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 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 $1$.

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

When a two digit number is reversed, the new number is reduced by $63$ and the sum of digits of these individual numbers is $9$. Now, if these numbers are converted into base $'x'$ the larger number becomes $5$ times that of smaller one, then the value of $x$ is :

  1. $36$
  2. $13$
  3. $15$
  4. $8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two-digit number be 10a + b. Reversing it gives 10b + a, and the problem states 10a + b - (10b + a) = 63, which means a - b = 7. Given the sum of digits a + b = 9, we find a = 8 and b = 1, so the numbers are 81 and 18. Converting to base x gives 81 in base x as 5 times 18 in base x, leading to the equation 8x + 1 = 5(x + 8), which solves to x = 13.

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

If the sum and the product of the digits of two digit number is the same, then the number is_____________

  1. $11$
  2. $23$
  3. $10$
  4. $22$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two-digit number be 10a + b. The sum of the digits is a + b, and the product of the digits is a * b. We are given a + b = a * b. Testing the options, for 22, the sum is 2 + 2 = 4 and the product is 2 * 2 = 4, which matches the condition.

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

In the correctly worked out multiplication problem at the below, each letter represent a different digit. What is the value of B ?

A A
A B

   B B
A A C

A 3 B

  1. 1

  2. 2

  3. 4

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

$B + C = B$

$C = 0$

AA.B $=$ BB $\Rightarrow $ (10 A + A) B $ = $BB= 10 B $+$ B

$AB = B,A = 1$

$ B+A = 3 $

$\Rightarrow B + 1 =3, \Rightarrow B = 2$

1 1 

11

12

22

110

132