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 forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Smallest 6-digit number that can be formed by the digits 9, 6, 0, 5, 8, 1 is

  1. $015,689$
  2. $1,05,689$
  3. $5,01,689$
  4. $9,86,510$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  The given numbers are $9,\,6,\,0,\,5,\,8,\,1$

$\Rightarrow$  To form smallest 6-digit number, we have to start number with smallest digit and end with largest digit.
$\Rightarrow$  Here, we can not use $0$ as first digit because then number will becomes 5 digit.
$\therefore$   The smallest 6-digit number = $1,05,689$.

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Smallest 6-digit number that can be formed by the digits 9, 6, 0, 5, 8, 1 is 

  1. 0,15,689

  2. 1,05,689

  3. 5,01,689

  4. 9,86,510
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Smallest  6  digit number that can be formed by the digits 9,6,0,5,8,1 is  1,05,689.  

 0 cannot  in the first place . Then it will become 5 digit number.

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Which of the following are the three digit numbers that can be formed by using $0, 1$ and $2$ only once.

  1. $102$
  2. $201$
  3. $012$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

Three digit numbers that can be formed from 0, 1 and 2 are $102$ and $201$.
So, (c) is not a three digit number.

So, options A and B are correct.

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Find the correct option such that the formation of $3$ numbers, using three digit number $128$? (Without repeating the numbers)

  1. $281, 221$ and $182$
  2. $281, 851$ and $182$
  3. $681, 821$ and $182$
  4. $281, 821$ and $182$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$128$ can be written using the general form $abc = 100 \times  a + 10 \times  b + c$
By changing the alphabetic orders of $a, b, c$, we get $3$ more numbers from $3$ digit number.
Here, $281, 821$ and $182$ are formed from the $3$ digit number $128$.

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

The smallest three-digit number using the digits $3, 9, 7, 8, 6$ (repetition not allowed) is

  1. $387$
  2. $367$
  3. $389$
  4. $386$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$3,9,7,8,6$

Smallest three digit number will be formed my smallest of the three digits from the given ones, i.e. $3,6,7$

Smallest three digits number possible $= 367$

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Let the given digits be $2, 3, 6,7$, find the greatest three digit number that can be formed with using the given digits only once.

  1. $763$
  2. $736$
  3. $723$
  4. $732$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$2,3,6,7$

Greatest three digit number will be formed my largest of the three digits from the given ones, i.e. $7,6,3$

Greatest three digits number possible $= 763$

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Find the greatest three-digit number using the digits $7, 6, 3$

  1. $763$
  2. $367$
  3. $637$
  4. $376$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The descending order of the given numbers $7,6,3$ is:

$7>6>3$ 

We observe that the smallest digit is $3$ and the largest digit is $7$, so the number should start with $7$ and end with $3$.
 
Thus, the largest number formed is $763$.

Hence, the greatest three digit number formed is $763$.
Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

$a, b, c (a > c)$ are three digits from left to right, of a three digits number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digits 4 in its unit place. The other two digits from left to right are

  1. 5 and 4

  2. 5 and 9

  3. 4 and 5

  4. 9 and 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ Let\quad the\quad number\quad be\quad written\quad as\quad follows\ Place\quad value\quad \longrightarrow Hundreds\quad \quad \quad Tens\quad \quad \quad Units\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a\quad \quad \quad \quad \quad \quad \quad \quad b\quad \quad \quad \quad \quad \quad c\ Reversing\quad \longrightarrow \quad \quad \quad \quad \quad c\quad \quad \quad \quad \quad \quad \quad \quad b\quad \quad \quad \quad \quad \quad a\ \ Units\quad place:-\quad Given\quad a>c\ \therefore \quad We\quad borrow\quad 10\quad and\quad the\quad result\quad is\quad \ \quad \quad c+10-a=4\ \Rightarrow a=c+6----(1)\ Tens\quad place:-\quad upper\quad row\quad b\quad has\quad become\quad b-1\ \therefore \quad We\quad borrow\quad 10\quad and\quad the\quad result\quad is\ \quad \quad (b-1+10)-b=9.\ Hundreds\quad place:-\quad a\quad has\quad become\quad a-1\ \therefore \quad (a-1)-c\quad is\quad the\quad result.\ Substituting\quad the\quad value\quad of\quad a\quad from\quad (1),\quad the\quad result\ will\quad be\quad c+6-1-c=5\ \therefore \quad The\quad other\quad two\quad numbers\quad are\quad 5,\quad 9\quad \quad (Ans)\ \quad \quad (i.e.\quad The\quad result\quad is\quad 594) $

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

How many positive integers less than $1000$ are $6$ times the sum of their digits ?

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

Let the number be 10x + y (for 2 digits) or 100x + 10y + z (for 3 digits). Solving 10x + y = 6(x + y) gives 4x = 5y, so x=5, y=4 (number 54). Checking 3 digits: 100x + 10y + z = 6(x + y + z) leads to 94x + 4y = 5z, which has no solutions for digits x, y, z.