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 many forms of ten thousand standard form of numbers number names, numerals and place values

Find the last two digits of $3^{1997}$.

  1. $67$
  2. $63$
  3. $80$
  4. $56$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is same as asking what is remainder when $3^{1997}\div 100$
$3^{4}\equiv 81  mod  100$
$3^{8}\equiv 61  mod  100$
$3^{12}\equiv 41  mod  100$
$3^{16}\equiv 21  mod  100$
$3^{20}\equiv 1  mod  100$


Now, $3^{40}, 3^{60}, 3^{80}, 3^{100}, ...., 3^{1980}$ all are $\equiv 1  mod  100$

We know $3^{16}\equiv 21  mod  100$

$3^{17}\equiv 21\times 3  mod  100$

$3^{17}\equiv 63  mod  100$

$\therefore 3^{1997}\equiv 3^{1980}\times 3^{17}$

since, $3^{1980}\equiv 1  mod  100$

and $3^{17}\equiv 63  mod  100$

$\therefore 3^{1997}\equiv 63  mod  100$

$\therefore $ Last two digit is 63

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

$025$ is square of $55$.What digit should replace $$?

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

Step 1: 

Multiply ten's digit with its next number.
$5 \times (5 + 1) = 5 \times 6 = 30 ---(1)$
Step 2:Find the square of unit's digit: 5
$5^2$ = 25 ----(2)
Step 3 :
Joining (1) and (2), we get
$3025 = 55 \times 55$
So, 3 is the missing number.

Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

A two digit number in such that the product of its digits is $8$. When $63$ is subtracted from the number, the digits interchange their places. Find the number.

  1. 18

  2. 72

  3. 27

  4. 81
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the digit at unit's place $= x$
$\displaystyle \therefore $ Digit at ten's place $\displaystyle \frac { 8 }{ x } $ and the number is $\displaystyle \left( \frac { 80 }{ x } +x \right) $
New number on interchanging the places of digits $\displaystyle =10x+\frac { 8 }{ x } $
$\displaystyle \therefore $ According to given condition
$\displaystyle \frac { 80 }{ x } +x-63=10x+\frac { 8 }{ x } $
$\displaystyle 80+{ x }^{ 2 }-63x=10{ x }^{ 2 }+8$
$\displaystyle { 9x }^{ 2 }+63x-72=0$
$\displaystyle { x }^{ 2 }-7x-8=0$
$\displaystyle { x }^{ 2 }+8x-x-8=0$
$\displaystyle x\left( x+8 \right) -1\left( x+8 \right) =0$
$\displaystyle \left( x+8 \right) \left( x-1 \right) =0$
$\displaystyle i.e.\quad x=-8$  and $ x=1$
Rejecting $\displaystyle x=-8$ and putting $\displaystyle x=1$ the required no. is $\displaystyle \left( \frac { 80 }{ 1 } +1 \right) =81$.

Multiple choice maths square and square root scientific notation use of exponents power of 10

The digit in the ten's place of a two-digit number is three times that in the one's places if the digits are reversed the new number will be 36 less than the original number Find the number 

  1. 64

  2. 52

  3. 62

  4. 42
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the digits be $ x $ and $ y $
Given, "The digit in the ten's place of a two-digit number is three times that in the one's places "
$ => x = 3y $ 

Now, when the digits are reversed, the number will be $ 10y + x $
Also,  if the digits are reversed the new number will be $ 36 $ less than the original number. $ => 10y + x = (10x + y) - 36 $
$ => 9x -9y = 36 $

Putting $ x = 3y $ in this,
$ 9(3y) -9y = 36 $
$ => 27y - 9y = 36 $
$ 18y = 36 => y = 2 $

So, $ x = 3y = 6 $
Hence, the number is $ 62 $

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.