Quantitative Aptitude

Number System and Digits

374 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

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.

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 a smallest four digit number using the digits $7,8,9,5$ such that the number thus formed has $9$ at its hundreds place and $8$ at its one's place.

  1. $5978$
  2. $7598$
  3. $7958$
  4. $7985$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The ascending order of the given numbers $7,8,9,5$ is:

$5 < 7 < 8 < 9$ 

We observe that the smallest digit is $5$ and the largest digit is $9$.
 
Therefore, the smallest number formed is $5789$.

But it is given that the number formed should have $9$ at its hundredth place and $8$ at its one's place, therfore, the required number is:

$5978$ where $8$ is at one's place, $7$ is at tens place, $9$ is at hundredth place and $5$ is at thousandth place. 

Hence, the smallest $4$ digit number formed is $5978$.

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

 Write the smallest $4$ digit number formed using the digits $8,3,0,1$.

  1. $1038$
  2. $1308$
  3. $1083$
  4. $0138$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The ascending order of the given numbers $8,3,0,1$ is:

$0 < 1 < 3 < 8$ 

A number cannot begin with $0$, so we will put it in the second place. 

The smallest digit (other than $0$) is $1$. 

Therefore, the number will begin with $1$.
 
Thus, the smallest number formed is $1038$.

Hence, the smallest $4$ digit number formed is $1038$.
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 an even $4$ digit number using $2, 7, 5,1$.

  1. $7512$
  2. $5217$
  3. $7125$
  4. $1275$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
An even number is an integer which is "evenly divisible" by two. This means that if the integer is divided by $2$, it yields no remainder.

(a) $7512$ is divisible by $2$ as $\dfrac {7512}{2}=3756$, so it is a four digit even number.

(b) $5217$ is not divisible by $2$, so it is not a four digit even number.

(c) $7125$ is not divisible by $2$, so it is not a four digit even number.

(d) $1275$ is not divisible by $2$, so it is not a four digit even number.

Hence, $7512$ is a four digit even number using the digits $2,7,5,1$.
Multiple choice maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

How many times does the digit $3$ appear while writing the integers from $1$ to $1000$?

  1. $298$
  2. $299$
  3. $300$
  4. $301$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To count the digit 3 from 1 to 1000: in each position (units, tens, hundreds), the digit 3 appears 100 times. For example, in the units place, it appears in 3, 13, 23, ..., 993 (100 times). The same applies to the tens and hundreds places, totaling 300 occurrences.

Multiple choice maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

The number of whole numbers between the smallest whole number and the greatest 2-digit number is:

  1. $101$
  2. $100$
  3. $99$
  4. $98$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The smallest whole number is $0$ and the two-digit greatest whole number is $99$.

So the numbers between $0$ and $99$ are $1,2,....,98$ i.e. there are $98$ whole numbers between $0$ and $99$.

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

$D$ is a real number with non terminating digits $a _1$ and $a _2$ after the decimal point. Let $D = 0, a _1 a _2 a _1 a _2 ........ $  with $a _1 &amp; a _2$ both not zero which of the following when multiplied by $D$ will necessarily give an integer ?

  1. $99$
  2. $18$
  3. $125$
  4. $75$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

its straight question
give $D=0.abababab$ $(say - 1)$ 
Multiply both sides by $100$ $i.e.$ 
$100D = ab.abababab$ $(say - 2)$
now subtract $1$ from $2 .$ That gives
$99D = ab => D = ab/99$ hence it should be multiplied by $99k$ to get an integer ab$.$