+(a-b=4)=2a=18$    $a=9,b=5$
$(a+b=14)-(a-b-4)=2a=10$      $a=5,b=9$
$\therefore   \text {Number}=95 (or)59$
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?
Step 1 : Let the units digit be x
Step 2 : Then, ten's digit = (9 - x)
$\therefore$  Number = 10 x (9 - x) + x
$\Rightarrow$  90 - 10x + x = (90 - 9x)
Step 3 : Adding 27 to the number 90 - 9x, we get 117 - 9x
Step 4 : Number with digits interchanged is 10x + (9 - x) = 9x + 9
Step 5 : 117 - 9x = 9x + 9
Step 6 : Therefore unit's digit = 6 and ten's digit = 3
Step 7 : Hence the number = 36.

  1. Only Step 4

  2. Both Step 1 and Step 2

  3. Step 1, 2, 3 and 4

  4. All steps are correct
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In given question we have to find the number.

$\Rightarrow$  To find the numbers $7$ steps are given.
$\Rightarrow$  All $7$ steps are correct to find the required  number.
$\therefore$   Correct answer is option $D.$

Multiple choice maths knowing our numbers indian system of numeration numbers to 1 million numbers in indian and international systems

The least two digit composite number is

  1. $11$
  2. $12$
  3. $10$
  4. $16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We know that-If a number has more than $2$ factors then it is a composite number.
$11$ is a prime number $\because$ it has only $2$ factors
$12$ is a composite number $\because$ it has more than $2$ factors
$10$ is a composite number $\because$ it has more than $2$ factors
$16$ is a composite number $\because$ it has more than $2$ factors
$\therefore\,10,12,16$ are composite numbers.
The least composite number is $10$