Reasoning

Number Systems and Series

143 Questions

Number systems and series questions assess the ability to manipulate numerical values and spot patterns. The focus includes digit arrangements, binary conversions, and identifying largest or smallest numbers. These reasoning tasks are common across major competitive examinations.

Digit manipulationLargest and smallest numbersBinary number systemsPositional numeral systemsNumber series ranking

Number Systems and Series Questions

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

What is the percentage of least number in the greatest number if $\displaystyle \frac{3}{5},\, \displaystyle \frac{9}{5},\, \displaystyle \frac{1}{5},\, \displaystyle \frac{7}{5}$ are arranged ascending or descending order?

  1. $11\, \displaystyle \frac{1}{9}\, \%$
  2. $10\, \%$
  3. $20\, \%$
  4. $25\, \%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The given numbers can be arranged in the ascending order as $\displaystyle \frac{1}{5}\, <\, \displaystyle \frac{3}{5}\, <\, \displaystyle \frac{7}{5}\, <\, \displaystyle \frac{9}{5}$
Greatest number $=\, \displaystyle \frac{9}{5}$;
Least number $=\, \displaystyle \frac{1}{5}$.
We have, $\displaystyle \frac{9}{5}\, \times\, \displaystyle \frac{x}{100}\, =\, \displaystyle \frac{1}{5}$
$x\, =\, \displaystyle \frac{100}{9}\, =\, 11\, \displaystyle \frac{1}{9}\, \%$

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

Roman numeral for the greatest three digit number is

  1. IXIXIX

  2. CMIXIX

  3. CMXCIX

  4. CMIC
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The largest $3$ digit number is $999$. Let's convert that into Roman numerals.

$M = 1000, D = 500, C = 100, X = 10, V = 5$ and $I = 1.$

$900 = CM$

$90 = XC$

$9 = IX$

$900+90+9=999$
$(1000-100)+(100-10)+(10-1)$

Therefore, $999 = CMXCIX$
$(1000-100)+(100-10)+(10-1)$

Let's crossverify,
$CMXCIX=(1000-100)+(100-10)+(10-1)$
$=900+90+9=999$
Multiple choice roman numbers and numbers upto hundred roman numerals knowing our numbers maths

Roman numeral for the greatest three digit number is ___________.

  1. IXIXIX

  2. CMXCIX

  3. CMIXIX

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

Consider the $3$ digit largest number in roman.


The largest $3$ digit number is$999$.


Let's convert that into Roman numerals,


$M=100$,$D=500$,X=100$,$X=10$,$V=5$ and $I=1$.

$900 = CM$

$90 = XC$

$9 = IX$

Therefore, $999 = CMXCIX$

 

Hence, this is the answer.

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

Difference of the greatest 7 digit number and the smallest 5 digit number is 

  1. 998999

  2. 9989999

  3. 99899

  4. 998099
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

the greatest $7$ digit number is $9999999$


the smallest $5$ digit number is $10000$

we have to find the difference between these two numbers 

$9999999-10000=9989999$

So option $B$ is the answer

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

If three is subtracted from each of the following numbers, then which of the following options is the difference between the second highest number and the second digit of the highest number?
$489$     $541$     $654$      $935$       $873$.

  1. $0$
  2. $3$
  3. $1$
  4. $4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given Numbers  489  541  654  935  873
 Subtraction  -3  -3  -3  -3  -3
 Required Numbers  486  538  651  932  870

Highest Number $\rightarrow$ $932$

Second digit of $932$  $\rightarrow$ $3$
Second highest Number $\rightarrow$ $870$
Second digit of $870$ $\rightarrow$  $7$ 
Difference between 7 and 3 $\rightarrow$ $4$
Hence, the required answer is $4$.

Multiple choice

What is the significance of the number '9' in the Indian Number System?

  1. It is the largest single-digit number.

  2. It is considered a lucky number.

  3. It is used as a placeholder for zero.

  4. It is the base of the Indian Number System.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In Indian culture, the number '9' is often associated with good luck and prosperity. It is commonly used in religious ceremonies, festivals, and other auspicious occasions.

Multiple choice

What is the term used to refer to the number system that uses a base other than 10?

  1. Non-Decimal Number System

  2. Binary Number System

  3. Hexadecimal Number System

  4. Octal Number System
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A non-decimal number system is a system that uses a base other than 10. Examples of non-decimal number systems include the binary system (base 2), the hexadecimal system (base 16), and the octal system (base 8).

Multiple choice

What is the term used to refer to the number system that uses a base of 2?

  1. Binary Number System

  2. Decimal Number System

  3. Hexadecimal Number System

  4. Octal Number System
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The binary number system is a base-2 number system that uses only two digits, 0 and 1. It is widely used in digital electronics and computer science.