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 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The positive two-digit integers $x$ and $y$ have the same digits, but in reverse order. Which of the following must be a factor of $x + y$? 

  1. $6$
  2. $9$
  3. $10$
  4. $11$
  5. $14$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  Let two positive integers are $x=17$ and $y=71$.

$\Rightarrow$  $x+y=17+71=88$
$\Rightarrow$  $88=11\times 2 \times 2\times 2$
$\therefore$   From the factors given in the options, $11$ will be the factor of $x+y$.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The digits in the tens place and units place of a two digit number are $t$ and $u$ respectively. If $1$ is placed between them, what is the value of the three digit number so formed?

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

Let the number in one's place be $ u$ and the number in ten's place be $10t$.

According the the question 
$\Rightarrow 10t + 1+ u $
Hence now the 10t will become 100t as it will take hundred's digit place and 1 will become 10 as it will take ten's digit place.
Hence the value  of 3 digit number will be $ 100t + 10 + u $.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

  1. 4

  2. 8

  3. 16

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

$\because $ The number is greater than the number obtained in reversing the digits and the ten's digit is greater than the unit's digit
Let ten's and unit's digit be $2x$ and $x$ respectively
Then, $(10\times 2x+x)-(10x+2x)=36$
$9x=36$
$x=4$
Required difference$=(2x+x)-(2x-x)=2x=8$

Multiple choice maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

What would be the difference between the place values of the digits at the tens and units places of a number formed by the addition of the greatest six-digit number and the smallest three-digit number?

  1. $81$
  2. $72$
  3. $63$
  4. $54$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The greatest 6 digit number is $=999999$.

The smallest 3 digit number is$=100$.
Therefore there sum$=1000099$.
The tens place value=$90$ and units place vaue $=9$.
Therefore the difference is $81$ .

Multiple choice logarithm and its uses basic mathematical concepts physics

The characteristic of a number having $m$ $(m>1)$ digits is given by,

  1. $m-1$
  2. $m+1$
  3. $m$

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

If a number is $N>0$, then $\log _{10}N$ will have two parts, the integral part is known the characteristic and the decimal part is known as mantissa.

$2$ digit belongs from $[10,100]$ where $\log _{10}10=1$ and $\log _{10}100=2$
Similarly, $m$ digit number belongs from $[10^{m-1},10^m]$, where $\log _{10}10^{m-1}=m-1$ and $\log _{10}10^m=m$.
Thus any number between $[10^{m-1},10^m]$ will have $m-1$ as the integral part.
Thus the characteristic of a number having $m$ digits is given by $m-1$.

Multiple choice roman numbers and numbers upto hundred roman numerals knowing our numbers maths

Which of the following statements is/are INCORRECT?
(i) Eighty four in Roman numeral is written as $CXXXIV$
(i) There are seven zeroes in $1$ crore.
(iii) There are ten thousand milligrams in $1kg$
(iv) The smallest $4$-digit number formed by using all the digits $4,3,0,8$ without repetition is $3048$

  1. Both (i) and (iii)

  2. Both (i) and (iv)

  3. Only (i)

  4. Only (ii)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
(i) $84=LXXXIV$
(ii) $1\quad crore=10000000$
(iii) $1kg=1000g=1000\times 10000mg=10000000mg$
(iv) Smallest number formed is $3048$
(i) and (iii) are INCORRECT
Answer : A

Multiple choice maths number systems existence of irrational numbers irrational numbers properties of irrational numbers

$A,B,C$ and $D$ are all different digits between $0$ and $9$. If $AB+DC=7B\ (AB,DC$ and $7B$ are two digit numbers), then the value of $C$ is

  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

AB + DC = 7B. (10A + B) + (10D + C) = 70 + B. 10A + 10D + C = 70. A + D + C/10 = 7. Since A, D, C are digits, C must be 0 for the equation to hold with integer digits A and D. If C=0, A+D=7.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

A combination of locks requires 3 numbers to open. The second number is $\displaystyle 2d + 5$ greater than the first number. The third number is $\displaystyle 3d - 20$ less than the second number. The sum of the three numbers is $\displaystyle 10d + 9$. The first number is 

  1. $\displaystyle 5d-11$
  2. $\displaystyle 3d-7$
  3. $\displaystyle 2d+19$
  4. $\displaystyle 3d-11$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the first number be $x$
Then, second number = $x + 2d + 5$
Third number = $x + 2d + 5 -(3d -20)$ = $x -d + 25$
Sum of the three numbers = $ x + x+2d + 5 + x - d +25$ = $ 3x + d +30$

Thus, $ 3x + d +30$ = $10d + 9$
$3x = 10d + 9 - d - 30$ = $9d - 21$
$x = 3d - 7$

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digit of that number ?

  1. 3

  2. 4

  3. 9

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let the ten's digit be $x$ and unit's digit be $y$.

Then, $(10x + y) - (10y + x) = 36$

$9(x - y) = 36$

$x - y = 4$

Therefore, the difference between the two digit of that number is $4$
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The sum of the digits of a two-digit number is 9 less then the number. Which of the following digits is at unit's place of the number ?

  1. 1

  2. 2

  3. 4

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let $x,y$ are the digits of a number. Then the number $= 10x+y$

as per condition : $10x+y-9 = x+y$

Then as per the given problem,

$x+y=10x+y-9$

or, $9x=9$

or, $x=1$

So, we can say that for any value of y from 1 to 9, the condition satisfies.

for eg: if the number is 18

18–9 = 1+8

9=9 , satisfied.


So the tenth's place digit is $1$.